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

Source: R/Kumaraswamy.R

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

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.

See also

mle2

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
# NOT RUN {
#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

# }