Estimating the shape parameters a,b and c for Gaussian Hypergeometric Generalized Beta Binomial Distribution

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

EstMLEGHGBB(x,freq,a,b,c,...)

Arguments

x	vector of binomial random variables.
freq	vector of frequencies.
a	single value for shape parameter alpha representing a.
b	single value for shape parameter beta representing b.
c	single value for shape parameter lambda representing c.
...	mle2 function inputs except data and estimating parameter.

Value

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

Details

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

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

References

Rodriguez-Avi, J., Conde-Sanchez, A., Saez-Castillo, A. J., & Olmo-Jimenez, M. J. (2007). A generalization of the beta-binomial distribution. Journal of the Royal Statistical Society. Series C (Applied Statistics), 56(1), 51-61.

Available at : http://dx.doi.org/10.1111/j.1467-9876.2007.00564.x

Pearson, J., 2009. Computation of Hypergeometric Functions. Transformation, (September), p.1--123.

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 <- EstMLEGHGBB(No.D.D,Obs.fre.1,a=0.1,b=0.2,c=0.5)

bbmle::coef(parameters)   #extracting the parameters
#>         a         b         c 
#> 1.3506788 0.3245485 0.7005253