# bp: The bivariate poisson distribution In bzinb: Bivariate Zero-Inflated Negative Binomial Model Estimator

## Description

random generation (`rbp`), maximum likelihood estimation (`bp`), and log-likelihood. (`lik.bp`) for the bivariate Poisson distribution with parameters equal to `(m0, m1, m2)`.

## Usage

 ```1 2 3 4 5``` ```lik.bp(xvec, yvec, m0, m1, m2, param = NULL) rbp(n, m0, m1, m2, param = NULL) bp(xvec, yvec, tol = 1e-06) ```

## Arguments

 `xvec, yvec` a pair of bp random vectors. nonnegative integer vectors. If not integers, they will be rounded to the nearest integers. `m0, m1, m2` mean parameters of the Poisson variables. They must be positive. `param` a vector of parameters (`(m0, m1, m2)`). Either `param` or individual parameters (`m0, m1, m2`) need to be provided. `n` number of observations. `tol` tolerance for judging convergence. `tol = 1e-8` by default.

## Value

• `rbp` gives a pair of random vectors following BP distribution.

• `bp` gives the maximum likelihood estimates of a BP pair.

• `lik.bp` gives the log-likelihood of a set of parameters for a BP pair.

## Author(s)

Hunyong Cho, Chuwen Liu, Jinyoung Park, and Di Wu

## References

Cho, H., Liu, C., Preisser, J., and Wu, D. (In preparation), "A bivariate zero-inflated negative binomial model for identifying underlying dependence"

Kocherlakota, S. & Kocherlakota, K. (1992). Bivariate Discrete Distributions. New York: Marcel Dekker.

## Examples

 ```1 2 3 4 5 6 7 8``` ```# generating a pair of random vectors set.seed(1) data1 <- rbp(n = 20, m0 = 1, m1 = 1, m2 = 1) lik.bp(xvec = data1[, 1], yvec = data1[ ,2], m0 = 1, m1 = 1, m2 = 1) bp(xvec = data1[,1], yvec = data1[,2]) ```

bzinb documentation built on Dec. 8, 2019, 9:12 a.m.