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.




vector of binomial random variables.


vector of frequencies.


single value for shape parameter alpha representing as a.


single value for shape parameter beta representing as b.


mle2 function inputs except data and estimating parameter.


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


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

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


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:

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

Available at:

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

Available at:

See also


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