Funções de afilamento com gamlss para as distribuições TF2 JSU e SST
Eliel
2026-02-26
Bases de dados Desenvolvida com dados de inventários florestais em povoamentos nativos e plantados.
library(gamlss)library(readxl)dados <- read_excel("dados_gamlss.xlsx")
head(dados)## # A tibble: 6 × 7
## cod tree d h hi di i
## <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 401833MUT 40 6.5 6.5 0.1 9.6 3
## 2 401833MUT 40 6.5 6.5 0.5 8 3
## 3 401833MUT 40 6.5 6.5 1 6.8 3
## 4 401833MUT 40 6.5 6.5 1.3 6.5 3
## 5 401833MUT 40 6.5 6.5 2 5.8 3
## 6 401833MUT 40 6.5 6.5 3 4.8 3d=dap; h= altura da arvore; hi=altura relativa da medida do diametro;
#di=diametro
estimação de modelos segmentados
$ y= d/di; 𝑥 = ℎi/ℎ$
attach(dados)MODELO SIMPLES DE DUAS VARIÁVEIS: Y_LM E X
tabela <- data.frame(hi/h, di)#gráfico da relação
plot(tabela,
xlab = "Altura relativa (hi/h)",
ylab = "Diâmetro (di/d)",
main = "Perfil de afilamento")
#ajusatndo modelos com GAMLSS
polinomio 3º grau
# transformar hi/h -> x
x <- hi/hdistribuição normal
m.p3 <- gamlss(di ~ x + I(x^2) + I(x^3),
family = NO)## GAMLSS-RS iteration 1: Global Deviance = 20562.24
## GAMLSS-RS iteration 2: Global Deviance = 20562.24Ajustando com distribuição SST
m.pm_sst <- gamlss(di ~ x + I(x^2) + I(x^3),
family = SST()
)## GAMLSS-RS iteration 1: Global Deviance = 20603.95
## GAMLSS-RS iteration 2: Global Deviance = 20548.07
## GAMLSS-RS iteration 3: Global Deviance = 20532.29
## GAMLSS-RS iteration 4: Global Deviance = 20531.55
## GAMLSS-RS iteration 5: Global Deviance = 20531.4
## GAMLSS-RS iteration 6: Global Deviance = 20531.34
## GAMLSS-RS iteration 7: Global Deviance = 20531.32
## GAMLSS-RS iteration 8: Global Deviance = 20531.32
## GAMLSS-RS iteration 9: Global Deviance = 20531.31
## GAMLSS-RS iteration 10: Global Deviance = 20531.31
## GAMLSS-RS iteration 11: Global Deviance = 20531.31gráfico e resíduo
summary(m.pm_sst)## ******************************************************************
## Family: c("SST", "SST")
##
## Call: gamlss(formula = di ~ x + I(x^2) + I(x^3), family = SST())
##
## Fitting method: RS()
##
## ------------------------------------------------------------------
## Mu link function: identity
## Mu Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 19.6485 0.1739 112.98 <2e-16 ***
## x -43.6174 1.8521 -23.55 <2e-16 ***
## I(x^2) 67.8399 5.1485 13.18 <2e-16 ***
## I(x^3) -46.0456 4.0190 -11.46 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## ------------------------------------------------------------------
## Sigma link function: log
## Sigma Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.16368 0.01277 91.14 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## ------------------------------------------------------------------
## Nu link function: log
## Nu Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.03067 0.03395 -0.903 0.366
##
## ------------------------------------------------------------------
## Tau link function: logshiftto2
## Tau Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.497 0.244 10.23 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## ------------------------------------------------------------------
## No. of observations in the fit: 3982
## Degrees of Freedom for the fit: 7
## Residual Deg. of Freedom: 3975
## at cycle: 11
##
## Global Deviance: 20531.31
## AIC: 20545.31
## SBC: 20589.34
## ******************************************************************plot(m.pm_sst)
## ******************************************************************
## Summary of the Quantile Residuals
## mean = -5.29143e-05
## variance = 1.000219
## coef. of skewness = -0.009684368
## coef. of kurtosis = 2.98733
## Filliben correlation coefficient = 0.9997728
## ******************************************************************wp(m.pm_sst) 
distribuição JSU
m.pm_jsu <- gamlss(di ~ x + I(x^2) + I(x^3),
family = JSU()
)## GAMLSS-RS iteration 1: Global Deviance = 20803.44
## GAMLSS-RS iteration 2: Global Deviance = 20684.88
## GAMLSS-RS iteration 3: Global Deviance = 20581.47
## GAMLSS-RS iteration 4: Global Deviance = 20535.42
## GAMLSS-RS iteration 5: Global Deviance = 20531.08
## GAMLSS-RS iteration 6: Global Deviance = 20530.61
## GAMLSS-RS iteration 7: Global Deviance = 20530.45
## GAMLSS-RS iteration 8: Global Deviance = 20530.4
## GAMLSS-RS iteration 9: Global Deviance = 20530.38
## GAMLSS-RS iteration 10: Global Deviance = 20530.38
## GAMLSS-RS iteration 11: Global Deviance = 20530.38
## GAMLSS-RS iteration 12: Global Deviance = 20530.37gráfico e resíduo
summary(m.pm_jsu)## ******************************************************************
## Family: c("JSU", "Johnson SU")
##
## Call: gamlss(formula = di ~ x + I(x^2) + I(x^3), family = JSU())
##
## Fitting method: RS()
##
## ------------------------------------------------------------------
## Mu link function: identity
## Mu Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 19.6540 0.1736 113.21 <2e-16 ***
## x -43.7020 1.8745 -23.31 <2e-16 ***
## I(x^2) 67.9927 5.1864 13.11 <2e-16 ***
## I(x^3) -46.1187 4.0361 -11.43 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## ------------------------------------------------------------------
## Sigma link function: log
## Sigma Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.16359 0.01274 91.36 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## ------------------------------------------------------------------
## Nu link function: identity
## Nu Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.1928 0.1877 -1.027 0.305
##
## ------------------------------------------------------------------
## Tau link function: log
## Tau Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.0634 0.1134 9.381 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## ------------------------------------------------------------------
## No. of observations in the fit: 3982
## Degrees of Freedom for the fit: 7
## Residual Deg. of Freedom: 3975
## at cycle: 12
##
## Global Deviance: 20530.37
## AIC: 20544.37
## SBC: 20588.4
## ******************************************************************plot(m.pm_jsu)
## ******************************************************************
## Summary of the Quantile Residuals
## mean = 0.0001165205
## variance = 1.000245
## coef. of skewness = -0.00161637
## coef. of kurtosis = 2.984853
## Filliben correlation coefficient = 0.9997888
## ******************************************************************wp(m.pm_jsu)
distribuição TF2
m.pm_tf2 <- gamlss(di ~ x + I(x^2) + I(x^3),
family = TF2()
)## GAMLSS-RS iteration 1: Global Deviance = 20603.99
## GAMLSS-RS iteration 2: Global Deviance = 20548.49
## GAMLSS-RS iteration 3: Global Deviance = 20532.71
## GAMLSS-RS iteration 4: Global Deviance = 20532.13
## GAMLSS-RS iteration 5: Global Deviance = 20532.13
## GAMLSS-RS iteration 6: Global Deviance = 20532.13gráfico e resíduo
summary(m.pm_tf2)## ******************************************************************
## Family: c("TF2", "t Family 2")
##
## Call: gamlss(formula = di ~ x + I(x^2) + I(x^3), family = TF2())
##
## Fitting method: RS()
##
## ------------------------------------------------------------------
## Mu link function: identity
## Mu Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 19.577 0.154 127.14 <2e-16 ***
## x -43.245 1.806 -23.94 <2e-16 ***
## I(x^2) 67.329 5.126 13.13 <2e-16 ***
## I(x^3) -45.691 4.007 -11.40 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## ------------------------------------------------------------------
## Sigma link function: log
## Sigma Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.16386 0.01282 90.75 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## ------------------------------------------------------------------
## Nu link function: logshiftto2
## Nu Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.4627 0.2371 10.39 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## ------------------------------------------------------------------
## No. of observations in the fit: 3982
## Degrees of Freedom for the fit: 6
## Residual Deg. of Freedom: 3976
## at cycle: 6
##
## Global Deviance: 20532.13
## AIC: 20544.13
## SBC: 20581.86
## ******************************************************************plot(m.pm_tf2)
## ******************************************************************
## Summary of the Quantile Residuals
## mean = -0.00166478
## variance = 1.00013
## coef. of skewness = -0.03413817
## coef. of kurtosis = 2.983983
## Filliben correlation coefficient = 0.9997298
## ******************************************************************wp(m.pm_tf2)
AIC
AIC(m.p3, m.pm_sst, m.pm_jsu, m.pm_tf2)## df AIC
## m.pm_tf2 6 20544.13
## m.pm_jsu 7 20544.37
## m.pm_sst 7 20545.31
## m.p3 5 20572.24modelo de Prodan / polinomio de 4? grau
mod_pol_4 <- gamlss(di ~ x + I(x^2) + I(x^3) + I(x^4),
family = NO)## GAMLSS-RS iteration 1: Global Deviance = 20467.65
## GAMLSS-RS iteration 2: Global Deviance = 20467.65summary(mod_pol_4)## ******************************************************************
## Family: c("NO", "Normal")
##
## Call: gamlss(formula = di ~ x + I(x^2) + I(x^3) + I(x^4), family = NO)
##
## Fitting method: RS()
##
## ------------------------------------------------------------------
## Mu link function: identity
## Mu Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 20.5818 0.1679 122.562 <2e-16 ***
## x -71.2103 3.1773 -22.412 <2e-16 ***
## I(x^2) 222.3415 16.1219 13.791 <2e-16 ***
## I(x^3) -333.4121 29.2956 -11.381 <2e-16 ***
## I(x^4) 169.4391 17.3181 9.784 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## ------------------------------------------------------------------
## Sigma link function: log
## Sigma Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.15108 0.01121 102.7 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## ------------------------------------------------------------------
## No. of observations in the fit: 3982
## Degrees of Freedom for the fit: 6
## Residual Deg. of Freedom: 3976
## at cycle: 2
##
## Global Deviance: 20467.65
## AIC: 20479.65
## SBC: 20517.39
## ******************************************************************plot(mod_pol_4) # resíduos assimétricos. É possível obter um ajuste melhor?
