# [R] Problem to find the Maximum likelihood estimates of generalized normal distribution in R

jawad hussain j_j@zb@ @end|ng |rom y@hoo@com
Wed Apr 17 07:14:10 CEST 2019

```First I estimated the parameters of exponentiated generalized normal distribution using the dataset (data1: generated from normal distribution). Then I used real dataset (data2) and tried to find the maximum likelihood estimates (MLE) using the AdequacyModel packages. It gives the error message (mentioned right below the code).
Why does the same code estimate for first dataset (data1), but it doesn't estimate for the second dataset (data2)?
Is my way of plugging the baseline distribution (normal) in generalized class of distributions F(x)= [1-(1-G(x))^beta]^gamma introduced by Cordeiro et al.(2013) in R environment right? Am I defining the cdf and pdf of an generalized normal distribution in R in right way?

# First Problem

data1 <- rnorm(100)

pdf_exps <- function(par,x){
beta = par[1]
gamma= par[2]
mean = par[3]
sd = par[4]
( beta*gamma* ((1-(1-(pnorm(x,mean,sd)))^beta)^(gamma-1)) * ((1-(pnorm(x,mean,sd)))^(beta-1)) ) * (dnorm(x,mean,sd))
}

cdf_exps <- function(par,x){
beta = par[1]
gamma= par[2]
mean = par[3]
sd = par[4]
( 1-(1-(pnorm(x,mean,sd)))^beta)^gamma
}

set.seed(1)
result_1 = goodness.fit(pdf = pdf_exps, cdf = cdf_exps,
starts = c(1,1,1,1),data = data1  , method = "BFGS",
domain = c(-Inf,Inf), lim_inf = c(0,0,0,0),
lim_sup = c(2,2,2,2), S = 250, prop=0.1, N=50)
result_1\$mle

5.688120 4.413153 1.115777 1.996108

#----------------------------------------

data2 <-c( 20.56, 20.67, 21.86, 21.88, 18.96, 21.04, 21.69, 20.62, 22.64, 19.44, 25.75, 21.20,
22.03, 25.44, 22.63, 21.86, 22.27, 21.27, 23.47, 23.19, 23.17, 24.54, 22.96, 19.76,
23.36, 22.67, 24.24, 24.21, 20.46, 20.81, 20.17, 23.06, 24.40, 23.97, 22.62, 19.16,
21.15, 21.40, 21.03, 21.77, 21.38, 21.47, 24.45, 22.63, 22.80, 23.58, 20.06, 23.01,
24.64, 18.26, 24.47, 23.99, 26.24, 20.04, 25.72, 25.64, 19.87, 23.35, 22.42, 20.42,
22.13, 25.17, 23.72, 21.28, 20.87, 19.00, 22.04, 20.12, 21.35, 28.57, 26.95, 28.13,
26.85, 25.27, 31.93, 16.75, 19.54, 20.42, 22.76, 20.12, 22.35, 19.16, 20.77, 19.37,
22.37, 17.54, 19.06, 20.30, 20.15, 25.36, 22.12, 21.25, 20.53, 17.06, 18.29, 18.37,
18.93, 17.79, 17.05, 20.31, 22.46, 23.88, 23.68, 23.15, 22.32, 24.02, 23.29, 25.11,
22.81, 26.25, 21.38, 22.52, 26.73, 23.57, 25.84, 24.06, 23.85, 25.09, 23.84, 25.31,
19.69, 26.07, 25.50, 23.69, 26.79, 25.61, 25.06, 24.93, 22.96, 20.69, 23.97, 24.64,
25.93, 23.69, 25.38, 22.68, 23.36, 22.44, 22.57, 19.81, 21.19, 20.39, 21.12, 21.89,
29.97, 27.39, 23.11, 21.75, 20.89, 22.83, 22.02, 20.07, 20.15, 21.24, 19.63, 23.58,
21.65, 25.17, 23.25, 32.52, 22.59, 30.18, 34.42, 21.86, 23.99, 24.81, 21.68, 21.04,
23.12, 20.76, 23.13, 22.35, 22.28, 23.55, 19.85, 26.51, 24.78, 33.73, 30.18, 23.31,
24.51, 25.37, 23.67, 24.28, 25.82, 21.93, 23.38, 23.07, 25.21, 23.25, 22.93, 26.86,
21.26, 25.43, 24.54, 27.79, 23.58, 27.56, 23.76, 22.01, 22.34, 21.07)

set.seed(1)
result_2 = goodness.fit(pdf = pdf_exps, cdf = cdf_exps,
starts = c(1,1,1,1),data = data2  , method = "BFGS",
domain = c(-Inf,Inf), lim_inf = c(0,0,0,0),
lim_sup = c(2,2,2,2), S = 250, prop=0.1, N=50)
result_2\$mle

Error in optim(par = starts, fn = likelihood, x = data, method = "BFGS",  :
non-finite finite-difference value [1]