fitODBOD (version 1.3.0)

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)

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

# NOT RUN {
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=suppressWarnings(bbmle::mle2(EstMLECOMPBin,start = list(p=0.5,v=0.050),
           data = list(x=No.D.D,freq=Obs.fre.1)))

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)

# }