## ******************************************************************
## Summary of the Quantile Residuals
## mean = -7.107643e-17
## variance = 1.000251
## coef. of skewness = -0.09472375
## coef. of kurtosis = 3.513196
## Filliben correlation coefficient = 0.9983102
## ******************************************************************wp(mod_pol_4) # Melhorar a modelagem!
Distribuição gamlss TF2, JSU e SST para o modelo polinomial de 4 grau
TF2
mod4_tf2 <- gamlss(di ~ x + I(x^2) + I(x^3) + I(x^4),
family = TF2()) # familia TF2## GAMLSS-RS iteration 1: Global Deviance = 20498.53
## GAMLSS-RS iteration 2: Global Deviance = 20447.67
## GAMLSS-RS iteration 3: Global Deviance = 20432.94
## GAMLSS-RS iteration 4: Global Deviance = 20432.4
## GAMLSS-RS iteration 5: Global Deviance = 20432.4
## GAMLSS-RS iteration 6: Global Deviance = 20432.39Gráfico e resíduos
summary(mod4_tf2) ### ******************************************************************
## Family: c("TF2", "t Family 2")
##
## Call: gamlss(formula = di ~ x + I(x^2) + I(x^3) + I(x^4),
## family = TF2())
##
## Fitting method: RS()
##
## ------------------------------------------------------------------
## Mu link function: identity
## Mu Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 20.5903 0.1822 113.01 <2e-16 ***
## x -71.1478 3.2945 -21.60 <2e-16 ***
## I(x^2) 222.3327 16.2260 13.70 <2e-16 ***
## I(x^3) -333.5181 28.8920 -11.54 <2e-16 ***
## I(x^4) 169.4197 16.8297 10.07 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## ------------------------------------------------------------------
## Sigma link function: log
## Sigma Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.15226 0.01302 88.52 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## ------------------------------------------------------------------
## Nu link function: logshiftto2
## Nu Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.3637 0.2236 10.57 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## ------------------------------------------------------------------
## No. of observations in the fit: 3982
## Degrees of Freedom for the fit: 7
## Residual Deg. of Freedom: 3975
## at cycle: 6
##
## Global Deviance: 20432.39
## AIC: 20446.39
## SBC: 20490.42
## ******************************************************************plot(mod4_tf2)
## ******************************************************************
## Summary of the Quantile Residuals
## mean = -0.003114746
## variance = 1.000117
## coef. of skewness = -0.06108055
## coef. of kurtosis = 2.977658
## Filliben correlation coefficient = 0.9996007
## ******************************************************************wp(mod4_tf2)
JSU
mod4_jsu <- gamlss(di ~ x + I(x^2) + I(x^3) + I(x^4),
family = JSU()) # familia jsu## GAMLSS-RS iteration 1: Global Deviance = 20701.24
## GAMLSS-RS iteration 2: Global Deviance = 20576.68
## GAMLSS-RS iteration 3: Global Deviance = 20476.29
## GAMLSS-RS iteration 4: Global Deviance = 20433.34
## GAMLSS-RS iteration 5: Global Deviance = 20429.09
## GAMLSS-RS iteration 6: Global Deviance = 20428.26
## GAMLSS-RS iteration 7: Global Deviance = 20427.94
## GAMLSS-RS iteration 8: Global Deviance = 20427.83
## GAMLSS-RS iteration 9: Global Deviance = 20427.79
## GAMLSS-RS iteration 10: Global Deviance = 20427.77
## GAMLSS-RS iteration 11: Global Deviance = 20427.77
## GAMLSS-RS iteration 12: Global Deviance = 20427.77
## GAMLSS-RS iteration 13: Global Deviance = 20427.77AIC e resíduos distribuição JSU
summary(mod4_jsu) ### ******************************************************************
## Family: c("JSU", "Johnson SU")
##
## Call: gamlss(formula = di ~ x + I(x^2) + I(x^3) + I(x^4),
## family = JSU())
##
## Fitting method: RS()
##
## ------------------------------------------------------------------
## Mu link function: identity
## Mu Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 20.7501 0.2017 102.86 <2e-16 ***
## x -72.4987 3.3662 -21.54 <2e-16 ***
## I(x^2) 226.3445 16.3477 13.85 <2e-16 ***
## I(x^3) -339.3666 29.0423 -11.69 <2e-16 ***
## I(x^4) 172.3489 16.8989 10.20 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## ------------------------------------------------------------------
## Sigma link function: log
## Sigma Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.15208 0.01291 89.27 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## ------------------------------------------------------------------
## Nu link function: identity
## Nu Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.3298 0.1911 -1.725 0.0845 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## ------------------------------------------------------------------
## Tau link function: log
## Tau Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.0298 0.1084 9.496 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## ------------------------------------------------------------------
## No. of observations in the fit: 3982
## Degrees of Freedom for the fit: 8
## Residual Deg. of Freedom: 3974
## at cycle: 13
##
## Global Deviance: 20427.77
## AIC: 20443.77
## SBC: 20494.08
## ******************************************************************plot(mod4_jsu)
## ******************************************************************
## Summary of the Quantile Residuals
## mean = 7.464459e-05
## variance = 1.000267
## coef. of skewness = -0.005496251
## coef. of kurtosis = 2.977614
## Filliben correlation coefficient = 0.9997765
## ******************************************************************wp(mod4_jsu)
#SST
mod4_sst <- gamlss(di ~ x + I(x^2) + I(x^3) + I(x^4),
family = SST()) # familia sst## GAMLSS-RS iteration 1: Global Deviance = 20498.44
## GAMLSS-RS iteration 2: Global Deviance = 20446.96
## GAMLSS-RS iteration 3: Global Deviance = 20431.77
## GAMLSS-RS iteration 4: Global Deviance = 20430.82
## GAMLSS-RS iteration 5: Global Deviance = 20430.56
## GAMLSS-RS iteration 6: Global Deviance = 20430.46
## GAMLSS-RS iteration 7: Global Deviance = 20430.41
## GAMLSS-RS iteration 8: Global Deviance = 20430.39
## GAMLSS-RS iteration 9: Global Deviance = 20430.39
## GAMLSS-RS iteration 10: Global Deviance = 20430.38
## GAMLSS-RS iteration 11: Global Deviance = 20430.38
## GAMLSS-RS iteration 12: Global Deviance = 20430.38Gráfico e resíduos
summary(mod4_sst) ### ******************************************************************
## Family: c("SST", "SST")
##
## Call: gamlss(formula = di ~ x + I(x^2) + I(x^3) + I(x^4),
## family = SST())
##
## Fitting method: RS()
##
## ------------------------------------------------------------------
## Mu link function: identity
## Mu Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 20.716 0.204 101.57 <2e-16 ***
## x -72.039 3.361 -21.43 <2e-16 ***
## I(x^2) 224.702 16.379 13.72 <2e-16 ***
## I(x^3) -336.729 29.157 -11.55 <2e-16 ***
## I(x^4) 170.786 16.994 10.05 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## ------------------------------------------------------------------
## Sigma link function: log
## Sigma Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.15211 0.01293 89.09 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## ------------------------------------------------------------------
## Nu link function: log
## Nu Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.04973 0.03557 -1.398 0.162
##
## ------------------------------------------------------------------
## Tau link function: logshiftto2
## Tau Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.4189 0.2333 10.37 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## ------------------------------------------------------------------
## No. of observations in the fit: 3982
## Degrees of Freedom for the fit: 8
## Residual Deg. of Freedom: 3974
## at cycle: 12
##
## Global Deviance: 20430.38
## AIC: 20446.38
## SBC: 20496.7
## ******************************************************************plot(mod4_sst)
## ******************************************************************
## Summary of the Quantile Residuals
## mean = -0.0006686717
## variance = 1.000101
## coef. of skewness = -0.0229191
## coef. of kurtosis = 2.981752
## Filliben correlation coefficient = 0.9997308
## ******************************************************************wp(mod4_sst)
AIC
AIC(mod_pol_4, mod4_tf2, mod4_jsu, mod4_sst)## df AIC
## mod4_jsu 8 20443.77
## mod4_sst 8 20446.38
## mod4_tf2 7 20446.39
## mod_pol_4 6 20479.65polinomio de 5? grau
modpol_5 <- gamlss(di ~ x + I(x^2) + I(x^3) + I(x^4)+ I(x^5),
family = NO)## GAMLSS-RS iteration 1: Global Deviance = 20459.3
## GAMLSS-RS iteration 2: Global Deviance = 20459.3summary(modpol_5)## ******************************************************************
## Family: c("NO", "Normal")
##
## Call: gamlss(formula = di ~ x + I(x^2) + I(x^3) + I(x^4) +
## I(x^5), family = NO)
##
## Fitting method: RS()
##
## ------------------------------------------------------------------
## Mu link function: identity
## Mu Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 20.8483 0.1925 108.293 < 2e-16 ***
## x -82.9567 5.2301 -15.861 < 2e-16 ***
## I(x^2) 328.6212 40.8767 8.039 1.18e-15 ***
## I(x^3) -680.3780 126.0024 -5.400 7.06e-08 ***
## I(x^4) 635.5655 165.4542 3.841 0.000124 ***
## I(x^5) -219.7360 77.5317 -2.834 0.004618 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## ------------------------------------------------------------------
## Sigma link function: log
## Sigma Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.15003 0.01121 102.6 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## ------------------------------------------------------------------
## No. of observations in the fit: 3982
## Degrees of Freedom for the fit: 7
## Residual Deg. of Freedom: 3975
## at cycle: 2
##
## Global Deviance: 20459.3
## AIC: 20473.3
## SBC: 20517.33
## ******************************************************************plot(modpol_5) 
## ******************************************************************
## Summary of the Quantile Residuals
## mean = -3.891138e-16
## variance = 1.000251
## coef. of skewness = -0.1039208
## coef. of kurtosis = 3.518281
## Filliben correlation coefficient = 0.9982397
## ******************************************************************wp(modpol_5) 
Ajuste com as distribuições TF2, JSU e SST com gamlss
TF2 polinomio 5° grau
modpol5_tf2 <- gamlss(di ~ x + I(x^2) + I(x^3) + I(x^4)+ I(x^5),
family = TF2()) # familia tf2## GAMLSS-RS iteration 1: Global Deviance = 20488.13
