fitODBOD (version 1.4.1-1)

NegLLMultiBin: Negative Log Likelihood value of Multiplicative Binomial distribution

Description

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.

Usage

NegLLMultiBin(x,freq,p,theta)

Value

The output of NegLLMultiBin will produce a single numeric value.

Arguments

x

vector of binomial random variables.

freq

vector of frequencies.

p

single value for probability of success.

theta

single value for theta parameter.

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