# EstMLEKumBin: Estimating the shape parameters a and b and iterations for... In Amalan-ConStat/R-fitODBOD: Modeling Over Dispersed Binomial Outcome Data Using BMD and ABD

## Description

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

 `1` ```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

## Details

0 < a,b

x = 0,1,2,...

freq ≥ 0

it > 0

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

## Value

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

## 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.

`mle2`
 ```1 2 3 4 5 6 7``` ```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 parameters1=suppressWarnings(bbmle::mle2(EstMLEKumBin,start = list(a=10.1,b=1.1,it=10000), data = list(x=No.D.D,freq=Obs.fre.1))) bbmle::coef(parameters1) #extracting the parameters ```