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

The functions will estimate the shape parameters using the maximum log likelihood method andmoment generating function method for the Beta-Binomial distribution when the binomialrandom 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 themle2 function ofbbmle packagetherefore 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.

See also

Examples

No.D.D<-0:7#assigning the random variablesObs.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 itestimate<-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 methodsEstMGFBetaBin(No.D.D,Obs.fre.1)#> Call:#> EstMGFBetaBin(x = No.D.D, freq = Obs.fre.1)#>#> Coefficients:#>         a         b#> 0.7161628 0.5963324