**'org.apache.commons.math3.distribution.PascalDistribution'**Java class

## Class PascalDistribution

- java.lang.Object
- org.apache.commons.math3.distribution.AbstractIntegerDistribution
- org.apache.commons.math3.distribution.PascalDistribution

- All Implemented Interfaces:
- Serializable, IntegerDistribution

public class PascalDistributionextends AbstractIntegerDistribution

Implementation of the Pascal distribution. The Pascal distribution is a special case of the Negative Binomial distribution where the number of successes parameter is an integer.

There are various ways to express the probability mass and distribution functions for the Pascal distribution. The present implementation represents the distribution of the number of failures before

`r`

successes occur. This is the convention adopted in e.g. MathWorld, but*not*in Wikipedia.For a random variable

`X`

whose values are distributed according to this distribution, the probability mass function is given by

`P(X = k) = C(k + r - 1, r - 1) * p^r * (1 - p)^k,`

where`r`

is the number of successes,`p`

is the probability of success, and`X`

is the total number of failures.`C(n, k)`

is the binomial coefficient (`n`

choose`k`

). The mean and variance of`X`

are

`E(X) = (1 - p) * r / p, var(X) = (1 - p) * r / p^2.`

Finally, the cumulative distribution function is given by

`P(X <= k) = I(p, r, k + 1)`

, where I is the regularized incomplete Beta function.

**Warning:**You cannot see the full API documentation of this class since the access to the DatMelt documentation for third-party Java classes is denied. Guests can only view jhplot Java API. To view the complete description of this class and its methods, please request the full DataMelt membership.

If you are already a full member, please login to the DataMelt member area before visiting this documentation.