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.

Usage

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, Bazan J (2014). “A COM--Poisson type generalization of the binomial distribution and its properties and applications.” Statistics and Probability Letters, 87, 158--166.

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