Estimating the probability of success and correlation for Correlated Binomial Distribution

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

Usage

EstMLECorrBin(x,freq,p,cov,...)

Arguments

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

Value

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

Details

$$x = 0,1,2,...$$ $$freq \ge 0$$ $$0 < p < 1$$ $$-\infty < cov < +\infty$$

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

References

Johnson NL, Kemp AW, Kotz S (2005). Univariate discrete distributions, volume 444. John Wiley and Sons. Kupper LL, Haseman JK (1978). “The use of a correlated binomial model for the analysis of certain toxicological experiments.” Biometrics, 69--76. Paul SR (1985). “A three-parameter generalization of the binomial distribution.” History and Philosophy of Logic, 14(6), 1497--1506. Morel JG, Neerchal NK (2012). Overdispersion models in SAS. SAS Publishing.

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 <- EstMLECorrBin(x=No.D.D,freq=Obs.fre.1,p=0.5,cov=0.0050)

bbmle::coef(parameters)           #extracting the parameters
#>          p        cov 
#> 0.54695394 0.05714648