Estimating the probability of success and correlation for Correlated Binomial Distribution
Source:R/CorrBin.R
EstMLECorrBin.Rd
The function will estimate the probability of success and correlation using the maximum log likelihood method for the Correlated Binomial distribution when the binomial random variables and corresponding frequencies are given.
Arguments
- x
vector of binomial random variables.
- freq
vector of frequencies.
- p
single value for probability of success.
- cov
single value for covariance.
- ...
mle2 function inputs except data and estimating parameter.
Value
EstMLECorrBin
here is used as a wrapper for the mle2
function of bbmle package
therefore output is of class of mle2.
Details
$$x = 0,1,2,...$$ $$freq \ge 0$$ $$0 < p < 1$$ $$-\infty < cov < +\infty$$
NOTE : If input parameters are not in given domain conditions necessary error messages will be provided to go further.
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.
Available at: doi: 10.1080/03610928508828990 .
Jorge G. Morel and Nagaraj K. Neerchal. Overdispersion Models in SAS. SAS Institute, 2012.
Examples
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 <- EstMLECorrBin(x=No.D.D,freq=Obs.fre.1,p=0.5,cov=0.0050)
bbmle::coef(parameters) #extracting the parameters
#> p cov
#> 0.54695394 0.05714648