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.

Usage

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 KA (2008). “Pooling overdispersed binomial data to estimate event rate.” BMC medical research methodology, 8, 1--12. Trenkler G (1996). “Continuous univariate distributions.” Computational Statistics and Data Analysis, 21(1), 119--119. HUGHES G, MADDEN L (1993). “Using the beta-binomial distribution to describe aggegated patterns of disease incidence.” Phytopathology, 83(7), 759--763.

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