Estimating the shape parameters a and b for Beta-Binomial Distribution
Source:R/Beta.R
EstMLEBetaBin.Rd
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.
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: doi: 10.1186/1471-2288-8-58 .
Trenkler, G., 1996. Continuous univariate distributions. Computational Statistics & Data Analysis, 21(1), p.119.
Available at: doi: 10.1016/0167-9473(96)90015-8 .
Hughes, G., 1993. Using the Beta-Binomial Distribution to Describe Aggregated Patterns of Disease Incidence. Phytopathology, 83(9), p.759.
Available at: doi: 10.1094/PHYTO-83-759
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