randomLogarithmic¶

Generates pseudorandom numbers from a logarithmic distribution.

Synopsis¶

randomLogarithmic (nRandom, a)

Required Arguments¶

int nRandom (Input): Number of random numbers to generate.
float a (Input): Parameter of the logarithmic distribution. Parameter a must be positive and less than 1.0.

Return Value¶

An integer array of length nRandom containing the random logarithmic deviates.

Description¶

Function randomLogarithmic generates pseudorandom numbers from a logarithmic distribution with parameter a. The probability function is

\[f(x) = - \frac{a^x}{x \ln (1-a)}\]

for \(x=1,2,3,\ldots\), and \(0<a<1\)

The methods used are described by Kemp (1981) and depend on the value of a. If a is less than 0.95, Kemp’s algorithm LS, which is a “chop-down” variant of an inverse CDF technique, is used. Otherwise, Kemp’s algorithm LK, which gives special treatment to the highly probable values of 1 and 2 is used.

Example¶

In this example, randomLogarithmic generates five pseudorandom logarithmic deviates from a logarithmic distribution with parameter a equal to 0.3.

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

n_random = 5
a = 0.3
randomSeedSet(123457)
ir = randomLogarithmic(n_random, a)
writeMatrix("Logarithmic random deviates:", ir,
            noColLabels=True)

Output¶

 
                 Logarithmic random deviates:
          2            1            1            1            2