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