Bivariate_NBsim {trawl}

Simulates from the bivariate negative binomial distribution

Description

Simulates from the bivariate negative binomial distribution

Usage

Bivariate_NBsim(N, kappa, p1, p2)

Arguments

N

number of data points to be simulated

kappa

parameter \kappa of the bivariate negative binomial distribution

p1

parameter p_1 of the bivariate negative binomial distribution

p2

parameter p_2 of the bivariate negative binomial distribution

Details

A random vector {\bf X}=(X_1,X_2)' is said to follow the bivariate negative binomial distribution with parameters \kappa, p_1, p_2 if its probability mass function is given by

P({\bf X}={\bf x})=\frac{\Gamma(x_1+x_2+\kappa)}{x_1!x_2! \Gamma(\kappa)}p_1^{x_1}p_2^{x_2}(1-p_1-p_2)^{\kappa},

where, for i=1,2, x_i\in\{0,1,\dots\}, 0<p_i<1 such that p_1+p_2<1 and \kappa>0.

Value

An N\times 2 matrix with N simulated values from the bivariate negative binomial distribution