The function will fit the McDonald Generalized Beta Binomial Distribution when random variables, corresponding frequencies and shape parameters are given. It will provide the expected frequencies, chi-squared test statistics value, p value, degree of freedom and over dispersion value so that it can be seen if this distribution fits the data.

fitMcGBB(x,obs.freq,a,b,c)

## Arguments

x vector of binomial random variables. vector of frequencies. single value for shape parameter alpha representing a. single value for shape parameter beta representing b. single value for shape parameter gamma representing c.

## Value

The output of fitMcGBB gives the class format fitMB and fit consisting a list

bin.ran.var binomial random variables.

obs.freq corresponding observed frequencies.

exp.freq corresponding expected frequencies.

statistic chi-squared test statistics.

df degree of freedom.

p.value probability value by chi-squared test statistic.

fitMB fitted values of dMcGBB.

NegLL Negative Log Likelihood value.

a estimated value for alpha parameter as a.

b estimated value for beta parameter as b.

c estimated value for gamma parameter as c.

AIC AIC value.

over.dis.para over dispersion value.

call the inputs of the function.

Methods summary, print, AIC, residuals and fitted can be used to extract specific outputs.

## Details

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

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.

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.

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=3.2)

aMcGBB <- bbmle::coef(parameters)[1]         #assigning the estimated a
bMcGBB <- bbmle::coef(parameters)[2]         #assigning the estimated b
cMcGBB <- bbmle::coef(parameters)[3]         #assigning the estimated c

#fitting when the random variable,frequencies,shape parameter values are given.
results <- fitMcGBB(No.D.D,Obs.fre.1,aMcGBB,bMcGBB,cMcGBB)
results

#extracting the expected frequencies
fitted(results)

#extracting the residuals
residuals(results)

# }