Negative Log Likelihood value of Correlated Binomial distribution

This function will calculate the negative log likelihood value when the vector of binomial random variables and vector of corresponding frequencies are given with the input parameters.

Usage

NegLLCorrBin(x,freq,p,cov)

Arguments

x: vector of binomial random variables.
freq: vector of frequencies.
p: single value for probability of success.
cov: single value for covariance.

Value

The output of NegLLCorrBin will produce a single numeric value.

Details

$$freq \ge 0$$ $$x = 0,1,2,..$$ $$0 < p < 1$$ $$-\infty < cov < +\infty$$

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

References

Johnson NL, Kemp AW, Kotz S (2005). Univariate discrete distributions, volume 444. John Wiley and Sons. Kupper LL, Haseman JK (1978). “The use of a correlated binomial model for the analysis of certain toxicological experiments.” Biometrics, 69--76. Paul SR (1985). “A three-parameter generalization of the binomial distribution.” History and Philosophy of Logic, 14(6), 1497--1506. Morel JG, Neerchal NK (2012). Overdispersion models in SAS. SAS Publishing.

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

NegLLCorrBin(No.D.D,Obs.fre.1,.5,.03)     #acquiring the negative log likelihood value
#> [1] 994.1944