Estimating the shape parameters a and b and iterations for Kumaraswamy Binomial Distribution

The function will estimate the shape parameters using the maximum log likelihood method for the Kumaraswamy Binomial distribution when the binomial random variables and corresponding frequencies are given

Usage

EstMLEKumBin(x,freq,a,b,it,...)

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.
it: number of iterations to converge as a proper probability function replacing infinity.
...: mle2 function inputs except data and estimating parameter.

Value

EstMLEKumBin here is used as a wrapper for the mle2 function of bbmle package therefore output is of class of mle2.

Details

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

NOTE : If input parameters are not in given domain conditions necessary error messages will be provided to go further.

References

Li, X. H., Huang, Y. Y., & Zhao, X. Y. (2011). The Kumaraswamy Binomial Distribution. Chinese Journal of Applied Probability and Statistics, 27(5), 511-521.

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

if (FALSE) {
#estimating the parameters using maximum log likelihood value and assigning it
parameters1 <- EstMLEKumBin(x=No.D.D,freq=Obs.fre.1,a=10.1,b=1.1,it=10000)

bbmle::coef(parameters1)   #extracting the parameters
}