## GAMLSS-RS iteration 2: Global Deviance = 20438.26
## GAMLSS-RS iteration 3: Global Deviance = 20423.66
## GAMLSS-RS iteration 4: Global Deviance = 20423.09
## GAMLSS-RS iteration 5: Global Deviance = 20423.08
## GAMLSS-RS iteration 6: Global Deviance = 20423.08summary(modpol5_tf2) ### ******************************************************************
## Family: c("TF2", "t Family 2")
##
## Call: gamlss(formula = di ~ x + I(x^2) + I(x^3) + I(x^4) +
## I(x^5), family = TF2())
##
## Fitting method: RS()
##
## ------------------------------------------------------------------
## Mu link function: identity
## Mu Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 20.9041 0.2084 100.297 < 2e-16 ***
## x -84.0745 5.3185 -15.808 < 2e-16 ***
## I(x^2) 335.6841 40.0822 8.375 < 2e-16 ***
## I(x^3) -696.3015 120.8864 -5.760 9.05e-09 ***
## I(x^4) 649.8730 156.4445 4.154 3.34e-05 ***
## I(x^5) -224.0062 72.5458 -3.088 0.00203 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## ------------------------------------------------------------------
## Sigma link function: log
## Sigma Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.15129 0.01306 88.16 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## ------------------------------------------------------------------
## Nu link function: logshiftto2
## Nu Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.3439 0.2214 10.59 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## ------------------------------------------------------------------
## No. of observations in the fit: 3982
## Degrees of Freedom for the fit: 8
## Residual Deg. of Freedom: 3974
## at cycle: 6
##
## Global Deviance: 20423.08
## AIC: 20439.08
## SBC: 20489.39
## ******************************************************************plot(modpol5_tf2)
## ******************************************************************
## Summary of the Quantile Residuals
## mean = -0.003493081
## variance = 1.000122
## coef. of skewness = -0.06779824
## coef. of kurtosis = 2.976877
## Filliben correlation coefficient = 0.9995651
## ******************************************************************wp(modpol5_tf2)
JSU
modpol5_jsu <- gamlss(di ~ x + I(x^2) + I(x^3) + I(x^4)+ I(x^5),
family = JSU()) # jsu## GAMLSS-RS iteration 1: Global Deviance = 20693.77
## GAMLSS-RS iteration 2: Global Deviance = 20566.66
## GAMLSS-RS iteration 3: Global Deviance = 20466.83
## GAMLSS-RS iteration 4: Global Deviance = 20423.63
## GAMLSS-RS iteration 5: Global Deviance = 20419.07
## GAMLSS-RS iteration 6: Global Deviance = 20418.11
## GAMLSS-RS iteration 7: Global Deviance = 20417.75
## GAMLSS-RS iteration 8: Global Deviance = 20417.63
## GAMLSS-RS iteration 9: Global Deviance = 20417.58
## GAMLSS-RS iteration 10: Global Deviance = 20417.57
## GAMLSS-RS iteration 11: Global Deviance = 20417.56
## GAMLSS-RS iteration 12: Global Deviance = 20417.56
## GAMLSS-RS iteration 13: Global Deviance = 20417.55
## GAMLSS-RS iteration 14: Global Deviance = 20417.55Gráfico e resíduos
summary(modpol5_jsu)## ******************************************************************
## Family: c("JSU", "Johnson SU")
##
## Call: gamlss(formula = di ~ x + I(x^2) + I(x^3) + I(x^4) +
## I(x^5), family = JSU())
##
## Fitting method: RS()
##
## ------------------------------------------------------------------
## Mu link function: identity
## Mu Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 21.0958 0.2301 91.691 < 2e-16 ***
## x -86.1500 5.5158 -15.619 < 2e-16 ***
## I(x^2) 345.2043 41.3638 8.346 < 2e-16 ***
## I(x^3) -719.1387 124.6815 -5.768 8.64e-09 ***
## I(x^4) 674.8257 161.1907 4.187 2.89e-05 ***
## I(x^5) -234.0445 74.6486 -3.135 0.00173 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## ------------------------------------------------------------------
## Sigma link function: log
## Sigma Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.15117 0.01294 88.97 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## ------------------------------------------------------------------
## Nu link function: identity
## Nu Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.3659 0.1959 -1.868 0.0619 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## ------------------------------------------------------------------
## Tau link function: log
## Tau Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.0249 0.1088 9.418 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## ------------------------------------------------------------------
## No. of observations in the fit: 3982
## Degrees of Freedom for the fit: 9
## Residual Deg. of Freedom: 3973
## at cycle: 14
##
## Global Deviance: 20417.55
## AIC: 20435.55
## SBC: 20492.16
## ******************************************************************plot(modpol5_jsu)
## ******************************************************************
## Summary of the Quantile Residuals
## mean = 0.0001969132
## variance = 1.000284
## coef. of skewness = -0.006530754
## coef. of kurtosis = 2.977196
## Filliben correlation coefficient = 0.9997686
## ******************************************************************wp(modpol5_jsu)
SST
modpol5_sst <- gamlss(di ~ x + I(x^2) + I(x^3) + I(x^4)+ I(x^5),
family = SST()) # sst## GAMLSS-RS iteration 1: Global Deviance = 20487.91
## GAMLSS-RS iteration 2: Global Deviance = 20437.2
## GAMLSS-RS iteration 3: Global Deviance = 20421.92
## GAMLSS-RS iteration 4: Global Deviance = 20420.84
## GAMLSS-RS iteration 5: Global Deviance = 20420.54
## GAMLSS-RS iteration 6: Global Deviance = 20420.42
## GAMLSS-RS iteration 7: Global Deviance = 20420.38
## GAMLSS-RS iteration 8: Global Deviance = 20420.36
## GAMLSS-RS iteration 9: Global Deviance = 20420.35
## GAMLSS-RS iteration 10: Global Deviance = 20420.34
## GAMLSS-RS iteration 11: Global Deviance = 20420.34
## GAMLSS-RS iteration 12: Global Deviance = 20420.34Gráfico e resíduo
summary(modpol5_sst)## ******************************************************************
## Family: c("SST", "SST")
##
## Call: gamlss(formula = di ~ x + I(x^2) + I(x^3) + I(x^4) +
## I(x^5), family = SST())
##
## Fitting method: RS()
##
## ------------------------------------------------------------------
## Mu link function: identity
## Mu Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 21.0601 0.2249 93.626 < 2e-16 ***
## x -85.4580 5.0934 -16.778 < 2e-16 ***
## I(x^2) 341.2648 37.4977 9.101 < 2e-16 ***
## I(x^3) -708.5257 112.4141 -6.303 3.24e-10 ***
## I(x^4) 662.0718 145.3495 4.555 5.39e-06 ***
## I(x^5) -228.7136 67.4933 -3.389 0.000709 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## ------------------------------------------------------------------
## Sigma link function: log
## Sigma Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.15122 0.01297 88.75 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## ------------------------------------------------------------------
## Nu link function: log
## Nu Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.05790 0.03552 -1.63 0.103
##
## ------------------------------------------------------------------
## Tau link function: logshiftto2
## Tau Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.406 0.232 10.37 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## ------------------------------------------------------------------
## No. of observations in the fit: 3982
## Degrees of Freedom for the fit: 9
## Residual Deg. of Freedom: 3973
## at cycle: 12
##
## Global Deviance: 20420.34
## AIC: 20438.34
## SBC: 20494.95
## ******************************************************************plot(modpol5_sst)
## ******************************************************************
## Summary of the Quantile Residuals
## mean = -0.000605207
## variance = 1.000112
## coef. of skewness = -0.0238492
## coef. of kurtosis = 2.98077
## Filliben correlation coefficient = 0.9997137
## ******************************************************************wp(modpol5_sst)
AIC
AIC(modpol_5, modpol5_tf2, modpol5_jsu, modpol5_sst)## df AIC
## modpol5_jsu 9 20435.55
## modpol5_sst 9 20438.34
## modpol5_tf2 8 20439.08
## modpol_5 7 20473.30modelo de Hradetzky
pot1 <- seq(0.005, 0.01, by = 0.001) ; pot1## [1] 0.005 0.006 0.007 0.008 0.009 0.010pot2 <- seq(0.01, 0.1, by = 0.01) ; pot2## [1] 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10pot3 <- seq(0.1, 1, by = 0.1) ; pot3## [1] 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0pot4 <- seq(1, 30, by = 1) ; pot4## [1] 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
## [26] 26 27 28 29 30m.hrad <- gamlss(di ~ I(x^0.005) + I(x^pot1[2]) + I(x^pot1[3])+ I(x^pot1[4]) + I(x^pot1[5]) + I(x^pot1[6]) +
I(x^pot2[1]) + I(x^pot2[2]) + I(x^pot2[3])+ I(x^pot2[4]) + I(x^pot2[5]) + I(x^pot2[6]) + I(x^pot2[7]) + I(x^pot2[8])+ I(x^pot2[9]) + I(x^pot2[10]) +
I(x^pot3[1]) + I(x^pot3[2]) + I(x^pot3[3])+ I(x^pot3[4]) + I(x^pot3[5]) + I(x^pot3[6]) + I(x^pot3[7]) + I(x^pot3[8])+ I(x^pot3[9]) + I(x^pot3[10]) +
I(x^pot4[1]) + I(x^pot4[2]) + I(x^pot4[3])+ I(x^pot4[4]) + I(x^pot4[5]) + I(x^pot4[6]) + I(x^pot4[7]) + I(x^pot4[8])+ I(x^pot4[9]) + I(x^pot4[10]) +
I(x^pot4[11]) + I(x^pot4[12]) + I(x^pot4[13])+ I(x^pot4[14]) + I(x^pot4[15]) + I(x^pot4[16]) + I(x^pot4[17]) + I(x^pot4[18])+ I(x^pot4[19]) + I(x^pot4[20]) +
I(x^pot4[21]) + I(x^pot4[22]) + I(x^pot4[23])+ I(x^pot4[24]) + I(x^pot4[25]) + I(x^pot4[26]) + I(x^pot4[27]) + I(x^pot4[28])+ I(x^pot4[29]) + I(x^pot4[30]),
#sigma.formula = ~ I(x^0.005) + I(x^pot1[2]) + I(x^pot1[3])+ I(x^pot1[4]) + I(x^pot1[5]) + I(x^pot1[6]) +
#I(x^pot2[1]) + I(x^pot2[2]) + I(x^pot2[3])+ I(x^pot2[4]) + I(x^pot2[5]) + I(x^pot2[6]) + I(x^pot2[7]) + I(x^pot2[8])+ I(x^pot2[9]) + I(x^pot2[10]) +
#I(x^pot3[1]) + I(x^pot3[2]) + I(x^pot3[3])+ I(x^pot3[4]) + I(x^pot3[5]) + I(x^pot3[6]) + I(x^pot3[7]) + I(x^pot3[8])+ I(x^pot3[9]) + I(x^pot3[10]) +
#I(x^pot4[1]) + I(x^pot4[2]) + I(x^pot4[3])+ I(x^pot4[4]) + I(x^pot4[5]) + I(x^pot4[6]) + I(x^pot4[7]) + I(x^pot4[8])+ I(x^pot4[9]) + I(x^pot4[10]) +
#I(x^pot4[11]) + I(x^pot4[12]) + I(x^pot4[13])+ I(x^pot4[14]) + I(x^pot4[15]) + I(x^pot4[16]) + I(x^pot4[17]) + I(x^pot4[18])+ I(x^pot4[19]) + I(x^pot4[20]) +
#I(x^pot4[21]) + I(x^pot4[22]) + I(x^pot4[23])+ I(x^pot4[24]) + I(x^pot4[25]) + I(x^pot4[26]) + I(x^pot4[27]) + I(x^pot4[28])+ I(x^pot4[29]) + I(x^pot4[30]),
type="realAll")## GAMLSS-RS iteration 1: Global Deviance = 19523.31
## GAMLSS-RS iteration 2: Global Deviance = 19507.33
## GAMLSS-RS iteration 3: Global Deviance = 19502.49
## GAMLSS-RS iteration 4: Global Deviance = 19493.17
## GAMLSS-RS iteration 5: Global Deviance = 19516.91
## GAMLSS-RS iteration 6: Global Deviance = 19543.02
## GAMLSS-RS iteration 7: Global Deviance = 19493.89
## GAMLSS-RS iteration 8: Global Deviance = 19551.07
## GAMLSS-RS iteration 9: Global Deviance = 19492.99
## GAMLSS-RS iteration 10: Global Deviance = 19503.32
## GAMLSS-RS iteration 11: Global Deviance = 19506.88
## GAMLSS-RS iteration 12: Global Deviance = 19499.44
## GAMLSS-RS iteration 13: Global Deviance = 19507.95
## GAMLSS-RS iteration 14: Global Deviance = 19498.01
## GAMLSS-RS iteration 15: Global Deviance = 19521.75
## GAMLSS-RS iteration 16: Global Deviance = 19521.04
## GAMLSS-RS iteration 17: Global Deviance = 19510.21
## GAMLSS-RS iteration 18: Global Deviance = 19502.98
## GAMLSS-RS iteration 19: Global Deviance = 19502.6
## GAMLSS-RS iteration 20: Global Deviance = 19544.24summary(m.hrad)## ******************************************************************
