Trivariate_LSDsim: Simulates from the trivariate logarithmic series distribution

Description Usage Arguments Details Value

View source: R/SimulateDiscreteDistributions.R

Description

Simulates from the trivariate logarithmic series distribution

Usage

1
Trivariate_LSDsim(N, p1, p2, p3)

Arguments

N

number of data points to be simulated

p1

parameter p1 of the trivariate logarithmic series distribution

p2

parameter p2 of the trivariate logarithmic series distribution

p3

parameter p3 of the trivariate logarithmic series distribution

Details

The probability mass function of a random vector X=(X_1,X_2,X_3)' following the trivariate logarithmic series distribution with parameters 0<p_1, p_2, p_3<1 with p:=p_1+p_2+p_3<1 is given by

P(X_1=x_1,X_2=x_2,X_3=x_3)=\frac{Γ(x_1+x_2+x_3)}{x_1!x_2!x_3!} \frac{p_1^{x_1}p_2^{x_2}p_3^{x_3}}{(-\log(1-p))},

for x_1,x_2,x_3=0,1,2,… such that x_1+x_2+x_3>0.

The simulation proceeds in two steps: First, X_1 is simulated from the modified logarithmic distribution with parameters \tilde p_1=p_1/(1-p_2-p_3) and δ_1=\log(1-p_2-p_3)/\log(1-p). Then we simulate (X_2,X_3)' conditional on X_1. We note that (X_2,X_3)'|X_1=x_1 follows the bivariate logarithmic series distribution with parameters (p_2,p_3) when x_1=0, and the bivariate negative binomial distribution with parameters (x_1,p_2,p_3) when x_1>0.

Value

An N \times 3 matrix with N simulated values from the trivariate logarithmic series distribution


trawl documentation built on Feb. 23, 2021, 1:06 a.m.