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.
fitMcGBB(x,obs.freq,a,b,c)
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. |
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.
$$0 < a,b,c$$ $$x = 0,1,2,...$$ $$obs.freq \ge 0$$
NOTE : If input parameters are not in given domain conditions necessary error messages will be provided to go further.
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.
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) # }