Fitting the COM Poisson Binomial Distribution when binomial random variable, frequency, probability of success and v parameter are given

The function will fit the COM Poisson Binomial Distribution when random variables, corresponding frequencies, probability of success and v parameter are given. It will provide the expected frequencies, chi-squared test statistics value, p value, and degree of freedom so that it can be seen if this distribution fits the data.

fitCOMPBin(x,obs.freq,p,v)

Arguments

x	vector of binomial random variables.
obs.freq	vector of frequencies.
p	single value for probability of success.
v	single value for v.

Value

The output of fitCOMPBin gives the class format fitCPB 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.

fitCPB fitted probability values of dCOMPBin.

NegLL Negative Log Likelihood value.

p estimated probability value.

v estimated v parameter value.

AIC AIC value.

call the inputs of the function.

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

Details

$$obs.freq \ge 0$$ $$x = 0,1,2,..$$ $$0 < p < 1$$ $$-\infty < v < +\infty$$

NOTE : If input parameters are not in given domain conditions necessary error messages will be provided to go further.

References

Borges, P., Rodrigues, J., Balakrishnan, N. and Bazan, J., 2014. A COM-Poisson type generalization of the binomial distribution and its properties and applications. Statistics & Probability Letters, 87, pp.158-166.

Available at: http://conteudo.icmc.usp.br/CMS/Arquivos/arquivos_enviados/BIBLIOTECA_113_NSE_90.pdf

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

#estimating the parameters using maximum log likelihood value and assigning it
parameters <- EstMLECOMPBin(x=No.D.D,freq=Obs.fre.1,p=0.5,v=0.050)

pCOMPBin <- bbmle::coef(parameters)[1]
vCOMPBin <- bbmle::coef(parameters)[2]

#fitting when the random variable,frequencies,probability and v parameter are given
results <- fitCOMPBin(No.D.D,Obs.fre.1,pCOMPBin,vCOMPBin)
results
#> Call: 
#> fitCOMPBin(x = No.D.D, obs.freq = Obs.fre.1, p = pCOMPBin, v = vCOMPBin)
#> 
#> Chi-squared test for COM Poisson Binomial Distribution 
#> 	
#>       Observed Frequency :  47 54 43 40 40 41 39 95 
#> 	
#>       expected Frequency :  57.21 43.81 38.52 37.28 39.23 44.86 56.47 81.63 
#> 	
#>       estimated p value : 0.5126926  ,estimated v parameter : -0.1632806 
#> 	
#>       X-squared : 12.8535   ,df : 5   ,p-value : 0.0248 

#extracting the AIC value
AIC(results)
#>        v 
#> 819.3116 

#extract fitted values
fitted(results)
#> [1] 57.21 43.81 38.52 37.28 39.23 44.86 56.47 81.63