# bnb: The bivariate negative binomial distribution In bzinb: Bivariate Zero-Inflated Negative Binomial Model Estimator

## Description

random generation (`rbnb`), maximum likelihood estimation (`bnb`), and log-likelihood. (`lik.bnb`) for the bivariate negative binomial distribution with parameters equal to `(a0, a1, a2, b1, b2)`.

## Usage

 ```1 2 3 4 5 6``` ```lik.bnb(xvec, yvec, a0, a1, a2, b1, b2, param = NULL) rbnb(n, a0, a1, a2, b1, b2, param = NULL) bnb(xvec, yvec, em = TRUE, tol = 1e-08, maxiter = 50000, vcov = TRUE, initial = NULL, showFlag = FALSE) ```

## Arguments

 `xvec, yvec` a pair of bnb random vectors. nonnegative integer vectors. If not integers, they will be rounded to the nearest integers. `a0, a1, a2` shape parameters of the latent gamma variables. must be positive. `b1, b2` scale parameters for the latent gamma variables. must be positive. `param` a vector of parameters (`(a0, a1, a2, b1, b2)`). Either `param` or individual parameters (`a0, a1, a2, b1, b2`) need to be provided. `n` number of observations. `em` if `TRUE` in `bnb`, EM algorithm is applied. Otherwise, direct opitmation is used. `tol, maxiter, vcov, initial, showFlag` optional arguments applied only when `em` is `TRUE` in `bnb`.

## Value

• `rbnb` gives a pair of random vectors following BNB distribution.

• `bnb` gives the maximum likelihood estimates of a BNB pair. Standard error and covariance matrix are provided when `em` is `TRUE`.

• `lik.bnb` gives the log-likelihood of a set of parameters for a BNB 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"

## Examples

 ```1 2 3 4 5 6 7 8 9``` ```# generating a pair of random vectors set.seed(1) data1 <- rbnb(n = 100, a0 = 2, a1 = 1, a2 = 1, b1 = 1, b2 = 1) lik.bnb(xvec = data1[, 1], yvec = data1[ ,2], a0 = 1, a1 = 1, a2 = 1, b1 = 1, b2 = 1) bnb(xvec = data1[,1], yvec = data1[,2], showFlag = FALSE) ```

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