## Family: c("NO", "Normal")
##
## Call: gamlss(formula = di ~ I(x^0.005) + I(x^pot1[2]) + I(x^pot1[3]) +
## I(x^pot1[4]) + I(x^pot1[5]) + I(x^pot1[6]) + I(x^pot2[1]) +
## I(x^pot2[2]) + I(x^pot2[3]) + I(x^pot2[4]) + I(x^pot2[5]) +
## I(x^pot2[6]) + I(x^pot2[7]) + I(x^pot2[8]) + I(x^pot2[9]) +
## I(x^pot2[10]) + I(x^pot3[1]) + I(x^pot3[2]) + I(x^pot3[3]) +
## I(x^pot3[4]) + I(x^pot3[5]) + I(x^pot3[6]) + I(x^pot3[7]) +
## I(x^pot3[8]) + I(x^pot3[9]) + I(x^pot3[10]) + I(x^pot4[1]) +
## I(x^pot4[2]) + I(x^pot4[3]) + I(x^pot4[4]) + I(x^pot4[5]) +
## I(x^pot4[6]) + I(x^pot4[7]) + I(x^pot4[8]) + I(x^pot4[9]) +
## I(x^pot4[10]) + I(x^pot4[11]) + I(x^pot4[12]) + I(x^pot4[13]) +
## I(x^pot4[14]) + I(x^pot4[15]) + I(x^pot4[16]) + I(x^pot4[17]) +
## I(x^pot4[18]) + I(x^pot4[19]) + I(x^pot4[20]) + I(x^pot4[21]) +
## I(x^pot4[22]) + I(x^pot4[23]) + I(x^pot4[24]) + I(x^pot4[25]) +
## I(x^pot4[26]) + I(x^pot4[27]) + I(x^pot4[28]) + I(x^pot4[29]) +
## I(x^pot4[30]), type = "realAll")
##
## Fitting method: RS()
##
## ------------------------------------------------------------------
## Mu link function: identity
## Mu Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -4.218e+14 1.407e+14 -2.999 0.002729 **
## I(x^0.005) -7.013e+14 4.977e+14 -1.409 0.158837
## I(x^pot1[2]) 1.618e+15 6.309e+14 2.565 0.010349 *
## I(x^pot2[2]) -7.436e+14 2.277e+14 -3.265 0.001102 **
## I(x^pot2[4]) 2.743e+14 8.496e+13 3.229 0.001252 **
## I(x^pot2[10]) -2.980e+13 9.521e+12 -3.130 0.001760 **
## I(x^pot3[2]) 4.061e+12 1.367e+12 2.971 0.002982 **
## I(x^pot3[4]) -4.926e+11 1.859e+11 -2.651 0.008068 **
## I(x^pot3[6]) 1.161e+11 4.998e+10 2.323 0.020236 *
## I(x^pot3[9]) -1.295e+10 7.107e+09 -1.822 0.068479 .
## I(x^pot4[2]) -5.669e+05 8.314e+08 -0.001 0.999456
## I(x^pot4[3]) 2.551e+09 1.732e+09 1.473 0.140770
## I(x^pot4[4]) -1.479e+10 5.546e+09 -2.667 0.007689 **
## I(x^pot4[5]) 6.671e+10 1.865e+10 3.577 0.000352 ***
## I(x^pot4[6]) -2.401e+11 5.656e+10 -4.244 2.24e-05 ***
## I(x^pot4[7]) 6.759e+11 1.432e+11 4.720 2.44e-06 ***
## I(x^pot4[8]) -1.450e+12 2.871e+11 -5.051 4.59e-07 ***
## I(x^pot4[9]) 2.280e+12 4.321e+11 5.276 1.39e-07 ***
## I(x^pot4[10]) -2.436e+12 4.491e+11 -5.423 6.21e-08 ***
## I(x^pot4[11]) 1.437e+12 2.606e+11 5.513 3.74e-08 ***
## I(x^pot4[13]) -5.178e+11 9.276e+10 -5.582 2.54e-08 ***
## I(x^pot4[15]) 3.221e+11 5.793e+10 5.561 2.86e-08 ***
## I(x^pot4[17]) -1.872e+11 3.408e+10 -5.492 4.22e-08 ***
## I(x^pot4[19]) 7.473e+10 1.384e+10 5.398 7.12e-08 ***
## I(x^pot4[22]) -1.627e+10 3.107e+09 -5.237 1.72e-07 ***
## I(x^pot4[25]) 3.616e+09 7.137e+08 5.067 4.22e-07 ***
## I(x^pot4[28]) -4.538e+08 9.262e+07 -4.900 9.95e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## ------------------------------------------------------------------
## Sigma link function: log
## Sigma Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.03513 0.01121 92.38 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## ------------------------------------------------------------------
## No. of observations in the fit: 3982
## Degrees of Freedom for the fit: 28
## Residual Deg. of Freedom: 3954
## at cycle: 20
##
## Global Deviance: 19544.24
## AIC: 19600.24
## SBC: 19776.35
## ******************************************************************plot(m.hrad)
## ******************************************************************
## Summary of the Quantile Residuals
## mean = 1.709549e-17
## variance = 1.000251
## coef. of skewness = -0.07772438
## coef. of kurtosis = 3.604238
## Filliben correlation coefficient = 0.9977339
## ******************************************************************wp(m.hrad)
dist_hrad <- chooseDist(m.hrad, type="realAll") ; dist_hrad## minimum GAIC(k= 2 ) family: WEI
## minimum GAIC(k= 3.84 ) family: WEI
## minimum GAIC(k= 8.29 ) family: WEI## 2 3.84 8.29
## NO 19600.24 19651.76 19776.36
## GU 19808.20 19859.72 19984.32
## RG 20142.89 20196.25 20325.30
## LO 19491.85 19545.21 19674.26
## NET 19650.04 19701.56 19826.16
## TF 19494.07 19547.43 19676.48
## TF2 19540.85 19594.21 19723.26
## PE 19543.54 19596.90 19725.95
## PE2 19517.43 19570.79 19699.84
## SN1 20812.01 20865.37 20994.42
## SN2 19646.61 19698.13 19822.73
## exGAUS NA NA NA
## SHASH 19503.91 19559.11 19692.61
## SHASHo 20373.52 20428.72 20562.22
## SHASHo2 19583.86 19639.06 19772.56
## EGB2 19518.13 19573.33 19706.83
## JSU 19491.80 19548.84 19686.79
## JSUo 19534.90 19591.94 19729.89
## SEP1 19509.21 19564.41 19697.91
## SEP2 19549.21 19604.41 19737.91
## SEP3 19499.00 19556.04 19693.99
## SEP4 19496.18 19553.22 19691.17
## ST1 19497.64 19552.84 19686.34
## ST2 19515.30 19570.50 19704.00
## ST3 19495.23 19550.43 19683.93
## ST4 19489.65 19544.85 19678.35
## ST5 19502.68 19557.88 19691.38
## SST 19497.03 19554.07 19692.02
## GT 19499.82 19555.02 19688.52
## EXP 26944.89 26994.57 27114.72
## GA 19136.63 19188.15 19312.75
## IG 19723.45 19774.97 19899.57
## LOGNO 19358.54 19410.06 19534.66
## LOGNO2 19355.54 19407.06 19531.66
## WEI 18857.81 18909.33 19033.93
## WEI2 19794.64 19846.16 19970.76
## WEI3 18859.71 18913.07 19042.12
## IGAMMA 19668.22 19719.74 19844.34
## PARETO2 27315.14 27366.66 27491.26
## PARETO2o NA NA NA
## GP 27315.00 27366.52 27491.12
## BCCG NA NA NA
## BCCGo 18889.48 18944.68 19078.18
## GG 18869.07 18922.43 19051.48
## GIG 19135.30 19188.66 19317.71
## LNO 19358.54 19410.06 19534.66
## BCTo 18889.56 18946.60 19084.55
## BCT 18903.07 18956.43 19085.48
## BCPEo 18877.66 18932.86 19066.36
## BCPE 18888.01 18941.37 19070.42
## GB2 18917.06 18974.10 19112.05Modelando com a distribuição selecionada WEI
m.hrad_wei <- gamlss(di ~ I(x^0.005) + I(x^pot1[2]) + I(x^pot1[3])+ I(x^pot1[4]) + I(x^pot1[5]) + I(x^pot1[6]) +
I(x^pot2[1]) + I(x^pot2[2]) + I(x^pot2[3])+ I(x^pot2[4]) + I(x^pot2[5]) + I(x^pot2[6]) + I(x^pot2[7]) + I(x^pot2[8])+ I(x^pot2[9]) + I(x^pot2[10]) +
I(x^pot3[1]) + I(x^pot3[2]) + I(x^pot3[3])+ I(x^pot3[4]) + I(x^pot3[5]) + I(x^pot3[6]) + I(x^pot3[7]) + I(x^pot3[8])+ I(x^pot3[9]) + I(x^pot3[10]) +
I(x^pot4[1]) + I(x^pot4[2]) + I(x^pot4[3])+ I(x^pot4[4]) + I(x^pot4[5]) + I(x^pot4[6]) + I(x^pot4[7]) + I(x^pot4[8])+ I(x^pot4[9]) + I(x^pot4[10]) +
I(x^pot4[11]) + I(x^pot4[12]) + I(x^pot4[13])+ I(x^pot4[14]) + I(x^pot4[15]) + I(x^pot4[16]) + I(x^pot4[17]) + I(x^pot4[18])+ I(x^pot4[19]) + I(x^pot4[20]) +
I(x^pot4[21]) + I(x^pot4[22]) + I(x^pot4[23])+ I(x^pot4[24]) + I(x^pot4[25]) + I(x^pot4[26]) + I(x^pot4[27]) + I(x^pot4[28])+ I(x^pot4[29]) + I(x^pot4[30]),
#sigma.formula = ~ I(x^0.005) + I(x^pot1[2]) + I(x^pot1[3])+ I(x^pot1[4]) + I(x^pot1[5]) + I(x^pot1[6]) +
#I(x^pot2[1]) + I(x^pot2[2]) + I(x^pot2[3])+ I(x^pot2[4]) + I(x^pot2[5]) + I(x^pot2[6]) + I(x^pot2[7]) + I(x^pot2[8])+ I(x^pot2[9]) + I(x^pot2[10]) +
#I(x^pot3[1]) + I(x^pot3[2]) + I(x^pot3[3])+ I(x^pot3[4]) + I(x^pot3[5]) + I(x^pot3[6]) + I(x^pot3[7]) + I(x^pot3[8])+ I(x^pot3[9]) + I(x^pot3[10]) +
#I(x^pot4[1]) + I(x^pot4[2]) + I(x^pot4[3])+ I(x^pot4[4]) + I(x^pot4[5]) + I(x^pot4[6]) + I(x^pot4[7]) + I(x^pot4[8])+ I(x^pot4[9]) + I(x^pot4[10]) +
#I(x^pot4[11]) + I(x^pot4[12]) + I(x^pot4[13])+ I(x^pot4[14]) + I(x^pot4[15]) + I(x^pot4[16]) + I(x^pot4[17]) + I(x^pot4[18])+ I(x^pot4[19]) + I(x^pot4[20]) +
#I(x^pot4[21]) + I(x^pot4[22]) + I(x^pot4[23])+ I(x^pot4[24]) + I(x^pot4[25]) + I(x^pot4[26]) + I(x^pot4[27]) + I(x^pot4[28])+ I(x^pot4[29]) + I(x^pot4[30]),
