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.


The output of EstMGFBetaBin will produce the class mgf format consisting

a shape parameter of beta distribution representing for alpha

b shape parameter of beta distribution representing for beta

min Negative loglikelihood value

AIC AIC value

call the inputs for the function

Methods print, summary, coef and AIC can be used to extract specific outputs.


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

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 results <- EstMGFBetaBin(No.D.D,Obs.fre.1) # extract the estimated parameters and summary coef(results)
#> a b #> 0.7161628 0.5963324
#> Coefficients: #> a b #> 0.7161628 0.5963324 #> #> Negative Log-likelihood : 813.5872 #> #> AIC : 1631.174
AIC(results) #show the AIC value
#> [1] 1631.174