Bivariate_NBsim {trawl}R Documentation

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 κ\kappa of the bivariate negative binomial distribution

p1

parameter p1p_1 of the bivariate negative binomial distribution

p2

parameter p2p_2 of the bivariate negative binomial distribution

Details

A random vector X=(X1,X2){\bf X}=(X_1,X_2)' is said to follow the bivariate negative binomial distribution with parameters κ,p1,p2\kappa, p_1, p_2 if its probability mass function is given by

P(X=x)=Γ(x1+x2+κ)x1!x2!Γ(κ)p1x1p2x2(1p1p2)κ, 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=1,2i=1,2, xi{0,1,}x_i\in\{0,1,\dots\}, 0<pi<10<p_i<1 such that p1+p2<1p_1+p_2<1 and κ>0\kappa>0.

Value

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


[Package trawl version 0.2.2 Index]