Generate Multivariate Discrete Data.
Overview
The R package MultiDiscreteRNG implements the algorithm of the paper in Generation of Multivariate Discrete Data with generalized Poisson, negative binomial and binomial marginal distributions: https://arxiv.org/abs/2602.07707
Installation
You can install the development verison from Github with:
devtools::install_github("ckchengtommy/MultiDiscreteRNG", force = TRUE)
library(MultiDiscreteRNG)
You can also get the official release version from CRAN
install.packages("MultiDiscreteRNG")
Example 1: Trivariate Generalized Poisson Distribution
To generate a trivariate generalized Poisson distribution with rate parameters $\theta_1 = 7, \theta_2 = 0.7, \theta_3 = 40$, dispersion parameters $\lambda_1 = 0.1, \lambda_2 = 0.2, \lambda_3 = 0.3$, with a correlation matrix $\rho_{12} = 0.3, \rho_{13} = 0.3, \rho_{23} = 0.3$
First, specify the marginal distribution parameters with
GPD.lambda.vec <- c(0.1, 0.2, 0.3)
GPD.theta.vec <- c(7, 0.7, 40)
Create the correlation matrix called cmat:
M<- c(0.3, 0.3, 0.3)
N <- diag(3)
N[lower.tri(N)] <- M
cmat<- N + t(N)
diag(cmat) <- 1
Then we generate the intermediate correlation matrix with:
binObj = simBinaryCorr.Mix(GPD.theta.vec, GPD.lambda.vec, cmat, 100000, steps= 0.025)
Lastly, generate the trivaiarte generalized Poisson distribution with n = 100 samples.
GPD.data = genMix(no.rows = 100, binObj)$y
Example 2: 4-variate Negative Binomial Distribution
Note: Let $y$ be the marginal negative binomial random variable. We define the parameterization of the negative binomial distribution as follows: y is the number of failures before $r^{th}$ success, n is the number of trials per observation and p is the probability of success.
To generate a 4-variate negative binomial distribution with number of trials parameter $r_1 = 3, r_2 = 6, r_3 = 9, r_4 = 10$, probability of success parameters $p_1 = 0.51, p_2 = 0.32, p_3 = 0.64, p_4 = 0.43$ and a unstructured correlation matrix with some arbitrary values.
First, specify the marginal distribution parameters with:
NB.r.vec <- c(3, 6, 9, 10)
NB.prob.vec <- c(0.51, 0.32, 0.64, 0.43)
Create a correlation matrix with some arbitrary values:
M<- c(-0.0544 ,0.0381, -0.2319 , 0.0145 , 0.0758 ,0.1048)
N <- diag(4)
N[lower.tri(N)] <- M
cmat<- N + t(N)
diag(cmat) <- 1
Then we generate the intermediate correlation matrix with:
binObj = simBinaryCorr.NB(NB.r.vec, NB.prob.vec, cmat, 100000, steps= 0.025)
Lastly, generate the 4-variate negative binomial distribution with n = 100 samples:
NB.data = genNB(no.rows = 100, binObj)$y
A multivariate binomial distribution can be generated using a similar procedure.
Example 3: Trivariate mixed distribution with Generalized Poisson, Negative Binomial and Binomial Distribution
To generate a trivariate mixed discrete distribution with generalized Poisson, negative binomial and binomial marginal distribution, we first specify the marginal distribution parameters: Generalized Poisson with rate parameter $\theta_{GPD} = 12$, dispersion parameter $\lambda_{GPD} = 0.03$, Negative Binomial distribution number of trials parameter $r_{NB} = 15$ and probability of success parameter $p_{NB} = 0.42$, Binomial distribution number of trials parameter $n_{B} = 20$ and probability of success $p_B = 0.61$.
GPD.theta = 0.12
GPD.lambda = 0.03
NB.r = 15
NB.prob = 0.42
B.n = 20
B.prob = 0.61
Create the correlation matrix called cmat:
M<- c(0.15, 0.2, 0.15)
N <- diag(3)
N[lower.tri(N)] <- M
cmat<- N + t(N)
diag(cmat) <- 1
Then we generate the intermediate correlation matrix with:
binObj = simBinaryCorr.Mix(GPD.theta.vec = GPD.theta, GPD.lambda.vec = GPD.lambda,
NB.r.vec = NB.r, NB.prob.vec = NB.prob,
B.n.vec = B.n , B.prob.vec = B.prob,
cmat, 100000, steps= 0.025)
Lastly, generate the trivaiarte mixed distribution with n = 100 samples.
Mix.data = genMix(no.rows = 100, binObj)$y