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
library(AdequacyModel)
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]
JAWAD HUSSAIN ASHRAF
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