family = WEI()) # wei## GAMLSS-RS iteration 1: Global Deviance = 19031.37
## GAMLSS-RS iteration 2: Global Deviance = 18827.84
## GAMLSS-RS iteration 3: Global Deviance = 18797.53
## GAMLSS-RS iteration 4: Global Deviance = 18801.51
## GAMLSS-RS iteration 5: Global Deviance = 18815.13
## GAMLSS-RS iteration 6: Global Deviance = 18801.67
## GAMLSS-RS iteration 7: Global Deviance = 18843.13
## GAMLSS-RS iteration 8: Global Deviance = 18809.88
## GAMLSS-RS iteration 9: Global Deviance = 18800.2
## GAMLSS-RS iteration 10: Global Deviance = 18799.98
## GAMLSS-RS iteration 11: Global Deviance = 18803.17
## GAMLSS-RS iteration 12: Global Deviance = 18805.35
## GAMLSS-RS iteration 13: Global Deviance = 18798.98
## GAMLSS-RS iteration 14: Global Deviance = 18795.58
## GAMLSS-RS iteration 15: Global Deviance = 18820.86
## GAMLSS-RS iteration 16: Global Deviance = 18847.31
## GAMLSS-RS iteration 17: Global Deviance = 18837.14
## GAMLSS-RS iteration 18: Global Deviance = 18800.83
## GAMLSS-RS iteration 19: Global Deviance = 18799.34
## GAMLSS-RS iteration 20: Global Deviance = 18801.81Gráfico e resíduos
summary(m.hrad_wei)## ******************************************************************
## Family: c("WEI", "Weibull")
##
## Call: gamlss(formula = di ~ I(x^0.005) + I(x^pot1[2]) + I(x^pot1[3]) +
## I(x^pot1[4]) + I(x^pot1[5]) + I(x^pot1[6]) + I(x^pot2[1]) +
## I(x^pot2[2]) + I(x^pot2[3]) + I(x^pot2[4]) + I(x^pot2[5]) +
## I(x^pot2[6]) + I(x^pot2[7]) + I(x^pot2[8]) + I(x^pot2[9]) +
## I(x^pot2[10]) + I(x^pot3[1]) + I(x^pot3[2]) + I(x^pot3[3]) +
## I(x^pot3[4]) + I(x^pot3[5]) + I(x^pot3[6]) + I(x^pot3[7]) +
## I(x^pot3[8]) + I(x^pot3[9]) + I(x^pot3[10]) + I(x^pot4[1]) +
## I(x^pot4[2]) + I(x^pot4[3]) + I(x^pot4[4]) + I(x^pot4[5]) +
## I(x^pot4[6]) + I(x^pot4[7]) + I(x^pot4[8]) + I(x^pot4[9]) +
## I(x^pot4[10]) + I(x^pot4[11]) + I(x^pot4[12]) + I(x^pot4[13]) +
## I(x^pot4[14]) + I(x^pot4[15]) + I(x^pot4[16]) + I(x^pot4[17]) +
## I(x^pot4[18]) + I(x^pot4[19]) + I(x^pot4[20]) + I(x^pot4[21]) +
## I(x^pot4[22]) + I(x^pot4[23]) + I(x^pot4[24]) + I(x^pot4[25]) +
## I(x^pot4[26]) + I(x^pot4[27]) + I(x^pot4[28]) + I(x^pot4[29]) +
## I(x^pot4[30]), family = WEI())
##
## Fitting method: RS()
##
## ------------------------------------------------------------------
## Mu link function: log
## Mu Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -3.356e+13 4.910e+12 -6.835 9.45e-12 ***
## I(x^0.005) 6.466e+12 9.012e+12 0.717 0.473151
## I(x^pot1[2]) 5.347e+13 1.016e+13 5.261 1.51e-07 ***
## I(x^pot2[2]) -3.366e+13 4.659e+12 -7.224 6.03e-13 ***
## I(x^pot2[5]) 7.760e+12 1.081e+12 7.178 8.43e-13 ***
## I(x^pot3[2]) -9.245e+11 1.299e+11 -7.115 1.33e-12 ***
## I(x^pot3[3]) 5.708e+11 8.061e+10 7.081 1.69e-12 ***
## I(x^pot3[5]) -1.858e+11 2.650e+10 -7.012 2.75e-12 ***
## I(x^pot3[7]) 8.010e+10 1.154e+10 6.938 4.61e-12 ***
## I(x^pot3[9]) -2.038e+10 2.971e+09 -6.860 7.94e-12 ***
## I(x^pot4[2]) 1.085e+09 1.705e+08 6.362 2.21e-10 ***
## I(x^pot4[3]) -1.797e+09 3.072e+08 -5.850 5.32e-09 ***
## I(x^pot4[4]) 4.775e+09 8.960e+08 5.329 1.04e-07 ***
## I(x^pot4[5]) -1.352e+10 2.799e+09 -4.830 1.41e-06 ***
## I(x^pot4[6]) 3.491e+10 7.984e+09 4.372 1.26e-05 ***
## I(x^pot4[7]) -7.596e+10 1.918e+10 -3.960 7.61e-05 ***
## I(x^pot4[8]) 1.321e+11 3.675e+10 3.595 0.000328 ***
## I(x^pot4[9]) -1.741e+11 5.318e+10 -3.274 0.001069 **
## I(x^pot4[10]) 1.598e+11 5.340e+10 2.992 0.002792 **
## I(x^pot4[11]) -8.250e+10 3.007e+10 -2.744 0.006104 **
## I(x^pot4[13]) 2.373e+10 1.017e+10 2.333 0.019719 *
## I(x^pot4[15]) -1.227e+10 6.102e+09 -2.010 0.044446 *
## I(x^pot4[17]) 6.095e+09 3.473e+09 1.755 0.079396 .
## I(x^pot4[19]) -2.126e+09 1.373e+09 -1.549 0.121506
## I(x^pot4[22]) 3.903e+08 2.981e+08 1.309 0.190538
## I(x^pot4[25]) -7.535e+07 6.670e+07 -1.130 0.258654
## I(x^pot4[28]) 8.414e+06 8.473e+06 0.993 0.320703
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## ------------------------------------------------------------------
## Sigma link function: log
## Sigma Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.56023 0.01173 133 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## ------------------------------------------------------------------
## No. of observations in the fit: 3982
## Degrees of Freedom for the fit: 28
## Residual Deg. of Freedom: 3954
## at cycle: 20
##
## Global Deviance: 18801.81
## AIC: 18857.81
## SBC: 19033.92
## ******************************************************************plot(m.hrad_wei)
## ******************************************************************
## Summary of the Quantile Residuals
## mean = -0.0004761144
## variance = 0.9983815
## coef. of skewness = 0.02656161
## coef. of kurtosis = 2.890655
## Filliben correlation coefficient = 0.99944
## ******************************************************************wp(m.hrad_wei)
Modeloando com as distribuições TF2 JSU e SST para o modelo de Hradetzky
dist TF2
m.hrad_tf2 <- gamlss(di ~ I(x^0.005) + I(x^pot1[2]) + I(x^pot1[3])+ I(x^pot1[4]) + I(x^pot1[5]) + I(x^pot1[6]) +
I(x^pot2[1]) + I(x^pot2[2]) + I(x^pot2[3])+ I(x^pot2[4]) + I(x^pot2[5]) + I(x^pot2[6]) + I(x^pot2[7]) + I(x^pot2[8])+ I(x^pot2[9]) + I(x^pot2[10]) +
I(x^pot3[1]) + I(x^pot3[2]) + I(x^pot3[3])+ I(x^pot3[4]) + I(x^pot3[5]) + I(x^pot3[6]) + I(x^pot3[7]) + I(x^pot3[8])+ I(x^pot3[9]) + I(x^pot3[10]) +
I(x^pot4[1]) + I(x^pot4[2]) + I(x^pot4[3])+ I(x^pot4[4]) + I(x^pot4[5]) + I(x^pot4[6]) + I(x^pot4[7]) + I(x^pot4[8])+ I(x^pot4[9]) + I(x^pot4[10]) +
I(x^pot4[11]) + I(x^pot4[12]) + I(x^pot4[13])+ I(x^pot4[14]) + I(x^pot4[15]) + I(x^pot4[16]) + I(x^pot4[17]) + I(x^pot4[18])+ I(x^pot4[19]) + I(x^pot4[20]) +
I(x^pot4[21]) + I(x^pot4[22]) + I(x^pot4[23])+ I(x^pot4[24]) + I(x^pot4[25]) + I(x^pot4[26]) + I(x^pot4[27]) + I(x^pot4[28])+ I(x^pot4[29]) + I(x^pot4[30]),
#sigma.formula = ~ I(x^0.005) + I(x^pot1[2]) + I(x^pot1[3])+ I(x^pot1[4]) + I(x^pot1[5]) + I(x^pot1[6]) +
#I(x^pot2[1]) + I(x^pot2[2]) + I(x^pot2[3])+ I(x^pot2[4]) + I(x^pot2[5]) + I(x^pot2[6]) + I(x^pot2[7]) + I(x^pot2[8])+ I(x^pot2[9]) + I(x^pot2[10]) +
#I(x^pot3[1]) + I(x^pot3[2]) + I(x^pot3[3])+ I(x^pot3[4]) + I(x^pot3[5]) + I(x^pot3[6]) + I(x^pot3[7]) + I(x^pot3[8])+ I(x^pot3[9]) + I(x^pot3[10]) +
#I(x^pot4[1]) + I(x^pot4[2]) + I(x^pot4[3])+ I(x^pot4[4]) + I(x^pot4[5]) + I(x^pot4[6]) + I(x^pot4[7]) + I(x^pot4[8])+ I(x^pot4[9]) + I(x^pot4[10]) +
#I(x^pot4[11]) + I(x^pot4[12]) + I(x^pot4[13])+ I(x^pot4[14]) + I(x^pot4[15]) + I(x^pot4[16]) + I(x^pot4[17]) + I(x^pot4[18])+ I(x^pot4[19]) + I(x^pot4[20]) +
#I(x^pot4[21]) + I(x^pot4[22]) + I(x^pot4[23])+ I(x^pot4[24]) + I(x^pot4[25]) + I(x^pot4[26]) + I(x^pot4[27]) + I(x^pot4[28])+ I(x^pot4[29]) + I(x^pot4[30]),
family = TF2())## GAMLSS-RS iteration 1: Global Deviance = 19487.28
