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NegativeBinomialDistribution Class

Represents a negative binomial distribution.
Inheritance Hierarchy

Namespace:  Meta.Numerics.Statistics.Distributions
Assembly:  Meta.Numerics (in Meta.Numerics.dll) Version: (
public sealed class NegativeBinomialDistribution : DiscreteDistribution

The NegativeBinomialDistribution type exposes the following members.

Public methodNegativeBinomialDistribution
Initializes a new negative binomial distribution.
Public methodCentralMoment
Gets a central moment of the distribution.
(Inherited from DiscreteDistribution.)
Public methodCumulant
Computes a cumulant of the distribution.
(Inherited from UnivariateDistribution.)
Public methodEquals
Determines whether the specified object is equal to the current object.
(Inherited from Object.)
Public methodExpectationValue
Computes the expectation value of an artibrary function.
(Inherited from DiscreteDistribution.)
Public methodGetHashCode
Serves as the default hash function.
(Inherited from Object.)
Public methodGetRandomValue
Produces a random integer drawn from the distribution.
(Inherited from DiscreteDistribution.)
Public methodGetType
Gets the Type of the current instance.
(Inherited from Object.)
Public methodInverseLeftProbability
Computes the value corresponding to the given percentile.
(Overrides DiscreteDistributionInverseLeftProbability(Double).)
Public methodLeftExclusiveProbability
Computes the probability of obtaining a value less than the given value.
(Inherited from DiscreteDistribution.)
Public methodLeftInclusiveProbability
Computes the probability of obtaining a value less than or equal to the given value.
(Overrides DiscreteDistributionLeftInclusiveProbability(Int32).)
Public methodProbabilityMass
Returns the probability of the obtaining the given value.
(Overrides DiscreteDistributionProbabilityMass(Int32).)
Public methodRawMoment
Gets a raw moment of the distribution.
(Overrides DiscreteDistributionRawMoment(Int32).)
Public methodRightExclusiveProbability
Computes the probability of obtaining a value greater than the given value.
(Overrides DiscreteDistributionRightExclusiveProbability(Int32).)
Public methodToString
Returns a string that represents the current object.
(Inherited from Object.)

Consider a series of independent, repeated Bernoulli trials, each of which results in success with probability p or failure with probability 1-p. If one repeats the trials until r failures occur, the negative binomial distribution gives the probability of having seen k successes before the rth failure.

Keep in mind that there are several different conventions for the meaning of r, p, and k. The most common are that k denotes the number of successes before the rth failure (used here and in the referenced Wikipedia article), and that k denotes the number of failures before the rth success (used by Mathematica). Since these two conventions simply switch success and failure, they can be interconverted by interchanging p and 1-p.

See Also