Estimating the covariance, alpha and beta parameter values for Beta-Correlated Binomial Distribution

The function will estimate the covariance, alpha and beta parameter values using the maximum log likelihood method for the Beta-Correlated Binomial distribution when the binomial random variables and corresponding frequencies are given.

Usage

EstMLEBetaCorrBin(x,freq,cov,a,b,...)

Arguments

x: vector of binomial random variables.
freq: vector of frequencies.
cov: single value for covariance.
a: single value for alpha parameter.
b: single value for beta parameter.
...: mle2 function inputs except data and estimating parameter.

Value

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

Details

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

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

References

Paul SR (1985). “A three-parameter generalization of the binomial distribution.” History and Philosophy of Logic, 14(6), 1497--1506.

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 <- EstMLEBetaCorrBin(x=No.D.D,freq=Obs.fre.1,cov=0.0050,a=10,b=10)

bbmle::coef(parameters)           #extracting the parameters
#>        cov          a          b 
#> 0.07068406 3.19944807 2.63292837