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

## Description

The function will fit the Multiplicative binomial distribution when random variables, corresponding frequencies, probability of success and theta parameter are given. It will provide the expected frequencies, chi-squared test statistics value, p value and degree of freedom value so that it can be seen if this distribution fits the data.

## Usage

 `1` ```fitMultiBin(x,obs.freq,p,theta,print) ```

## Arguments

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

obs.freq ≥ 0

x = 0,1,2,..

0 < p < 1

0 < theta

## Value

The output of `fitMultiBin` 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

## References

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.

`mle2`
 ``` 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(EstMLEMultiBin,start = list(p=0.1,theta=.3), data = list(x=No.D.D,freq=Obs.fre.1))) pMultiBin=bbmle::coef(parameters)[1] #assigning the estimated probability value thetaMultiBin=bbmle::coef(parameters)[2] #assigning the estimated theta value #fitting when the random variable,frequencies,probability and theta are given fitMultiBin(No.D.D,Obs.fre.1,pMultiBin,thetaMultiBin) #extracting the expected frequencies fitMultiBin(No.D.D,Obs.fre.1,pMultiBin,thetaMultiBin,FALSE)\$exp.freq ```