[R] Maximum Likelihood estimation of KB distribution

[chamilka]

Hi, The following distribution is known as Kumaraswamy binomial Distribution.
http://r.789695.n4.nabble.com/file/n4636782/kb.png 

For a given data I need to estimate the paramters (alpha and beta) of this
distribution(Known as Kumaraswamy binomial Distribution, A Binomial Like
Distribution). For that, in order to use *optim()*, I first declared the
Negative Log-likelihood of this distribution as follows;

*Loglik.newdis2<-function(x,a,b,n,imax) { 
      term<-0 
      for (i in 0:imax) { 
           term=term+(((-1)**i)*(choose(b-1,i))*(beta(x+a+a*i,n-x+1))) 
           } 
      dens=a*b*choose(n,x)*term 
      KBLL2<-sum(log(dens)) 
      return(-KBLL2) 
      }  *

since there is an infinite convergent series in this PMF, I decided to
specify a maximum value as imax instead of infinity without loss of any
information, and n is the binomial trials. 

Please tell me whether the declared negative loglikelihood (NLL) is correct
for this distribution?  

***I couldn't get the result of this
paper(http://aps.ecnu.edu.cn/EN/abstract/abstract8722.shtml) with my NLL

Thanks in advance. 

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