# EstMLEMultiBin: Estimating the probability of success and theta for... In Amalan-ConStat/R-fitODBOD: Modeling Over Dispersed Binomial Outcome Data Using BMD and ABD

## Description

The function will estimate the probability of success and theta parameter using the maximum log likelihood method for the Multiplicative Binomial distribution when the binomial random variables and corresponding frequencies are given

## Usage

 `1` ```EstMLEMultiBin(x,freq,p,theta) ```

## Arguments

 `x` vector of binomial random variables `freq` vector of frequencies `p` single value for probability of success `theta` single value for theta parameter

freq ≥ 0

x = 0,1,2,..

0 < p < 1

0 < theta

## Value

`EstMLEMultiBin` here is used as a input parameter for the `mle2` function of bbmle package therefore output is of class of mle2.

## 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``` ```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=0.5,theta=15), data = list(x=No.D.D,freq=Obs.fre.1))) bbmle::coef(parameters) #extracting the parameters ```