Negative Log Likelihood value of Gaussian Hypergeometric Generalized Beta Binomial Distribution

This function will calculate the negative log likelihood value when the vector of binomial random variables and vector of corresponding frequencies are given with the shape parameters a,b and c.

Usage

NegLLGHGBB(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.

Value

The output of NegLLGHGBB will produce a single numeric value.

Details

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

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 AJ, Olmo-Jimenez MJ (2007). “A generalization of the beta--binomial distribution.” Journal of the Royal Statistical Society Series C: Applied Statistics, 56(1), 51--61. Pearson JW (2009). Computation of hypergeometric functions. Ph.D. thesis, University of Oxford.

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
NegLLGHGBB(No.D.D,Obs.fre.1,.2,.3,1)     #acquiring the negative log likelihood value
#> [1] 897.6074