NegativeBinomialDistribution (Smile Math 1.0.3 API)

java.lang.Object
- smile.stat.distribution.AbstractDistribution
- - smile.stat.distribution.DiscreteDistribution
  - - smile.stat.distribution.NegativeBinomialDistribution

All Implemented Interfaces:

Distribution
```
public class NegativeBinomialDistribution
extends DiscreteDistribution
```
Negative binomial distribution arises as the probability distribution of the number of successes in a series of independent and identically distributed Bernoulli trials needed to get a specified (non-random) number r of failures. If r is an integer, it is usually called Pascal distribution. Otherwise, it is often called Polya distribution for the real-valued case. When r = 1 we get the probability distribution of number of successes before the first failure, which is a geometric distribution.
An alternative definition is that X is the total number of trials needed to get r failures, not simply the number of successes. This alternative parameterization can be used as an alternative to the Poisson distribution. It is especially useful for discrete data over an unbounded positive range whose sample variance exceeds the sample mean. If a Poisson distribution is used to model such data, the model mean and variance are equal. In that case, the observations are overdispersed with respect to the Poisson model. Since the negative binomial distribution has one more parameter than the Poisson, the second parameter can be used to adjust the variance independently of the mean. In the case of modest overdispersion, this may produce substantially similar results to an overdispersed Poisson distribution.
The negative binomial distribution also arises as a continuous mixture of Poisson distributions where the mixing distribution of the Poisson rate is a gamma distribution. That is, we can view the negative binomial as a Poisson(λ) distribution, where λ is itself a random variable, distributed according to Γ(r, p/(1 - p)).

Author:

Haifeng Li

Constructor Summary

Constructors
Constructor and Description

NegativeBinomialDistribution(double r, double p)
Constructor.

Constructors
Constructor and Description
`NegativeBinomialDistribution(double r, double p)` Constructor.

Method Summary

Methods
Modifier and Type	Method and Description
`double`	`cdf(double k)` Cumulative distribution function.
`double`	`entropy()` Shannon entropy.
`double`	`logp(int k)` The probability mass function in log scale.
`double`	`mean()` The mean of distribution.
`int`	`npara()` The number of parameters of the distribution.
`double`	`p(int k)` The probability mass function.
`double`	`quantile(double p)` The quantile, the probability to the left of quantile is p.
`double`	`rand()` Generates a random number following this distribution.
`double`	`sd()` The standard deviation of distribution.
`String`	`toString()`
`double`	`var()` The variance of distribution.

Methods inherited from class smile.stat.distribution.DiscreteDistribution
likelihood, logLikelihood, logp, p, quantile

Methods inherited from class smile.stat.distribution.AbstractDistribution
inverseTransformSampling, likelihood, logLikelihood, quantile, quantile, rejection

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

- Constructor Detail
  - NegativeBinomialDistribution
```
public NegativeBinomialDistribution(double r,
                            double p)
```
    Constructor.
    
    Parameters:
    r - the number of failures until the experiment is stopped.
    p - success probability in each experiment.
- Method Detail
  - npara
```
public int npara()
```
    Description copied from interface: Distribution
    
    The number of parameters of the distribution.
  - mean
```
public double mean()
```
    Description copied from interface: Distribution
    
    The mean of distribution.
  - var
```
public double var()
```
    Description copied from interface: Distribution
    
    The variance of distribution.
  - sd
```
public double sd()
```
    Description copied from interface: Distribution
    
    The standard deviation of distribution.
  - entropy
```
public double entropy()
```
    Shannon entropy. Not supported.
  - toString
```
public String toString()
```
    Overrides:
    
    toString in class Object
  - rand
```
public double rand()
```
    Description copied from interface: Distribution
    
    Generates a random number following this distribution.
  - p
```
public double p(int k)
```
    Description copied from class: DiscreteDistribution
    
    The probability mass function.
    
    Specified by:
    
    p in class DiscreteDistribution
  - logp
```
public double logp(int k)
```
    Description copied from class: DiscreteDistribution
    
    The probability mass function in log scale.
    
    Specified by:
    
    logp in class DiscreteDistribution
  - cdf
```
public double cdf(double k)
```
    Description copied from interface: Distribution
    
    Cumulative distribution function. That is the probability to the left of x.
  - quantile
```
public double quantile(double p)
```
    Description copied from interface: Distribution
    
    The quantile, the probability to the left of quantile is p. It is actually the inverse of cdf.

Class NegativeBinomialDistribution

Constructor Summary

Method Summary

Methods inherited from class smile.stat.distribution.DiscreteDistribution

Methods inherited from class smile.stat.distribution.AbstractDistribution

Methods inherited from class java.lang.Object

Constructor Detail

NegativeBinomialDistribution

Method Detail

npara

mean

var

sd

entropy

toString

rand

p

logp

cdf

quantile