# 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. ```r 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. ## Returns 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. ## Examples ```r 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) ``` ## References \insertRef borges2014poissonfitODBOD

fitCOMPBin function