Estimating the probability of success and v parameter for COM Poisson Binomial Distribution

The function will estimate the probability of success and v parameter using the maximum log likelihood method for the COM Poisson Binomial distribution when the binomial random variables and corresponding frequencies are given.

EstMLECOMPBin(x,freq,p,v,...)

Arguments

x	vector of binomial random variables.
freq	vector of frequencies.
p	single value for probability of success.
v	single value for v.
...	mle2 function inputs except data and estimating parameter.

Value

EstMLECOMPBin here is used as a wrapper for the mle2 function of bbmle package therefore output is of class of mle2.

Details

$$x = 0,1,2,...$$ $$freq \ge 0$$ $$0 < p < 1$$ $$-\infty < v < +\infty$$

NOTE : If input parameters are not in given domain conditions necessary error messages will be provided to go further.

References

Borges, P., Rodrigues, J., Balakrishnan, N. and Bazan, J., 2014. A COM-Poisson type generalization of the binomial distribution and its properties and applications. Statistics & Probability Letters, 87, pp.158-166.

Available at: http://conteudo.icmc.usp.br/CMS/Arquivos/arquivos_enviados/BIBLIOTECA_113_NSE_90.pdf

Examples

No.D.D <- 0:7               #assigning the random variables
Obs.fre.1 <- c(47,54,43,40,40,41,39,95)     #assigning the corresponding frequencies

#estimating the parameters using maximum log likelihood value and assigning it
parameters <- EstMLECOMPBin(x=No.D.D,freq=Obs.fre.1,p=0.5,v=0.1)

bbmle::coef(parameters)           #extracting the parameters
#>          p          v 
#>  0.5126844 -0.1631013