randomBeta

Generates pseudorandom numbers from a beta distribution.

Synopsis

randomBeta (nRandom, pin, qin)

Required Arguments

int nRandom (Input)

Number of random numbers to generate.

float pin (Input)

First beta distribution parameter. Argument pin must be positive.

float qin (Input)

Second beta distribution parameter. Argument qin must be positive.

Return Value

If no optional arguments are used, randomBeta returns an array of length nRandom containing the random standard beta deviates.

Description

Function randomBeta generates pseudorandom numbers from a beta distribution with parameters pin and qin, both of which must be positive. With p = pin and q = qin, the probability density function is

\[f(x) = \frac{\mathit{\Gamma}(p+q)}{\mathit{\Gamma}(p)\mathit{\Gamma}(q)} x^{p-1}(1-x)^{q-1}\text{ for } 0 \leq x \leq 1\]

where Γ (⋅) is the gamma function.

The algorithm used depends on the values of p and q. Except for the trivial cases of \(p=1\) or \(q=1\), in which the inverse CDF method is used, all of the methods use acceptance/rejection. If p and q are both less than 1, the method of Jöhnk (1964) is used. If either p or q is less than 1 and the other is greater than 1, the method of Atkinson (1979) is used. If both p and q are greater than 1, algorithm BB (Cheng 1978), which requires very little setup time, is used if nRandom is less than 4; and algorithm B4PE of Schmeiser and Babu (1980) is used if nRandom is greater than or equal to 4. Note that for p and q both greater than 1, calling randomBeta in a loop getting less than four variates on each call will not yield the same set of deviates as calling randomBeta once and getting all the deviates at once because two different algorithms are used.

The values returned in r are less than 1.0 and greater than ɛ, where ɛ is the smallest positive number such that \(1.0-\varepsilon\) is less than 1.0.

Function randomSeedSet can be used to initialize the seed of the random number generator; function randomOption can be used to select the form of the generator.

Example

In this example, randomBeta generates five pseudorandom beta (3, 2) variates.

from numpy import *
from pyimsl.stat.randomBeta import randomBeta
from pyimsl.stat.randomSeedSet import randomSeedSet
from pyimsl.stat.writeMatrix import writeMatrix

n_random = 5
pin = 3.0
qin = 2.0
randomSeedSet(123457)
r = randomBeta(n_random, pin, qin)
writeMatrix("Beta(3,2) random deviates", r)

Output

 
                   Beta(3,2) random deviates
          1            2            3            4            5
     0.2814       0.9483       0.3984       0.3103       0.8296