UnivRNG (version 1.2.3)

draw.beta.binomial: Generates variates from Beta-binomial distribution

Description

This function implements pseudo-random number generation for a Beta-binomial distribution with pmf

$$f(x|n,\alpha,\beta) = \frac{n!}{x!(n-x)!B(\alpha,\beta)}\int_{0}^{1}\pi^{\alpha-1+x}(1-\pi)^{n+\beta-1-x}d\pi$$

for \(x=0,1,2,...\), \(\alpha>0\), and \(\beta>0\), where \(n\) is the sample size, \(\alpha\) and \(\beta\) are the shape parameters and \(B(\alpha,\beta)\) is the complete beta function.

Usage

draw.beta.binomial(nrep,alpha,beta,n)

Arguments

nrep

Number of data points to generate.

alpha

First shape parameter.

beta

Second shape parameter.

n

Number of trials.

Value

A list of length five containing generated data, the theoretical mean, the empirical mean, the theoretical variance, and the empirical variance with names y, theo.mean, emp.mean, theo.var, and emp.var, respectively.

Examples

# NOT RUN {
draw.beta.binomial(nrep=100000,alpha=0.2,beta=0.25,n=10)

draw.beta.binomial(nrep=100000,alpha=2,beta=3,n=10)

draw.beta.binomial(nrep=100000,alpha=600,beta=400,n=20)
# }