Simulates from the bivariate negative binomial distribution
Bivariate_NBsim(N, kappa, p1, p2)number of data points to be simulated
parameter \(\kappa\) of the bivariate negative binomial distribution
parameter \(p_1\) of the bivariate negative binomial distribution
parameter \(p_2\) of the bivariate negative binomial distribution
An \(N\times 2\) matrix with \(N\) simulated values from the bivariate negative binomial distribution
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 \(\kappa>0\).