SSJ
V. 2.6.

## umontreal.iro.lecuyer.probdist Class PascalDist

```java.lang.Object
umontreal.iro.lecuyer.probdist.DiscreteDistributionInt
umontreal.iro.lecuyer.probdist.NegativeBinomialDist
umontreal.iro.lecuyer.probdist.PascalDist
```
All Implemented Interfaces:
Distribution

`public class PascalDistextends NegativeBinomialDist`

The Pascal distribution is a special case of the negative binomial distribution with parameters n and p, where n is a positive integer and 0 <= p <= 1. Its mass function is

p(x) = nCr(n + x - 1, x)pn(1 - p)x,        for x = 0, 1, 2,…

where nCr is defined in `BinomialDist`. This p(x) can be interpreted as the probability of having x failures before the nth success in a sequence of independent Bernoulli trials with probability of success p. For n = 1, this gives the geometric distribution.

Field Summary

Fields inherited from class umontreal.iro.lecuyer.probdist.NegativeBinomialDist
`MAXN`

Fields inherited from class umontreal.iro.lecuyer.probdist.DiscreteDistributionInt
`EPSILON`

Constructor Summary
```PascalDist(int n, double p)```
Creates an object that contains the probability terms and the distribution function for the Pascal distribution with parameter n and p.

Method Summary
`static PascalDist` ```getInstanceFromMLE(int[] x, int m)```
Creates a new instance of a Pascal distribution with parameters n and p estimated using the maximum likelihood method based on the m observations x[i], i = 0, 1,…, m - 1.
`static double[]` ```getMLE(int[] x, int m)```
Estimates the parameter (n, p) of the Pascal distribution using the maximum likelihood method, from the m observations x[i], i = 0, 1,…, m - 1.
` int` `getN1()`
Returns the parameter n of this object.
` void` ```setParams(int n, double p)```
Sets the parameter n and p of this object.
` String` `toString()`

Methods inherited from class umontreal.iro.lecuyer.probdist.NegativeBinomialDist
`barF, barF, cdf, cdf, getGamma, getInstanceFromMLE, getInstanceFromMLE1, getMean, getMean, getMLE, getMLE1, getMLEninv, getN, getP, getParams, getStandardDeviation, getStandardDeviation, getVariance, getVariance, inverseF, inverseFInt, prob, prob, setParams`

Methods inherited from class umontreal.iro.lecuyer.probdist.DiscreteDistributionInt
`barF, cdf, getXinf, getXsup, inverseF`

Methods inherited from class java.lang.Object
`equals, getClass, hashCode, notify, notifyAll, wait, wait, wait`

Constructor Detail

### PascalDist

```public PascalDist(int n,
double p)```
Creates an object that contains the probability terms and the distribution function for the Pascal distribution with parameter n and p.

Method Detail

### getMLE

```public static double[] getMLE(int[] x,
int m)```
Estimates the parameter (n, p) of the Pascal distribution using the maximum likelihood method, from the m observations x[i], i = 0, 1,…, m - 1. The estimates are returned in a two-element array, in regular order: [n, p].

Parameters:
`x` - the list of observations used to evaluate parameters
`m` - the number of observations used to evaluate parameters
Returns:
returns the parameters [hat(n), hat(p)]

### getInstanceFromMLE

```public static PascalDist getInstanceFromMLE(int[] x,
int m)```
Creates a new instance of a Pascal distribution with parameters n and p estimated using the maximum likelihood method based on the m observations x[i], i = 0, 1,…, m - 1.

Parameters:
`x` - the list of observations to use to evaluate parameters
`m` - the number of observations to use to evaluate parameters

### getN1

`public int getN1()`
Returns the parameter n of this object.

### setParams

```public void setParams(int n,
double p)```
Sets the parameter n and p of this object.

### toString

`public String toString()`
Overrides:
`toString` in class `NegativeBinomialDist`

SSJ
V. 2.6.

To submit a bug or ask questions, send an e-mail to Pierre L'Ecuyer.