The hardware and bandwidth for this mirror is donated by dogado GmbH, the Webhosting and Full Service-Cloud Provider. Check out our Wordpress Tutorial.
If you wish to report a bug, or if you are interested in having us mirror your free-software or open-source project, please feel free to contact us at mirror[@]dogado.de.

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

These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.
Health stats visible at Monitor.