library(EstimationTools)
Sebaran Normal
set.seed(1701)
data <- rnorm(n = 10000, mean = 12, sd = 5)
hist(data, nclass=50)
## Diduga sebagai sebaran Normal
dugaan <- maxlogL(x = data, dist = 'dnorm', start=c(1, 1), optimizer = 'nlminb')
summary(dugaan)
## _______________________________________________________________
## Optimization routine: nlminb
## Standard Error calculation: Hessian from optim
## _______________________________________________________________
## AIC BIC
## 60718.69 60733.11
## _______________________________________________________________
## Estimate Std. Error Z value Pr(>|z|)
## mean 12.01788 0.05037 238.6 <2e-16 ***
## sd 5.03692 0.03562 141.4 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## _______________________________________________________________
## Note: p-values valid under asymptotic normality of estimators
## ---
## Diduga sebagai sebaran Gamma, bandingkan nilai AIC atau BIC-nya
dugaan <- maxlogL(x = data, dist = 'dgamma', start=c(1, 1), optimizer = 'nlminb')
summary(dugaan)
## _______________________________________________________________
## Optimization routine: nlminb
## Standard Error calculation: 'optim' failed
## _______________________________________________________________
## AIC BIC
## Inf Inf
## _______________________________________________________________
## Estimate Std. Error Z value Pr(>|z|)
## shape 1 NA NA NA
## rate 1 NA NA NA
## _______________________________________________________________
## Note: p-values valid under asymptotic normality of estimators
## ---
Sebaran Gamma
set.seed(1701)
data <- rgamma(n = 10000, shape = 5, rate = 10)
hist(data, nclass=50)
## Diduga sebagai sebaran Gamma
dugaan <- maxlogL(x = data, dist = 'dgamma', start=c(1, 1), optimizer = 'nlminb')
summary(dugaan)
## _______________________________________________________________
## Optimization routine: nlminb
## Standard Error calculation: Hessian from optim
## _______________________________________________________________
## AIC BIC
## -3004.141 -2989.72
## _______________________________________________________________
## Estimate Std. Error Z value Pr(>|z|)
## shape 5.00455 0.06855 73.01 <2e-16 ***
## rate 10.01929 0.14436 69.41 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## _______________________________________________________________
## Note: p-values valid under asymptotic normality of estimators
## ---
## Diduga sebagai sebaran Normal, bandingkan nilai AIC atau BIC-nya
dugaan <- maxlogL(x = data, dist = 'dnorm', start=c(1, 1), optimizer = 'nlminb')
summary(dugaan)
## _______________________________________________________________
## Optimization routine: nlminb
## Standard Error calculation: Hessian from optim
## _______________________________________________________________
## AIC BIC
## -1529.547 -1515.127
## _______________________________________________________________
## Estimate Std. Error Z value Pr(>|z|)
## mean 0.499492 0.002241 222.9 <2e-16 ***
## sd 0.224110 0.001585 141.4 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## _______________________________________________________________
## Note: p-values valid under asymptotic normality of estimators
## ---
Sebaran Beta
set.seed(701)
data <- rbeta(n = 10000, shape1 = 15, shape2 = 9, ncp = 0)
hist(data, nclass=50)
## Diduga sebagai sebaran Beta
dugaan <- maxlogL(x = data, dist = 'dbeta', start=c(1, 1), optimizer = 'nlminb')
summary(dugaan)
## _______________________________________________________________
## Optimization routine: nlminb
## Standard Error calculation: Hessian from optim
## _______________________________________________________________
## AIC BIC
## -18315.77 -18308.56
## _______________________________________________________________
## Estimate Std. Error Z value Pr(>|z|)
## shape1 14.8279 0.2087 71.06 <2e-16 ***
## shape2 8.9396 0.1244 71.86 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## _______________________________________________________________
## Note: p-values valid under asymptotic normality of estimators
## ---
## Diduga sebagai sebaran Gamma, bandingkan nilai AIC atau BIC-nya
dugaan <- maxlogL(x = data, dist = 'dgamma', start=c(1, 1), optimizer = 'nlminb')
summary(dugaan)
## _______________________________________________________________
## Optimization routine: nlminb
## Standard Error calculation: Hessian from optim
## _______________________________________________________________
## AIC BIC
## -17843.82 -17829.4
## _______________________________________________________________
## Estimate Std. Error Z value Pr(>|z|)
## shape 38.9305 0.5482 71.01 <2e-16 ***
## rate 62.4022 0.8844 70.56 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## _______________________________________________________________
## Note: p-values valid under asymptotic normality of estimators
## ---
## Diduga sebagai sebaran Normal, bandingkan nilai AIC atau BIC-nya
dugaan <- maxlogL(x = data, dist = 'dnorm', start=c(1, 1), optimizer = 'nlminb')
summary(dugaan)
## _______________________________________________________________
## Optimization routine: nlminb
## Standard Error calculation: Hessian from optim
## _______________________________________________________________
## AIC BIC
## -18204.93 -18190.51
## _______________________________________________________________
## Estimate Std. Error Z value Pr(>|z|)
## mean 0.6238640 0.0009736 640.8 <2e-16 ***
## sd 0.0973555 0.0006881 141.5 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## _______________________________________________________________
## Note: p-values valid under asymptotic normality of estimators
## ---