randomGamma¶

Generates pseudorandom numbers from a standard gamma distribution.

Synopsis¶

randomGamma (nRandom, a)

Required Arguments¶

int nRandom (Input): Number of random numbers to generate.
float a (Input): The shape parameter of the gamma distribution. This parameter must be positive.

Return Value¶

randomGamma returns a vector of length nRandom containing the random standard gamma deviates.

Description¶

The function randomGamma generates pseudorandom numbers from a gamma distribution with shape parameter a and unit scale parameter. The probability density function is

\[f(x) = \frac{1}{\mathit{\Gamma}(a)}x^{a-1}e^{-x}\text{ for } x \geq 0\]

Various computational algorithms are used depending on the value of the shape parameter a. For the special case of \(a=0.5\), squared and halved normal deviates are used; and for the special case of \(a=1.0\), exponential deviates are generated. Otherwise, if a is less than 1.0, an acceptance-rejection method due to Ahrens, described in Ahrens and Dieter (1974), is used. If a is greater than 1.0, a ten-region rejection procedure developed by Schmeiser and Lal (1980) is used.

Deviates from the two-parameter gamma distribution with shape parameter a and scale parameter b can be generated by using randomGamma and then multiplying each entry in r by b.

The Erlang distribution is a standard gamma distribution with the shape parameter having a value equal to a positive integer; hence, randomGamma generates pseudorandom deviates from an Erlang distribution with no modifications required.

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

Example¶

In this example, randomGamma is used to generate five pseudorandom deviates from a gamma (Erlang) distribution with shape parameter equal to 3.0.

from numpy import *
from pyimsl.math.randomGamma import randomGamma
from pyimsl.math.randomSeedSet import randomSeedSet
from pyimsl.math.writeMatrix import writeMatrix

randomSeedSet(123457)
a = 3.0
r = randomGamma(5, a)
writeMatrix("Gamma(3) random deviates", r)

Output¶

 
                   Gamma(3) random deviates
          1            2            3            4            5
      6.843        3.445        1.853        3.999        0.779