R/Gamma.R
fitGammaBin.Rd
The function will fit the Gamma 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.
fitGammaBin(x,obs.freq,c,l)
x | vector of binomial random variables. |
---|---|
obs.freq | vector of frequencies. |
c | single value for shape parameter c. |
l | single value for shape parameter l. |
The output of fitGammaBin
gives the class format fitGaB
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 dGammaBin
.
NegLL
Negative Log Likelihood value.
c
estimated value for shape parameter c.
l
estimated value for shape parameter l.
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.
$$0 < c,l$$ $$x = 0,1,2,...$$ $$obs.freq \ge 0$$
NOTE : If input parameters are not in given domain conditions necessary error messages will be provided to go further.
Grassia, A., 1977. On a family of distributions with argument between 0 and 1 obtained by transformation of the gamma and derived compound distributions. Australian Journal of Statistics, 19(2), pp.108-114.
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 #estimating the parameters using maximum log likelihood value and assigning it parameters <- EstMLEGammaBin(x=No.D.D,freq=Obs.fre.1,c=0.1,l=0.1) cGBin <- bbmle::coef(parameters)[1] #assigning the estimated c lGBin <- bbmle::coef(parameters)[2] #assigning the estimated l #fitting when the random variable,frequencies,shape parameter values are given. results <- fitGammaBin(No.D.D,Obs.fre.1,cGBin,lGBin) results#> Call: #> fitGammaBin(x = No.D.D, obs.freq = Obs.fre.1, c = cGBin, l = lGBin) #> #> Chi-squared test for Gamma Binomial Distribution #> #> Observed Frequency : 47 54 43 40 40 41 39 95 #> #> expected Frequency : 54.59 41.39 38.7 38.71 40.54 44.69 53.79 86.58 #> #> estimated c parameter : 0.6036041 ,estimated l parameter : 0.6030764 #> #> X-squared : 10.6152 ,df : 5 ,p-value : 0.0596 #> #> over dispersion : 0.4308118#> [1] 54.59 41.39 38.70 38.71 40.54 44.69 53.79 86.58#> [1] -7.59 12.61 4.30 1.29 -0.54 -3.69 -14.79 8.42