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

Source: R/Gbeta1.R

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.

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, R.D., 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), pp.24-41.

Available at: http://www.ccsenet.org/journal/index.php/ijsp/article/view/23491.

Janiffer, N.M., Islam, A. & Luke, O., 2014. Estimating Equations for Estimation of Mcdonald Generalized Beta - Binomial Parameters. , (October), pp.702-709.

Roozegar, R., Tahmasebi, S. & Jafari, A.A., 2015. The McDonald Gompertz Distribution: Properties and Applications. Communications in Statistics - Simulation and Computation, (May), pp.0-0.

Available at: http://www.tandfonline.com/doi/full/10.1080/03610918.2015.1088024.

See also

mle2

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
# NOT RUN {
#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

# }