"maximum likelihood estimation of beta-normal" & "simulation the gini index of beta-normal distribution" in R

Regarding "beta-normal distribution formula" which has been uploaded, I want to debug my scripts to estimate the parameters of the beta-normal distribution. I've used the maxLik package in r: ------------------------------------------------------------------------------------------------------------------ library(VGAM) llibrary(VGAM) library(maxLik) alfa=4;beta=3;mu=0;sigma=1 n=100 x=rbetanorm(n,alfa,beta,mu,sigma) logLikFun=function(w){ alfa=w[1] beta=w[2] mu=w[3] sigma=w[4] z=(x-mu)/sigma ll={-1*(n*gamma(alfa+beta)-n*log(gamma(alfa))-n*log(gamma(beta))-(n/2)*log(2*pi)-n*log(sigma)+sum((alfa-1)*(pnorm(z,mean=0,sd=1))+(beta-1)*(log(1-pnorm(z,mean=0,sd=1)))-((z^2)/2)))} ll } mle=maxLik(logLikFun,start=c(alfa=5,beta=2.5,mu=1,sigma=1)) summary(mle) ------------------------------------------------------------------------------------------------------------------ the results are quite wrong as shown below: ------------------------------------------------------------------------------------------------------------------ ------------------------------------------— Maximum Likelihood estimation Newton-Raphson maximisation, 3 iterations Return code 3: Last step could not find a value above the current. Boundary of parameter space? Consider switching to a more robust optimisation method temporarily. Log-Likelihood: -131157.7 4 free parameters Estimates: Estimate Std. error t value Pr(> t) alfa 5.1037852 NA NA NA beta 2.3962128 NA NA NA mu 1.5954536 0.0099872 159.8 <2e-16 * sigma 0.0444610 0.0001726 257.6 <2e-16 * —- Signif. codes: 0 ‘’ 0.001 ‘’ 0.01 ‘’ 0.05 ‘.’ 0.1 ‘ ’ 1 —------------------------------------------ Warning messages: 1: In sqrt(diag(vc)) : NaNs produced 2: In sqrt(diag(vc)) : NaNs produced ------------------------------------------------------------------------------------------------------------------ and I don't know what's the meaning of the fallowing warnings: > mle=maxLik(logLikFun,start=c(alfa=5,beta=2.5,mu=1,sigma=1)) There were 50 or more warnings (use warnings() to see the first 50) > summary(mle) the problem is the NA value for the errors which is not acceptable. I would be pleased if someone could solve this problem and send me the current scripts which I can edit or add it to my scripts. More over, regarding "gini index of beta-normal distribution" formula which has been uploaded, I want to simulate this formula by the above method please inform me about the duration of the project.