Negative Log Likelihood value of Multiplicative Binomial distribution

Source: R/MultiBin.R

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

NegLLMultiBin(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.

Value

The output of NegLLMultiBin will produce a single numeric value.

Details

$$freq \ge 0$$ $$x = 0,1,2,..$$ $$0 < p < 1$$ $$0 < theta $$

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

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

NegLLMultiBin(No.D.D,Obs.fre.1,.5,3)    #acquiring the negative log likelihood value
#> [1] 3669.494