Estimating the shape parameters a,b and c for McDonald Generalized Beta Binomial distribution

The function will estimate the shape parameters using the maximum log likelihood method for the McDonald Generalized Beta Binomial distribution when the binomial random variables and corresponding frequencies are given.

Usage

EstMLEMcGBB(x,freq,a,b,c,...)

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.
c: single value for shape parameter gamma representing as c.
...: mle2 function inputs except data and estimating parameter.

Value

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

Details

$$0 < a,b,c$$ $$x = 0,1,2,...$$ $$freq \ge 0$$

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

References

Manoj C, Wijekoon P, Yapa RD (2013). “The McDonald generalized beta-binomial distribution: A new binomial mixture distribution and simulation based comparison with its nested distributions in handling overdispersion.” International journal of statistics and probability, 2(2), 24. Janiffer NM, Islam A, Luke O, others (2014). “Estimating Equations for Estimation of Mcdonald Generalized Beta—Binomial Parameters.” Open Journal of Statistics, 4(09), 702. Roozegar R, Tahmasebi S, Jafari AA (2017). “The McDonald Gompertz distribution: properties and applications.” Communications in Statistics-Simulation and Computation, 46(5), 3341--3355.

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

if (FALSE) {
#estimating the parameters using maximum log likelihood value and assigning it
parameters <- EstMLEMcGBB(x=No.D.D,freq=Obs.fre.1,a=0.1,b=0.1,c=0.2)

bbmle::coef(parameters)         #extracting the parameters
}