# fitBetaCorrBin: Fitting the Beta-Correlated Binomial Distribution when... In Amalan-ConStat/R-fitODBOD: Modeling Over Dispersed Binomial Outcome Data Using BMD and ABD

## Description

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.

## Usage

 `1` ```fitBetaCorrBin(x,obs.freq,cov,a,b,print) ```

## 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 `print` logical value for print or not

## Details

obs.freq ≥ 0

x = 0,1,2,..

-∞ < cov < +∞

0 < a,b

NOTE : If input parameters are not in given domain conditions necessary error messages will be provided to go further

## Value

The output of `fitBetaCorrBin` gives a list format consisting

`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

## References

Paul, S.R., 1985. A three-parameter generalization of the binomial distribution. Communications in Statistics - Theory and Methods, 14(6), pp.1497-1506.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13``` ```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(EstMLEBetaCorrBin,start = list(cov=0.0050,a=10,b=10), data = list(x=No.D.D,freq=Obs.fre.1))) 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 fitBetaCorrBin(No.D.D,Obs.fre.1,covBetaCorrBin,aBetaCorrBin,bBetaCorrBin) #extracting the expected frequencies fitBetaCorrBin(No.D.D,Obs.fre.1,covBetaCorrBin,aBetaCorrBin,bBetaCorrBin,FALSE)\$exp.freq ```

Amalan-ConStat/R-fitODBOD documentation built on Oct. 1, 2018, 7:13 p.m.