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This is an extension of an earlier question asked here. I have a data-set coming from a distribution given by:

$$Pr(X=k)=p \left({n\choose k}a^k(1-a)^{n-k}\right)+(1-p) \left({n\choose k}b^k(1-b)^{n-k}\right)$$

which is a mixture of two binomial distributions.

My aim is to estimate the parameter values, namely: n, p, a, b. To this I want to optimize the maximum likelihood function using "JDEoptim" package via R software.

fn<-function(x){
  #x(1)=p; x(2)=n; x(3)=a; x(4)=b;
  -prod(DensityFn(x, dataset[1:length(dataset)]))
}

DensityFn<-function(x, val){
  x[1]*dbinom(val, floor(x[2]), x[3])+(1-x[1])*dbinom(val, floor(x[2]), x[4])
}

lower=c(0, 11, 0, 0);
upper=c(0.5, 20, 1, 1);

print(JDEoptim(lower, upper, fn))

The variable "data-set" contains the values generated by this density function. The output upon running this program gives me:

$par [1]  0.07007818 11.85238114  0.86411002  0.64941201

$value [1] 0

$iter [1] 0

$convergence [1] 0

'iter' is 0 while 'convergence' is 0...indicating convergence has occured, however the parameter values outputted are far off from the actual values. Also, every time I run the program, the parameter estimates differ, but 'iter' and 'convergence' are always 0.

Is my code and logic correct?

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    $\begingroup$ At minimum, you should provide a link to your earlier question stats.stackexchange.com/questions/327702/… $\endgroup$ Feb 10, 2018 at 14:30
  • $\begingroup$ Thank you for pointing that out. Is it usually bad practice to ask follow-up questions within a short time-frame to an already answered question? I'm asking because I'm a relatively new user to the stack community $\endgroup$ Feb 10, 2018 at 14:36

1 Answer 1

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Fixed the problem by using log-likelihood instead.

used

-sum(log(DensityFn(x, dataset[1:length(dataset)]))) 

instead of

-prod(DensityFn(x, dataset[1:length(dataset)]))
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