Trivariate_LSDsim: Simulates from the trivariate logarithmic series distribution

In trawl: Estimation and Simulation of Trawl Processes

Description

Simulates from the trivariate logarithmic series distribution

Usage

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.