# Fitting the Beta-Binomial Distribution when binomial random variable, frequency and shape parameters a and b are given The function will fit the Beta-Binomial distribution when random variables, corresponding frequencies and shape parameters are given. It will provide the expected frequencies, chi-squared test statistics value, p value, degree of freedom and over dispersion value so that it can be seen if this distribution fits the data. ```r fitBetaBin(x,obs.freq,a,b) ``` ## Arguments - `x`: vector of binomial random variables. - `obs.freq`: vector of frequencies. - `a`: single value for shape parameter alpha representing as a. - `b`: single value for shape parameter beta representing as b. ## Returns The output of `fitBetaBin` gives the class format `fitBB` 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. `fitBB` fitted values of `dBetaBin`. `NegLL` Negative Log Likelihood value. `a` estimated value for alpha parameter as a. `b` estimated value for alpha parameter as b. `AIC` AIC value. `over.dis.para` over dispersion value. `call` the inputs of the function. Methods `summary`, `print`, `AIC`, `residuals` and `fitted` can be used to extract specific outputs. ## Details $$ 0 < a,b $$ $$ x = 0,1,2,...,n $$ $$ obs.freq \ge 0 $$ 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 <- EstMLEBetaBin(No.D.D,Obs.fre.1,0.1,0.1) bbmle::coef(parameters) #extracting the parameters a and b aBetaBin <- bbmle::coef(parameters)[1] #assigning the parameter a bBetaBin <- bbmle::coef(parameters)[2] #assigning the parameter b #fitting when the random variable,frequencies,shape parameter values are given. fitBetaBin(No.D.D,Obs.fre.1,aBetaBin,bBetaBin) #estimating the parameters using moment generating function methods results <- EstMGFBetaBin(No.D.D,Obs.fre.1) results aBetaBin1 <- results$a #assigning the estimated a bBetaBin1 <- results$b #assigning the estimated b #fitting when the random variable,frequencies,shape parameter values are given. BB <- fitBetaBin(No.D.D,Obs.fre.1,aBetaBin1,bBetaBin1) #extracting the expected frequencies fitted(BB) #extracting the residuals residuals(BB) ``` ## References \insertRef young2008poolingfitODBOD \insertRef trenkler1996continuousfitODBOD \insertRef hughes1993usingfitODBOD ## See Also `mle2`

fitBetaBin function