# Fitting the Beta-Correlated Binomial Distribution when binomial random variable, frequency, covariance, alpha and beta parameters are given The function will fit the Beta-Correlated Binomial Distribution when random variables, corresponding frequencies, covariance, alpha and beta parameters 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 fitBetaCorrBin(x,obs.freq,cov,a,b) ``` ## Arguments - `x`: vector of binomial random variables. - `obs.freq`: vector of frequencies. - `cov`: single value for covariance. - `a`: single value for alpha parameter. - `b`: single value for beta parameter. ## Returns The output of `fitBetaCorrBin` gives the class format `fitBCB` 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. `fitBCB` fitted probability values of `dBetaCorrBin`. `NegLL` Negative Log Likelihood value. `a` estimated shape parameter value a. `b` estimated shape parameter value b. `cov` estimated covariance 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 $$ obs.freq \ge 0 $$ $$ x = 0,1,2,.. $$ $$ -\infty < cov < +\infty $$ $$ 0 < a,b $$ 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 <- EstMLEBetaCorrBin(x=No.D.D,freq=Obs.fre.1,cov=0.0050,a=10,b=10) covBetaCorrBin <- bbmle::coef(parameters)[1] aBetaCorrBin <- bbmle::coef(parameters)[2] bBetaCorrBin <- bbmle::coef(parameters)[3] #fitting when the random variable,frequencies,covariance, a and b are given results <- fitBetaCorrBin(No.D.D,Obs.fre.1,covBetaCorrBin,aBetaCorrBin,bBetaCorrBin) results #extract AIC value AIC(results) #extract fitted values fitted(results) ``` ## References \insertRef paul1985threefitODBOD

fitBetaCorrBin function