Fitting the McDonald Generalized Beta Binomial distribution when binomial random variable, frequency and shape parameters are given
Source:R/Gbeta1.R
fitMcGBB.Rd
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.
Arguments
- x
vector of binomial random variables.
- obs.freq
vector of frequencies.
- a
single value for shape parameter alpha representing a.
- b
single value for shape parameter beta representing b.
- c
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.
Available at: doi: 10.5539/ijsp.v2n2p24 .
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: doi: 10.1080/03610918.2015.1088024 .
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=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)
}