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

Description

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.

Usage

fitCOMPBin(x,obs.freq,p,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.

Arguments

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

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

Run this code

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

#extracting the AIC value
AIC(results)

#extract fitted values
fitted(results)

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