Estimating the probability of success and theta for Lovinson Multiplicative Binomial Distribution

The function will estimate the probability of success and phi parameter using the maximum log likelihood method for the Lovinson Multiplicative Binomial distribution when the binomial random variables and corresponding frequencies are given.

EstMLELMBin(x,freq,p,phi,...)

Arguments

x	vector of binomial random variables.
freq	vector of frequencies.
p	single value for probability of success.
phi	single value for phi parameter.
...	mle2 function inputs except data and estimating parameter.

Value

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

Details

$$freq \ge 0$$ $$x = 0,1,2,..$$ $$0 < p < 1$$ $$0 < phi $$

References

Elamir, E.A., 2013. Multiplicative-Binomial Distribution: Some Results on Characterization, Inference and Random Data Generation. Journal of Statistical Theory and Applications, 12(1), pp.92-105.

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

#estimating the parameters using maximum log likelihood value and assigning it
parameters <- EstMLELMBin(x=No.D.D,freq=Obs.fre.1,p=0.5,phi=15)

bbmle::coef(parameters)           #extracting the parameters
#>         p       phi 
#> 0.5127016 0.7060526