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

Description Usage Arguments Details Value References Examples

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.

1	fitCorrBin(x,obs.freq,p,cov,print)

`x`	vector of binomial random variables
`obs.freq`	vector of frequencies
`p`	single value for probability of success
`cov`	single value for covariance
`print`	logical value for print or not

obs.freq ≥ 0

x = 0,1,2,..

0 < p < 1

-∞ < cov < +∞

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

The output of fitCorrBin 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

Johnson, N. L., Kemp, A. W., & Kotz, S. (2005). Univariate discrete distributions (Vol. 444). Hoboken, NJ: Wiley-Interscience.

L. L. Kupper, J.K.H., 1978. The Use of a Correlated Binomial Model for the Analysis of Certain Toxicological Experiments. Biometrics, 34(1), pp.69-76.

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

Available at: http://www.tandfonline.com/doi/abs/10.1080/03610928508828990 .

Jorge G. Morel and Nagaraj K. Neerchal. Overdispersion Models in SAS. SAS Institute, 2012.

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(EstMLECorrBin,start = list(p=0.5,cov=0.0050),
           data = list(x=No.D.D,freq=Obs.fre.1)))
pCorrBin=bbmle::coef(parameters)[1]
covCorrBin=bbmle::coef(parameters)[2]
#fitting when the random variable,frequencies,probability and covariance are given
fitCorrBin(No.D.D,Obs.fre.1,pCorrBin,covCorrBin)
#extracting the expected frequencies
fitCorrBin(No.D.D,Obs.fre.1,pCorrBin,covCorrBin,FALSE)$exp.freq