Estimating the shape parameters a and b for Beta-Binomial Distribution

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

EstMLEBetaBin(x,freq,a,b,...)

Arguments

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

Value

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

Details

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

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

References

Young-Xu, Y. & Chan, K.A., 2008. Pooling overdispersed binomial data to estimate event rate. BMC medical research methodology, 8(1), p.58.

Available at: http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=2538541&tool=pmcentrez&rendertype=abstract.

Trenkler, G., 1996. Continuous univariate distributions. Computational Statistics & Data Analysis, 21(1), p.119.

Available at: http://linkinghub.elsevier.com/retrieve/pii/0167947396900158.

Hughes, G., 1993. Using the Beta-Binomial Distribution to Describe Aggregated Patterns of Disease Incidence. Phytopathology, 83(9), p.759.

Available at: http://www.apsnet.org/publications/phytopathology/backissues/Documents/1993Abstracts/Phyto_83_759.htm

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
estimate <- EstMLEBetaBin(No.D.D,Obs.fre.1,a=0.1,b=0.1)

bbmle::coef(estimate)   #extracting the parameters
#>         a         b 
#> 0.7229420 0.5808483 

#estimating the parameters using moment generating function methods
EstMGFBetaBin(No.D.D,Obs.fre.1)
#> Call: 
#> EstMGFBetaBin(x = No.D.D, freq = Obs.fre.1)
#> 
#> Coefficients: 
#>         a         b 
#> 0.7161628 0.5963324