# Problem in Reproducing the MLEs for a Given Distribution

I am testing a code I am using in R to compute estimates for the MLEs of the parameters for a given distribution. As an example, to check if the code works, I have chosen the paper A New Two-parameter Modified Half-logistic Distribution... by G. Mohammad. However, in trying to reproduce the parameter estimates for the MHL distribution (defined on page 1 of the attached paper) when using Data Set II (see page 14), I obtain estimates of $$0.630$$ and $$0.228$$ for $$\alpha$$ and $$\beta$$, respectively. This is markedly different to those obtained by the author ($$0.975$$ and $$0.298$$). What has gone wrong here? Is there a mistake somewhere in my code? It doesn't seem obvious to me.

The code I am using is as follows:

library(bbmle)
x <- scan(textConnection("0.036   0.058   0.102   0.103   0.114   0.116   0.061   0.074   0.078   0.086   0.381   0.538
0.570   0.574   0.590   0.618   0.645   0.961   1.228   10.94   11.02   13.88   1.600   0.148   0.183   0.192   0.254   0.262   0.379   2.006   2.054   2.804   3.058   3.076   3.147   3.625   3.704   3.931   4.073   4.393   4.534   4.893   6.274   6.816   7.896
7.904   8.022   9.337   14.73   15.08"))
dL <- function(x,alpha,beta) {
r <- max(exp(-x)*(1-exp(-x))^(alpha-1)*(beta*exp(-(beta-1)*x)+alpha+(alpha-beta)*exp(-beta*x))/(1+exp(-beta*x))^2, 0.00000001)
}
vdL <- Vectorize(dL)
LL <- function(x, alpha, beta){ -sum( log( vdL(x, alpha, beta))) }
(m0 <- mle2(LL,start=list(alpha=1,beta=0.3),data=list(x=x)))


For convenience, the MHL pdf is given by

$$f(x) = e^{-x}(1-e^{-x})^{-1+\alpha}\frac{\beta e^{-(\beta-1)x}+\alpha+(\alpha-\beta)e^{-\beta x}}{(1+e^{-\beta x})^2}$$

Second check: is the density right? I took the (much simpler) expression for the CDF from the paper, symbolically differentiated it using deriv(), and evaluated it. I match Figure 1 in the paper, and I match your loglikelihood. So the difference isn't explained by the paper getting its derivative wrong or you getting the implementation wrong.