Estimating the probability of success and theta for Multiplicative Binomial Distribution

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

EstMLEMultiBin(x,freq,p,theta,...)

Arguments

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

Value

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

Details

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

References

Johnson, N. L., Kemp, A. W., & Kotz, S. (2005). Univariate discrete distributions (Vol. 444). Hoboken, NJ: Wiley-Interscience.

L. L. Kupper, J.K.H., 1978. The Use of a Correlated Binomial Model for the Analysis of Certain Toxicological Experiments. Biometrics, 34(1), pp.69-76.

Paul, S.R., 1985. A three-parameter generalization of the binomial distribution. Communications in Statistics - Theory and Methods, 14(6), pp.1497-1506.

Available at: http://www.tandfonline.com/doi/abs/10.1080/03610928508828990 .

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 <- EstMLEMultiBin(x=No.D.D,freq=Obs.fre.1,p=0.5,theta=15)

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