par(mfrow=c(1,2))
plot(variables$DE, variables$DL)
smoothScatter(variables$DE, variables$DL, bandwidth = 0.03)

library(ggplot2)

library(ggplot2)


ggplot(variables)+
  geom_boxplot(aes(x=1, y=DE))+
  geom_boxplot(aes(x=2, y=DL))

library(growthmodels)

time = 0:10
growth <- blumberg(time, 10, 2, 0.5)
plot(time, growth, pch = 16)

library(growthmodels)

time = 0:10
growth <- blumberg(time, 10, 2, 0.5)
growth[5] = 10
plot(time, growth, pch = 16, cex=2)

boxplot(growth, pch=16)

library(growthmodels)

time = 0:10
growth <- blumberg(time, 10, 2, 0.5)
correlacion = cor(time,growth)
plot(time, growth, pch = 16, cex=2, main = correlacion)

boxplot(growth, pch=16)

library(growthmodels)

time = 0:10
growth <- blumberg(time, 10, 2, 0.5)
correlacion_p = cor(time,growth)
correlacion_s = cor(time,growth, method='spearman')
plot(time, growth, pch = 16, cex=2, main = correlacion_s)

boxplot(growth, pch=16)

library(growthmodels)

time = 0:10
growth <- blumberg(time, 10, 2, 0.5)
correlacion_p = cor(time,growth)
correlacion_s = cor(time,growth, method='spearman')
correlacion_k = cor(time,growth, method='kendall')
plot(time, growth, pch = 16, cex=2, main = correlacion_k)

boxplot(growth, pch=16)

curve(expr = x^2,from = 0,to = 10)

curve(expr = 0.5*x^3,from = 0,to = 10)

# Funciones APPLY
apply(variables, MARGIN = 2, FUN = median)
##   DE   DL 
## 4.52 5.23
apply(variables, MARGIN = 2, FUN = min)
##   DE   DL 
## 3.82 4.52
apply(variables, MARGIN = 2, FUN = max)
##   DE   DL 
## 5.28 5.92
apply(variables, MARGIN = 2, FUN = var)
##     DE     DL 
## 0.0796 0.0837
# Matriz de varianzas y covarianzas
cov(variables)
##        DE     DL
## DE 0.0796 0.0548
## DL 0.0548 0.0837
#Matriz Correlaciones
cor(variables)
##       DE    DL
## DE 1.000 0.672
## DL 0.672 1.000
ggplot(variables)+
  geom_density(aes(DE), fill = 'green', alpha=0.5)+
  geom_density(aes(DL), fill = 'blue', alpha=0.5)

mi_scorez=function(x)
  {z=(x-mean(x))/sd(x)
return(z)}
mi_scorez = function(x){
  z = (x-mean(x))/sd(x)
  return(z)
}
mi_scorez(variables$DE)
##   [1] -0.36147 -0.47159  1.48081  0.08729  0.41222  1.54242  0.65873 -0.61741
##   [9] -0.63016 -0.97372  1.30329 -0.05721  0.97033 -0.00348 -0.90285  1.45820
##  [17]  0.29914 -1.75138  0.91987 -0.13748 -1.21933  0.07477 -0.90896 -0.72588
##  [25] -1.55759 -1.47586  0.57010 -0.02148 -0.80815  1.10830 -0.36412 -0.62069
##  [33]  0.71169  0.90110  1.57026  0.02828  1.04854 -0.52337 -1.27818  0.13806
##  [41] -1.11801 -0.21967 -0.66026  2.63339  1.74319 -0.98490  0.12433 -0.89145
##  [49] -0.31345  0.35557 -0.23993 -0.50404 -0.32399  1.63516 -0.30029  1.45495
##  [57] -1.88180  0.59521 -0.44904  0.23985 -0.23546 -0.15490  0.10219 -2.55807
##  [65] -0.98593  0.02587  0.01552  0.13085  0.52681  1.68245 -0.51407 -2.39581
##  [73]  0.85202 -1.76525 -0.47099  1.34253 -0.42710 -1.45269 -0.15364 -0.06589
##  [81]  0.34243 -0.32342 -0.33814  0.87182 -0.24333  0.27306  0.43230  0.24787
##  [89] -0.78480  1.19678  0.72989  0.53901  0.05363 -0.34454  1.76171 -1.60171
##  [97]  1.71223  1.90148 -0.09163 -0.60092
mi_scorez(variables$DL)
##   [1] -0.9107 -0.1875  1.4625 -0.1153 -0.2930  1.7037  0.1155 -2.0168 -0.9109
##  [10] -0.1488  0.9870  0.5609 -0.2755  0.0415 -0.4204  1.9146  0.5053 -2.3364
##  [19]  0.3384 -0.9439 -1.1081 -0.6503 -1.3050 -0.9054  0.0309 -2.0515  0.9078
##  [28]  0.1383 -1.6069  1.2167  0.9600 -0.1777  0.8904  0.6898 -0.0124  1.1073
##  [37] -0.0551  0.1771  0.3865 -1.0142 -0.4919 -0.3694 -1.9794  1.5927  0.5652
##  [46] -1.4213 -1.0444 -0.2617  1.5841 -0.6452  0.5218  0.2231  0.0359  0.9654
##  [55] -0.3315  1.4056 -1.4293  0.4062  0.4627  0.0243  0.7569 -0.9843 -0.8928
##  [64]  0.1758 -1.3232  0.3804  0.6635 -0.1872  1.1062  2.2134 -0.6435 -2.4117
##  [73]  0.9750  0.0563 -1.0547  0.5763 -0.3304 -1.1900  0.3087 -0.3755 -0.4648
##  [82]  0.8459 -0.5721  0.2733 -0.3721  0.2141  1.5207  0.4322 -0.0901  0.9392
##  [91]  1.0604  0.3876  0.2331 -1.0534  0.8378  0.1171  2.4467  1.0390 -0.5358
## [100] -1.5797
var_z = apply(variables, 2, mi_scorez)

colMeans(var_z)
##       DE       DL 
## 6.36e-16 1.51e-15
apply(var_z, 2, var)
## DE DL 
##  1  1
var_z = as.data.frame(var_z)
ggplot(var_z)+
  geom_density(aes(DE), fill = 'green', alpha=0.5)+
  geom_density(aes(DL), fill = 'blue', alpha=0.5)

cor(variables)
##       DE    DL
## DE 1.000 0.672
## DL 0.672 1.000
cor(var_z)
##       DE    DL
## DE 1.000 0.672
## DL 0.672 1.000

\[cv=100*\frac{s}{\bar{x}}\]

par(mfrow=c(1,2))
plot(variables$DE, variables$DL, pch = 16, asp=1)
plot(var_z$DE, var_z$DL, pch = 16, asp=1)

set.seed(123)

mi_excen = function(diam_menor, diam_mayor){
  a = diam_mayor/2
  b = diam_menor/2
  c = sqrt(a^2 - b^2)
  e = c/a
  return(e)}
variables$EXC = mi_excen(
  diam_menor = variables$DE,
  diam_mayor = variables$DL)
hist(variables$EXC)
abline(v=mean(variables$EXC), lwd=2, col='red')
abline(v=quantile(variables$EXC, 0.05), lwd=2, col='blue')

#Usar la funcion ‘mi_excen’ para calcular también el cociente $DL’..