# Fitting the Correlated Binomial Distribution when binomial random variable, frequency, probability of success and covariance are given The function will fit the Correlated Binomial Distribution when random variables, corresponding frequencies, probability of success and covariance 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 fitCorrBin(x,obs.freq,p,cov) ``` ## Arguments - `x`: vector of binomial random variables. - `obs.freq`: vector of frequencies. - `p`: single value for probability of success. - `cov`: single value for covariance. ## Returns The output of `fitCorrBin` gives the class format `fitCB` 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. `corr` Correlation value. `fitCB` fitted probability values of `dCorrBin`. `NegLL` Negative Log Likelihood 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 $$ obs.freq \ge 0 $$ $$ x = 0,1,2,.. $$ $$ 0 < p < 1 $$ $$ -\infty < cov < +\infty $$ 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 <- EstMLECorrBin(x=No.D.D,freq=Obs.fre.1,p=0.5,cov=0.0050) pCorrBin <- bbmle::coef(parameters)[1] covCorrBin <- bbmle::coef(parameters)[2] #fitting when the random variable,frequencies,probability and covariance are given results <- fitCorrBin(No.D.D,Obs.fre.1,pCorrBin,covCorrBin) results #extracting the AIC value AIC(results) #extract fitted values fitted(results) ``` ## References \insertRef johnson2005univariatefitODBOD \insertRef kupper1978usefitODBOD \insertRef paul1985threefitODBOD \insertRef morel2012overdispersionfitODBOD

fitCorrBin function