## GAMLSS-RS iteration 2: Global Deviance = 19479.53
## GAMLSS-RS iteration 3: Global Deviance = 19449.48
## GAMLSS-RS iteration 4: Global Deviance = 19438.98
## GAMLSS-RS iteration 5: Global Deviance = 19433.5
## GAMLSS-RS iteration 6: Global Deviance = 19470.82
## GAMLSS-RS iteration 7: Global Deviance = 19433.45
## GAMLSS-RS iteration 8: Global Deviance = 19433.32
## GAMLSS-RS iteration 9: Global Deviance = 19475.55
## GAMLSS-RS iteration 10: Global Deviance = 19432.83
## GAMLSS-RS iteration 11: Global Deviance = 19466.43
## GAMLSS-RS iteration 12: Global Deviance = 19440.04
## GAMLSS-RS iteration 13: Global Deviance = 19425.13
## GAMLSS-RS iteration 14: Global Deviance = 19443.07
## GAMLSS-RS iteration 15: Global Deviance = 19438.52
## GAMLSS-RS iteration 16: Global Deviance = 19476.4
## GAMLSS-RS iteration 17: Global Deviance = 19439.66
## GAMLSS-RS iteration 18: Global Deviance = 19438.21
## GAMLSS-RS iteration 19: Global Deviance = 19448.74
## GAMLSS-RS iteration 20: Global Deviance = 19482.85summary e resíduos
summary(m.hrad_tf2)## ******************************************************************
## Family: c("TF2", "t Family 2")
##
## Call: gamlss(formula = di ~ I(x^0.005) + I(x^pot1[2]) + I(x^pot1[3]) +
## I(x^pot1[4]) + I(x^pot1[5]) + I(x^pot1[6]) + I(x^pot2[1]) +
## I(x^pot2[2]) + I(x^pot2[3]) + I(x^pot2[4]) + I(x^pot2[5]) +
## I(x^pot2[6]) + I(x^pot2[7]) + I(x^pot2[8]) + I(x^pot2[9]) +
## I(x^pot2[10]) + I(x^pot3[1]) + I(x^pot3[2]) + I(x^pot3[3]) +
## I(x^pot3[4]) + I(x^pot3[5]) + I(x^pot3[6]) + I(x^pot3[7]) +
## I(x^pot3[8]) + I(x^pot3[9]) + I(x^pot3[10]) + I(x^pot4[1]) +
## I(x^pot4[2]) + I(x^pot4[3]) + I(x^pot4[4]) + I(x^pot4[5]) +
## I(x^pot4[6]) + I(x^pot4[7]) + I(x^pot4[8]) + I(x^pot4[9]) +
## I(x^pot4[10]) + I(x^pot4[11]) + I(x^pot4[12]) + I(x^pot4[13]) +
## I(x^pot4[14]) + I(x^pot4[15]) + I(x^pot4[16]) + I(x^pot4[17]) +
## I(x^pot4[18]) + I(x^pot4[19]) + I(x^pot4[20]) + I(x^pot4[21]) +
## I(x^pot4[22]) + I(x^pot4[23]) + I(x^pot4[24]) + I(x^pot4[25]) +
## I(x^pot4[26]) + I(x^pot4[27]) + I(x^pot4[28]) + I(x^pot4[29]) +
## I(x^pot4[30]), family = TF2())
##
## Fitting method: RS()
##
## ------------------------------------------------------------------
## Mu link function: identity
## Mu Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -2.950e+14 1.105e+14 -2.670 0.007610 **
## I(x^0.005) -1.117e+15 5.041e+14 -2.217 0.026712 *
## I(x^pot1[2]) 1.841e+15 6.340e+14 2.904 0.003709 **
## I(x^pot2[2]) -6.359e+14 1.971e+14 -3.226 0.001266 **
## I(x^pot2[4]) 2.289e+14 7.245e+13 3.159 0.001593 **
## I(x^pot2[10]) -2.442e+13 8.062e+12 -3.029 0.002469 **
## I(x^pot3[2]) 3.274e+12 1.155e+12 2.834 0.004615 **
## I(x^pot3[4]) -3.842e+11 1.571e+11 -2.446 0.014497 *
## I(x^pot3[6]) 8.672e+10 4.230e+10 2.050 0.040404 *
## I(x^pot3[9]) -8.731e+09 6.030e+09 -1.448 0.147731
## I(x^pot4[2]) -5.103e+08 7.161e+08 -0.713 0.476168
## I(x^pot4[3]) 3.632e+09 1.517e+09 2.394 0.016695 *
## I(x^pot4[4]) -1.825e+10 4.937e+09 -3.696 0.000222 ***
## I(x^pot4[5]) 7.805e+10 1.684e+10 4.635 3.69e-06 ***
## I(x^pot4[6]) -2.730e+11 5.170e+10 -5.280 1.36e-07 ***
## I(x^pot4[7]) 7.542e+11 1.322e+11 5.704 1.26e-08 ***
## I(x^pot4[8]) -1.595e+12 2.673e+11 -5.968 2.61e-09 ***
## I(x^pot4[9]) 2.480e+12 4.051e+11 6.120 1.03e-09 ***
## I(x^pot4[10]) -2.623e+12 4.235e+11 -6.194 6.46e-10 ***
## I(x^pot4[11]) 1.534e+12 2.469e+11 6.214 5.70e-10 ***
## I(x^pot4[13]) -5.447e+11 8.852e+10 -6.154 8.31e-10 ***
## I(x^pot4[15]) 3.347e+11 5.556e+10 6.023 1.86e-09 ***
## I(x^pot4[17]) -1.924e+11 3.281e+10 -5.863 4.92e-09 ***
## I(x^pot4[19]) 7.607e+10 1.336e+10 5.693 1.34e-08 ***
## I(x^pot4[22]) -1.636e+10 3.008e+09 -5.440 5.64e-08 ***
## I(x^pot4[25]) 3.600e+09 6.921e+08 5.202 2.07e-07 ***
## I(x^pot4[28]) -4.480e+08 8.991e+07 -4.983 6.55e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## ------------------------------------------------------------------
## Sigma link function: log
## Sigma Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.03784 0.01289 80.5 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## ------------------------------------------------------------------
## Nu link function: logshiftto2
## Nu Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.94785 0.08299 23.47 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## ------------------------------------------------------------------
## No. of observations in the fit: 3982
## Degrees of Freedom for the fit: 29
## Residual Deg. of Freedom: 3953
## at cycle: 20
##
## Global Deviance: 19482.85
## AIC: 19540.85
## SBC: 19723.25
## ******************************************************************plot(m.hrad_tf2)
## ******************************************************************
## Summary of the Quantile Residuals
## mean = -0.002165408
## variance = 1.002374
## coef. of skewness = -0.03752153
## coef. of kurtosis = 2.979175
## Filliben correlation coefficient = 0.9995485
## ******************************************************************wp(m.hrad_tf2)
Distribuição JSU
m.hrad_jsu <- gamlss(di ~ I(x^0.005) + I(x^pot1[2]) + I(x^pot1[3])+ I(x^pot1[4]) + I(x^pot1[5]) + I(x^pot1[6]) +
I(x^pot2[1]) + I(x^pot2[2]) + I(x^pot2[3])+ I(x^pot2[4]) + I(x^pot2[5]) + I(x^pot2[6]) + I(x^pot2[7]) + I(x^pot2[8])+ I(x^pot2[9]) + I(x^pot2[10]) +
I(x^pot3[1]) + I(x^pot3[2]) + I(x^pot3[3])+ I(x^pot3[4]) + I(x^pot3[5]) + I(x^pot3[6]) + I(x^pot3[7]) + I(x^pot3[8])+ I(x^pot3[9]) + I(x^pot3[10]) +
I(x^pot4[1]) + I(x^pot4[2]) + I(x^pot4[3])+ I(x^pot4[4]) + I(x^pot4[5]) + I(x^pot4[6]) + I(x^pot4[7]) + I(x^pot4[8])+ I(x^pot4[9]) + I(x^pot4[10]) +
I(x^pot4[11]) + I(x^pot4[12]) + I(x^pot4[13])+ I(x^pot4[14]) + I(x^pot4[15]) + I(x^pot4[16]) + I(x^pot4[17]) + I(x^pot4[18])+ I(x^pot4[19]) + I(x^pot4[20]) +
I(x^pot4[21]) + I(x^pot4[22]) + I(x^pot4[23])+ I(x^pot4[24]) + I(x^pot4[25]) + I(x^pot4[26]) + I(x^pot4[27]) + I(x^pot4[28])+ I(x^pot4[29]) + I(x^pot4[30]),
#sigma.formula = ~ I(x^0.005) + I(x^pot1[2]) + I(x^pot1[3])+ I(x^pot1[4]) + I(x^pot1[5]) + I(x^pot1[6]) +
#I(x^pot2[1]) + I(x^pot2[2]) + I(x^pot2[3])+ I(x^pot2[4]) + I(x^pot2[5]) + I(x^pot2[6]) + I(x^pot2[7]) + I(x^pot2[8])+ I(x^pot2[9]) + I(x^pot2[10]) +
#I(x^pot3[1]) + I(x^pot3[2]) + I(x^pot3[3])+ I(x^pot3[4]) + I(x^pot3[5]) + I(x^pot3[6]) + I(x^pot3[7]) + I(x^pot3[8])+ I(x^pot3[9]) + I(x^pot3[10]) +
#I(x^pot4[1]) + I(x^pot4[2]) + I(x^pot4[3])+ I(x^pot4[4]) + I(x^pot4[5]) + I(x^pot4[6]) + I(x^pot4[7]) + I(x^pot4[8])+ I(x^pot4[9]) + I(x^pot4[10]) +
#I(x^pot4[11]) + I(x^pot4[12]) + I(x^pot4[13])+ I(x^pot4[14]) + I(x^pot4[15]) + I(x^pot4[16]) + I(x^pot4[17]) + I(x^pot4[18])+ I(x^pot4[19]) + I(x^pot4[20]) +
#I(x^pot4[21]) + I(x^pot4[22]) + I(x^pot4[23])+ I(x^pot4[24]) + I(x^pot4[25]) + I(x^pot4[26]) + I(x^pot4[27]) + I(x^pot4[28])+ I(x^pot4[29]) + I(x^pot4[30]),
family = JSU()) # jsu## GAMLSS-RS iteration 1: Global Deviance = 19693.26
## GAMLSS-RS iteration 2: Global Deviance = 19564.63
## GAMLSS-RS iteration 3: Global Deviance = 19493.38
## GAMLSS-RS iteration 4: Global Deviance = 19449.68
## GAMLSS-RS iteration 5: Global Deviance = 19437.76
## GAMLSS-RS iteration 6: Global Deviance = 19428.12
## GAMLSS-RS iteration 7: Global Deviance = 19489.08
## GAMLSS-RS iteration 8: Global Deviance = 19455.93
## GAMLSS-RS iteration 9: Global Deviance = 19434.79
## GAMLSS-RS iteration 10: Global Deviance = 19440.94
## GAMLSS-RS iteration 11: Global Deviance = 19430.39
## GAMLSS-RS iteration 12: Global Deviance = 19442.88
## GAMLSS-RS iteration 13: Global Deviance = 19432.26
## GAMLSS-RS iteration 14: Global Deviance = 19442.74
## GAMLSS-RS iteration 15: Global Deviance = 19429.19
## GAMLSS-RS iteration 16: Global Deviance = 19427.95
## GAMLSS-RS iteration 17: Global Deviance = 19427.15
## GAMLSS-RS iteration 18: Global Deviance = 19450.76
## GAMLSS-RS iteration 19: Global Deviance = 19432.46
## GAMLSS-RS iteration 20: Global Deviance = 19429.8Summary e residuos
summary(m.hrad_jsu)## ******************************************************************
