This function will calculate the Negative Log Likelihood value when the vector of binomial random variables and vector of corresponding frequencies are given with the shape parameters a and b.

NegLLBetaBin(x,freq,a,b)

## Arguments

x 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.

## Value

The output of NegLLBetaBin will produce a single numeric value.

## Details

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

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.

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

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

NegLLBetaBin(No.D.D,Obs.fre.1,.3,.4)   #acquiring the negative log likelihood value#> [1] 857.597