UnivRNG (version 1.2.3)

draw.beta.alphabeta.less.than.one: Generates variates from Beta distribution with max\((\alpha,\beta)<1\)

Description

This function implements pseudo-random number generation for a Beta distribution for \(\max(\alpha,\beta)<1\) with pdf

$$f(x|\alpha,\beta)=\frac{1}{B(\alpha,\beta)}x^{\alpha-1}(1-x)^{\beta-1}$$

for \(0 \leq x \leq 1\), \(0 < \alpha < 1\), and \(0 < \beta < 1\) where \(\alpha\) and \(\beta\) are the shape parameters and \(B(\alpha,\beta)\) is the complete beta function.

Usage

draw.beta.alphabeta.less.than.one(nrep,alpha,beta)

Arguments

nrep

Number of data points to generate.

alpha

First shape parameter. Must be less than 1.

beta

Second shape parameter. Must be less than 1.

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.

References

Jhonk, M. D. (1964). Erzeugung von betaverteilter und gammaverteilter zufallszahlen. Metrika, 8, 5-15.

Examples

# NOT RUN {
draw.beta.alphabeta.less.than.one(nrep=100000,alpha=0.7,beta=0.4)
# }