Estimating the shape parameters c and l for Gamma Binomial distribution

The function will estimate the shape parameters using the maximum log likelihood method for the Gamma Binomial distribution when the binomial random variables and corresponding frequencies are given.

EstMLEGammaBin(x,freq,c,l,...)

Arguments

x	vector of binomial random variables.
freq	vector of frequencies.
c	single value for shape parameter c.
l	single value for shape parameter l.
...	mle2 function inputs except data and estimating parameter.

Value

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

Details

$$0 < c,l$$ $$x = 0,1,2,...$$ $$freq \ge 0$$

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

References

Grassia, A., 1977. On a family of distributions with argument between 0 and 1 obtained by transformation of the gamma and derived compound distributions. Australian Journal of Statistics, 19(2), pp.108-114.

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 <- EstMLEGammaBin(x=No.D.D,freq=Obs.fre.1,c=0.1,l=0.1)

bbmle::coef(parameters)         #extracting the parameters
#>         c         l 
#> 0.6036041 0.6030764