## Family: c("JSU", "Johnson SU")
##
## Call: gamlss(formula = di ~ I(x^0.005) + I(x^pot1[2]) + I(x^pot1[3]) +
## I(x^pot1[4]) + I(x^pot1[5]) + I(x^pot1[6]) + I(x^pot2[1]) +
## I(x^pot2[2]) + I(x^pot2[3]) + I(x^pot2[4]) + I(x^pot2[5]) +
## I(x^pot2[6]) + I(x^pot2[7]) + I(x^pot2[8]) + I(x^pot2[9]) +
## I(x^pot2[10]) + I(x^pot3[1]) + I(x^pot3[2]) + I(x^pot3[3]) +
## I(x^pot3[4]) + I(x^pot3[5]) + I(x^pot3[6]) + I(x^pot3[7]) +
## I(x^pot3[8]) + I(x^pot3[9]) + I(x^pot3[10]) + I(x^pot4[1]) +
## I(x^pot4[2]) + I(x^pot4[3]) + I(x^pot4[4]) + I(x^pot4[5]) +
## I(x^pot4[6]) + I(x^pot4[7]) + I(x^pot4[8]) + I(x^pot4[9]) +
## I(x^pot4[10]) + I(x^pot4[11]) + I(x^pot4[12]) +
## I(x^pot4[13]) + I(x^pot4[14]) + I(x^pot4[15]) +
## I(x^pot4[16]) + I(x^pot4[17]) + I(x^pot4[18]) +
## I(x^pot4[19]) + I(x^pot4[20]) + I(x^pot4[21]) +
## I(x^pot4[22]) + I(x^pot4[23]) + I(x^pot4[24]) +
## I(x^pot4[25]) + I(x^pot4[26]) + I(x^pot4[27]) +
## I(x^pot4[28]) + I(x^pot4[29]) + I(x^pot4[30]), family = JSU())
##
## Fitting method: RS()
##
## ------------------------------------------------------------------
## Mu link function: identity
## Mu Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -3.146e+14 4.903e+05 -641667081 <2e-16 ***
## I(x^0.005) 3.361e+14 5.222e+05 643647473 <2e-16 ***
## I(x^pot1[2]) 1.933e+14 3.096e+05 624220024 <2e-16 ***
## I(x^pot2[2]) -2.756e+14 4.333e+05 -636040284 <2e-16 ***
## I(x^pot2[5]) 6.471e+13 1.116e+05 579665303 <2e-16 ***
## I(x^pot3[2]) -7.562e+12 1.567e+04 -482624943 <2e-16 ***
## I(x^pot3[3]) 4.581e+12 1.003e+04 456761157 <2e-16 ***
## I(x^pot3[5]) -1.431e+12 3.555e+03 -402451768 <2e-16 ***
## I(x^pot3[7]) 5.888e+11 1.622e+03 362974857 <2e-16 ***
## I(x^pot3[9]) -1.424e+11 4.561e+02 -312178148 <2e-16 ***
## I(x^pot4[2]) 5.019e+09 2.625e+01 191202957 <2e-16 ***
## I(x^pot4[3]) -3.399e+09 2.126e+01 -159875722 <2e-16 ***
## I(x^pot4[4]) -7.392e+09 4.562e+01 -162044201 <2e-16 ***
## I(x^pot4[5]) 7.964e+10 3.943e+02 201951660 <2e-16 ***
## I(x^pot4[6]) -3.995e+11 1.821e+03 -219447222 <2e-16 ***
## I(x^pot4[7]) 1.423e+12 6.206e+03 229356237 <2e-16 ***
## I(x^pot4[8]) -3.795e+12 1.621e+04 -234174678 <2e-16 ***
## I(x^pot4[9]) 7.566e+12 3.232e+04 234069068 <2e-16 ***
## I(x^pot4[10]) -1.096e+13 4.790e+04 -228700850 <2e-16 ***
## I(x^pot4[11]) 1.074e+13 4.944e+04 217151916 <2e-16 ***
## I(x^pot4[12]) -5.795e+12 2.946e+04 -196705390 <2e-16 ***
## I(x^pot4[14]) 1.729e+12 1.092e+04 158444331 <2e-16 ***
## I(x^pot4[16]) -8.604e+11 6.587e+03 -130622028 <2e-16 ***
## I(x^pot4[18]) 3.506e+11 3.420e+03 102524998 <2e-16 ***
## I(x^pot4[21]) -9.376e+10 1.361e+03 -68909379 <2e-16 ***
## I(x^pot4[24]) 3.073e+10 6.554e+02 46895439 <2e-16 ***
## I(x^pot4[27]) -7.825e+09 2.675e+02 -29250247 <2e-16 ***
## I(x^pot4[30]) 1.041e+09 7.932e+01 13119025 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## ------------------------------------------------------------------
## Sigma link function: log
## Sigma Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.03274 0.01139 90.67 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## ------------------------------------------------------------------
## Nu link function: identity
## Nu Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.28065 0.03588 -7.821 6.68e-15 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## ------------------------------------------------------------------
## Tau link function: log
## Tau Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.8402792 0.0004014 2093 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## ------------------------------------------------------------------
## No. of observations in the fit: 3982
## Degrees of Freedom for the fit: 31
## Residual Deg. of Freedom: 3951
## at cycle: 20
##
## Global Deviance: 19429.8
## AIC: 19491.8
## SBC: 19686.78
## ******************************************************************plot(m.hrad_jsu)
## ******************************************************************
## Summary of the Quantile Residuals
## mean = 0.002002395
## variance = 0.9998629
## coef. of skewness = -0.007694447
## coef. of kurtosis = 2.980014
## Filliben correlation coefficient = 0.9997123
## ******************************************************************wp(m.hrad_jsu)
SST
m.hrad_sst <- gamlss(di ~ I(x^0.005) + I(x^pot1[2]) + I(x^pot1[3])+ I(x^pot1[4]) + I(x^pot1[5]) + I(x^pot1[6]) +
I(x^pot2[1]) + I(x^pot2[2]) + I(x^pot2[3])+ I(x^pot2[4]) + I(x^pot2[5]) + I(x^pot2[6]) + I(x^pot2[7]) + I(x^pot2[8])+ I(x^pot2[9]) + I(x^pot2[10]) +
I(x^pot3[1]) + I(x^pot3[2]) + I(x^pot3[3])+ I(x^pot3[4]) + I(x^pot3[5]) + I(x^pot3[6]) + I(x^pot3[7]) + I(x^pot3[8])+ I(x^pot3[9]) + I(x^pot3[10]) +
I(x^pot4[1]) + I(x^pot4[2]) + I(x^pot4[3])+ I(x^pot4[4]) + I(x^pot4[5]) + I(x^pot4[6]) + I(x^pot4[7]) + I(x^pot4[8])+ I(x^pot4[9]) + I(x^pot4[10]) +
I(x^pot4[11]) + I(x^pot4[12]) + I(x^pot4[13])+ I(x^pot4[14]) + I(x^pot4[15]) + I(x^pot4[16]) + I(x^pot4[17]) + I(x^pot4[18])+ I(x^pot4[19]) + I(x^pot4[20]) +
I(x^pot4[21]) + I(x^pot4[22]) + I(x^pot4[23])+ I(x^pot4[24]) + I(x^pot4[25]) + I(x^pot4[26]) + I(x^pot4[27]) + I(x^pot4[28])+ I(x^pot4[29]) + I(x^pot4[30]),
#sigma.formula = ~ I(x^0.005) + I(x^pot1[2]) + I(x^pot1[3])+ I(x^pot1[4]) + I(x^pot1[5]) + I(x^pot1[6]) +
#I(x^pot2[1]) + I(x^pot2[2]) + I(x^pot2[3])+ I(x^pot2[4]) + I(x^pot2[5]) + I(x^pot2[6]) + I(x^pot2[7]) + I(x^pot2[8])+ I(x^pot2[9]) + I(x^pot2[10]) +
#I(x^pot3[1]) + I(x^pot3[2]) + I(x^pot3[3])+ I(x^pot3[4]) + I(x^pot3[5]) + I(x^pot3[6]) + I(x^pot3[7]) + I(x^pot3[8])+ I(x^pot3[9]) + I(x^pot3[10]) +
#I(x^pot4[1]) + I(x^pot4[2]) + I(x^pot4[3])+ I(x^pot4[4]) + I(x^pot4[5]) + I(x^pot4[6]) + I(x^pot4[7]) + I(x^pot4[8])+ I(x^pot4[9]) + I(x^pot4[10]) +
#I(x^pot4[11]) + I(x^pot4[12]) + I(x^pot4[13])+ I(x^pot4[14]) + I(x^pot4[15]) + I(x^pot4[16]) + I(x^pot4[17]) + I(x^pot4[18])+ I(x^pot4[19]) + I(x^pot4[20]) +
#I(x^pot4[21]) + I(x^pot4[22]) + I(x^pot4[23])+ I(x^pot4[24]) + I(x^pot4[25]) + I(x^pot4[26]) + I(x^pot4[27]) + I(x^pot4[28])+ I(x^pot4[29]) + I(x^pot4[30]),
family = SST()) # sst## GAMLSS-RS iteration 1: Global Deviance = 19523.67
## GAMLSS-RS iteration 2: Global Deviance = 19462.91
## GAMLSS-RS iteration 3: Global Deviance = 19434.3
## GAMLSS-RS iteration 4: Global Deviance = 19444.8
## GAMLSS-RS iteration 5: Global Deviance = 19440.79
## GAMLSS-RS iteration 6: Global Deviance = 19447.37
## GAMLSS-RS iteration 7: Global Deviance = 19443.83
## GAMLSS-RS iteration 8: Global Deviance = 19436.81
## GAMLSS-RS iteration 9: Global Deviance = 19453.88
## GAMLSS-RS iteration 10: Global Deviance = 19442.14
## GAMLSS-RS iteration 11: Global Deviance = 19440.06
## GAMLSS-RS iteration 12: Global Deviance = 19456.97
## GAMLSS-RS iteration 13: Global Deviance = 19441.4
## GAMLSS-RS iteration 14: Global Deviance = 19433.53
## GAMLSS-RS iteration 15: Global Deviance = 19445.96
## GAMLSS-RS iteration 16: Global Deviance = 19433.25
## GAMLSS-RS iteration 17: Global Deviance = 19439.72
## GAMLSS-RS iteration 18: Global Deviance = 19444.02
## GAMLSS-RS iteration 19: Global Deviance = 19431.49
## GAMLSS-RS iteration 20: Global Deviance = 19435.03Summary e resíduos
summary(m.hrad_sst)## ******************************************************************
