randomNegBinomial¶

Generates pseudorandom numbers from a negative binomial distribution.

Synopsis¶

randomNegBinomial (nRandom, rk, p)

Required Arguments¶

int nRandom (Input): Number of random numbers to generate.
float rk (Input): Negative binomial parameter. Parameter rk must be positive. If rk is an integer, the generated deviates can be thought of as the number of failures in a sequence of Bernoulli trials before rk successes occur.
float p (Input): Probability of failure on each trial. Parameter p must be greater than machine epsilon (see machine, Chapter 15, Utilities) and less than 1.0.

Return Value¶

An integer array of length nRandom containing the random negative binomial deviates.

Description¶

Function randomNegBinomial generates pseudorandom numbers from a negative binomial distribution with parameters rk and p. Parameters rk and p must be positive and p must be less than 1. The probability function (with r = rk and p = p) is

\[f(x) = \binom{r+x-1}{x} (1-p)^r p^x\]

for \(x=0,1,2,\ldots\)

If r is an integer, the distribution is often called the Pascal distribution and can be thought of as modeling the length of a sequence of Bernoulli trials until r successes are obtained, where p is the probability of getting a failure on any trial. In this form, the random variable takes values r, r + 1, r + 2, … and can be obtained from the negative binomial random variable defined above by adding r to the negative binomial variable. This latter form is also equivalent to the sum of r geometric random variables defined as taking values 1, 2, 3, …

If \(rp/(1-p)\) is less than 100 and \((1-p)^r\) is greater than the machine epsilon, randomNegBinomial uses the inverse CDF technique; otherwise, for each negative binomial deviate, randomNegBinomial generates a gamma \((r,p/(1-p))\) deviate Y and then generates a Poisson deviate with parameter Y.

Example¶

In this example, randomNegBinomial generates five pseudorandom negative binomial deviates from a negative binomial (Pascal) distribution with parameters r equal to 4 and p equal to 0.3.

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

n_random = 5
rk = 4.0
p = 0.3
randomSeedSet(123457)
ir = randomNegBinomial(n_random, rk, p)
writeMatrix("Negative Binomial (4.0, 0.3) random deviates:", ir,
            noColLabels=True, writeFormat="%5i")

Output¶

 
Negative Binomial (4.0, 0.3) random deviates:
          5      1      3      2      3