## Family: c("SST", "SST")
##
## Call: gamlss(formula = di ~ I(x^0.005) + I(x^pot1[2]) + I(x^pot1[3]) +
## I(x^pot1[4]) + I(x^pot1[5]) + I(x^pot1[6]) + I(x^pot2[1]) +
## I(x^pot2[2]) + I(x^pot2[3]) + I(x^pot2[4]) + I(x^pot2[5]) +
## I(x^pot2[6]) + I(x^pot2[7]) + I(x^pot2[8]) + I(x^pot2[9]) +
## I(x^pot2[10]) + I(x^pot3[1]) + I(x^pot3[2]) + I(x^pot3[3]) +
## I(x^pot3[4]) + I(x^pot3[5]) + I(x^pot3[6]) + I(x^pot3[7]) +
## I(x^pot3[8]) + I(x^pot3[9]) + I(x^pot3[10]) + I(x^pot4[1]) +
## I(x^pot4[2]) + I(x^pot4[3]) + I(x^pot4[4]) + I(x^pot4[5]) +
## I(x^pot4[6]) + I(x^pot4[7]) + I(x^pot4[8]) + I(x^pot4[9]) +
## I(x^pot4[10]) + I(x^pot4[11]) + I(x^pot4[12]) + I(x^pot4[13]) +
## I(x^pot4[14]) + I(x^pot4[15]) + I(x^pot4[16]) + I(x^pot4[17]) +
## I(x^pot4[18]) + I(x^pot4[19]) + I(x^pot4[20]) + I(x^pot4[21]) +
## I(x^pot4[22]) + I(x^pot4[23]) + I(x^pot4[24]) + I(x^pot4[25]) +
## I(x^pot4[26]) + I(x^pot4[27]) + I(x^pot4[28]) + I(x^pot4[29]) +
## I(x^pot4[30]), family = SST())
##
## Fitting method: RS()
##
## ------------------------------------------------------------------
## Mu link function: identity
## Mu Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -3.346e+14 1.025e+14 -3.265 0.00110 **
## I(x^0.005) 3.279e+14 1.250e+14 2.622 0.00877 **
## I(x^pot1[2]) 2.386e+14 1.192e+14 2.002 0.04538 *
## I(x^pot2[2]) -2.973e+14 9.295e+13 -3.199 0.00139 **
## I(x^pot2[5]) 6.965e+13 2.188e+13 3.184 0.00147 **
## I(x^pot3[2]) -8.146e+12 2.670e+12 -3.050 0.00230 **
## I(x^pot3[3]) 4.941e+12 1.670e+12 2.958 0.00311 **
## I(x^pot3[5]) -1.547e+12 5.580e+11 -2.773 0.00558 **
## I(x^pot3[7]) 6.389e+11 2.471e+11 2.586 0.00974 **
## I(x^pot3[9]) -1.551e+11 6.466e+10 -2.399 0.01651 *
## I(x^pot4[2]) 5.668e+09 4.097e+09 1.383 0.16663
## I(x^pot4[3]) -4.371e+09 8.181e+09 -0.534 0.59318
## I(x^pot4[4]) -5.391e+09 2.679e+10 -0.201 0.84054
## I(x^pot4[5]) 7.715e+10 9.538e+10 0.809 0.41865
## I(x^pot4[6]) -4.078e+11 3.152e+11 -1.294 0.19580
## I(x^pot4[7]) 1.497e+12 8.956e+11 1.671 0.09475 .
## I(x^pot4[8]) -4.090e+12 2.087e+12 -1.959 0.05015 .
## I(x^pot4[9]) 8.345e+12 3.836e+12 2.175 0.02966 *
## I(x^pot4[10]) -1.238e+13 5.304e+12 -2.335 0.01961 *
## I(x^pot4[11]) 1.246e+13 5.087e+12 2.449 0.01435 *
## I(x^pot4[12]) -6.932e+12 2.740e+12 -2.530 0.01145 *
## I(x^pot4[14]) 2.237e+12 8.549e+11 2.616 0.00892 **
## I(x^pot4[16]) -1.260e+12 4.777e+11 -2.637 0.00838 **
## I(x^pot4[18]) 6.693e+11 2.555e+11 2.620 0.00883 **
## I(x^pot4[20]) -2.458e+11 9.531e+10 -2.579 0.00995 **
## I(x^pot4[23]) 4.706e+10 1.887e+10 2.494 0.01266 *
## I(x^pot4[26]) -8.598e+09 3.587e+09 -2.397 0.01658 *
## I(x^pot4[30]) 6.093e+08 2.693e+08 2.263 0.02371 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## ------------------------------------------------------------------
## Sigma link function: log
## Sigma Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.03311 0.01278 80.84 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## ------------------------------------------------------------------
## Nu link function: log
## Nu Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.06133 0.02199 -2.789 0.00531 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## ------------------------------------------------------------------
## Tau link function: logshiftto2
## Tau Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.998 0.180 11.1 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## ------------------------------------------------------------------
## No. of observations in the fit: 3982
## Degrees of Freedom for the fit: 31
## Residual Deg. of Freedom: 3951
## at cycle: 20
##
## Global Deviance: 19435.03
## AIC: 19497.03
## SBC: 19692
## ******************************************************************plot(m.hrad_sst)
## ******************************************************************
## Summary of the Quantile Residuals
## mean = -0.001849683
## variance = 1.000286
## coef. of skewness = -0.02248771
## coef. of kurtosis = 2.980156
## Filliben correlation coefficient = 0.9996515
## ******************************************************************wp(m.hrad_sst)
distribuição bcpeo
m.hrad_bcpeo <- gamlss(di ~ I(x^0.005) + I(x^pot1[2]) + I(x^pot1[3])+ I(x^pot1[4]) + I(x^pot1[5]) + I(x^pot1[6]) +
I(x^pot2[1]) + I(x^pot2[2]) + I(x^pot2[3])+ I(x^pot2[4]) + I(x^pot2[5]) + I(x^pot2[6]) + I(x^pot2[7]) + I(x^pot2[8])+ I(x^pot2[9]) + I(x^pot2[10]) +
I(x^pot3[1]) + I(x^pot3[2]) + I(x^pot3[3])+ I(x^pot3[4]) + I(x^pot3[5]) + I(x^pot3[6]) + I(x^pot3[7]) + I(x^pot3[8])+ I(x^pot3[9]) + I(x^pot3[10]) +
I(x^pot4[1]) + I(x^pot4[2]) + I(x^pot4[3])+ I(x^pot4[4]) + I(x^pot4[5]) + I(x^pot4[6]) + I(x^pot4[7]) + I(x^pot4[8])+ I(x^pot4[9]) + I(x^pot4[10]) +
I(x^pot4[11]) + I(x^pot4[12]) + I(x^pot4[13])+ I(x^pot4[14]) + I(x^pot4[15]) + I(x^pot4[16]) + I(x^pot4[17]) + I(x^pot4[18])+ I(x^pot4[19]) + I(x^pot4[20]) +
I(x^pot4[21]) + I(x^pot4[22]) + I(x^pot4[23])+ I(x^pot4[24]) + I(x^pot4[25]) + I(x^pot4[26]) + I(x^pot4[27]) + I(x^pot4[28])+ I(x^pot4[29]) + I(x^pot4[30]),
#sigma.formula = ~ I(x^0.005) + I(x^pot1[2]) + I(x^pot1[3])+ I(x^pot1[4]) + I(x^pot1[5]) + I(x^pot1[6]) +
#I(x^pot2[1]) + I(x^pot2[2]) + I(x^pot2[3])+ I(x^pot2[4]) + I(x^pot2[5]) + I(x^pot2[6]) + I(x^pot2[7]) + I(x^pot2[8])+ I(x^pot2[9]) + I(x^pot2[10]) +
#I(x^pot3[1]) + I(x^pot3[2]) + I(x^pot3[3])+ I(x^pot3[4]) + I(x^pot3[5]) + I(x^pot3[6]) + I(x^pot3[7]) + I(x^pot3[8])+ I(x^pot3[9]) + I(x^pot3[10]) +
#I(x^pot4[1]) + I(x^pot4[2]) + I(x^pot4[3])+ I(x^pot4[4]) + I(x^pot4[5]) + I(x^pot4[6]) + I(x^pot4[7]) + I(x^pot4[8])+ I(x^pot4[9]) + I(x^pot4[10]) +
#I(x^pot4[11]) + I(x^pot4[12]) + I(x^pot4[13])+ I(x^pot4[14]) + I(x^pot4[15]) + I(x^pot4[16]) + I(x^pot4[17]) + I(x^pot4[18])+ I(x^pot4[19]) + I(x^pot4[20]) +
#I(x^pot4[21]) + I(x^pot4[22]) + I(x^pot4[23])+ I(x^pot4[24]) + I(x^pot4[25]) + I(x^pot4[26]) + I(x^pot4[27]) + I(x^pot4[28])+ I(x^pot4[29]) + I(x^pot4[30]),
family = BCPEo()) # bcpeo## GAMLSS-RS iteration 1: Global Deviance = 18948.77
## GAMLSS-RS iteration 2: Global Deviance = 18818.91
## GAMLSS-RS iteration 3: Global Deviance = 18856
## GAMLSS-RS iteration 4: Global Deviance = 18819.2
## GAMLSS-RS iteration 5: Global Deviance = 18812.26
## GAMLSS-RS iteration 6: Global Deviance = 18810.9
## GAMLSS-RS iteration 7: Global Deviance = 18818.29
## GAMLSS-RS iteration 8: Global Deviance = 18810.59
## GAMLSS-RS iteration 9: Global Deviance = 18812.12
## GAMLSS-RS iteration 10: Global Deviance = 18818.09
## GAMLSS-RS iteration 11: Global Deviance = 18845.63
## GAMLSS-RS iteration 12: Global Deviance = 18816.73
## GAMLSS-RS iteration 13: Global Deviance = 18811.05
## GAMLSS-RS iteration 14: Global Deviance = 18815.06
## GAMLSS-RS iteration 15: Global Deviance = 18798.46
## GAMLSS-RS iteration 16: Global Deviance = 18791.69
## GAMLSS-RS iteration 17: Global Deviance = 18813.38
## GAMLSS-RS iteration 18: Global Deviance = 18812.53
## GAMLSS-RS iteration 19: Global Deviance = 18817.77
## GAMLSS-RS iteration 20: Global Deviance = 18817.66Summary e resíduos
summary(m.hrad_bcpeo)## ******************************************************************
## Family: c("BCPEo", "Box-Cox Power Exponential-orig.")
##
## Call: gamlss(formula = di ~ I(x^0.005) + I(x^pot1[2]) + I(x^pot1[3]) +
## I(x^pot1[4]) + I(x^pot1[5]) + I(x^pot1[6]) + I(x^pot2[1]) +
## I(x^pot2[2]) + I(x^pot2[3]) + I(x^pot2[4]) + I(x^pot2[5]) +
## I(x^pot2[6]) + I(x^pot2[7]) + I(x^pot2[8]) + I(x^pot2[9]) +
## I(x^pot2[10]) + I(x^pot3[1]) + I(x^pot3[2]) + I(x^pot3[3]) +
## I(x^pot3[4]) + I(x^pot3[5]) + I(x^pot3[6]) + I(x^pot3[7]) +
## I(x^pot3[8]) + I(x^pot3[9]) + I(x^pot3[10]) + I(x^pot4[1]) +
## I(x^pot4[2]) + I(x^pot4[3]) + I(x^pot4[4]) + I(x^pot4[5]) +
## I(x^pot4[6]) + I(x^pot4[7]) + I(x^pot4[8]) + I(x^pot4[9]) +
## I(x^pot4[10]) + I(x^pot4[11]) + I(x^pot4[12]) + I(x^pot4[13]) +
## I(x^pot4[14]) + I(x^pot4[15]) + I(x^pot4[16]) + I(x^pot4[17]) +
## I(x^pot4[18]) + I(x^pot4[19]) + I(x^pot4[20]) + I(x^pot4[21]) +
## I(x^pot4[22]) + I(x^pot4[23]) + I(x^pot4[24]) + I(x^pot4[25]) +
## I(x^pot4[26]) + I(x^pot4[27]) + I(x^pot4[28]) + I(x^pot4[29]) +
## I(x^pot4[30]), family = BCPEo())
##
## Fitting method: RS()
##
## ------------------------------------------------------------------
## Mu link function: log
## Mu Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -2.309e+13 4.467e+12 -5.168 2.48e-07 ***
## I(x^0.005) -4.990e+13 2.317e+13 -2.153 0.03134 *
## I(x^pot1[2]) 9.742e+13 2.477e+13 3.933 8.53e-05 ***
## I(x^pot2[2]) -3.083e+13 4.823e+12 -6.392 1.83e-10 ***
## I(x^pot2[5]) 6.804e+12 1.064e+12 6.397 1.77e-10 ***
## I(x^pot3[2]) -7.957e+11 1.256e+11 -6.333 2.67e-10 ***
## I(x^pot3[3]) 4.900e+11 7.780e+10 6.297 3.36e-10 ***
## I(x^pot3[5]) -1.590e+11 2.554e+10 -6.224 5.35e-10 ***
## I(x^pot3[7]) 6.833e+10 1.112e+10 6.147 8.69e-10 ***
## I(x^pot3[9]) -1.735e+10 2.860e+09 -6.065 1.44e-09 ***
## I(x^pot4[2]) 9.098e+08 1.639e+08 5.550 3.04e-08 ***
## I(x^pot4[3]) -1.485e+09 2.953e+08 -5.028 5.17e-07 ***
## I(x^pot4[4]) 3.880e+09 8.615e+08 4.503 6.88e-06 ***
## I(x^pot4[5]) -1.079e+10 2.694e+09 -4.008 6.25e-05 ***
## I(x^pot4[6]) 2.736e+10 7.692e+09 3.557 0.00038 ***
## I(x^pot4[7]) -5.840e+10 1.850e+10 -3.156 0.00161 **
## I(x^pot4[8]) 9.959e+10 3.551e+10 2.805 0.00506 **
## I(x^pot4[9]) -1.286e+11 5.146e+10 -2.499 0.01250 *
## I(x^pot4[10]) 1.156e+11 5.175e+10 2.233 0.02560 *
## I(x^pot4[11]) -5.843e+10 2.918e+10 -2.002 0.04533 *
## I(x^pot4[13]) 1.610e+10 9.901e+09 1.626 0.10403
## I(x^pot4[15]) -7.962e+09 5.953e+09 -1.337 0.18115
## I(x^pot4[17]) 3.780e+09 3.396e+09 1.113 0.26574
## I(x^pot4[19]) -1.259e+09 1.345e+09 -0.936 0.34917
## I(x^pot4[22]) 2.154e+08 2.928e+08 0.736 0.46198
## I(x^pot4[25]) -3.872e+07 6.563e+07 -0.590 0.55523
## I(x^pot4[28]) 4.030e+06 8.350e+06 0.483 0.62940
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## ------------------------------------------------------------------
## Sigma link function: log
## Sigma Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.44659 0.01019 -142 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## ------------------------------------------------------------------
## Nu link function: identity
## Nu Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.27042 0.04686 27.11 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## ------------------------------------------------------------------
## Tau link function: log
## Tau Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.87990 0.03726 23.61 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## ------------------------------------------------------------------
## No. of observations in the fit: 3982
## Degrees of Freedom for the fit: 30
## Residual Deg. of Freedom: 3952
## at cycle: 20
##
## Global Deviance: 18817.66
## AIC: 18877.66
## SBC: 19066.35
## ******************************************************************plot(m.hrad_bcpeo)
## ******************************************************************
## Summary of the Quantile Residuals
## mean = 0.00385027
## variance = 0.9991065
## coef. of skewness = -0.008143525
## coef. of kurtosis = 2.962754
## Filliben correlation coefficient = 0.99931
## ******************************************************************wp(m.hrad_bcpeo)
AIC dos modelos
AIC(m.hrad, m.hrad_wei, m.hrad_tf2, m.hrad_jsu, m.hrad_sst, m.hrad_bcpeo)## df AIC
## m.hrad_wei 28 18857.81
## m.hrad_bcpeo 30 18877.66
## m.hrad_jsu 31 19491.80
## m.hrad_sst 31 19497.03
## m.hrad_tf2 29 19540.85
## m.hrad 28 19600.24