Namespaces

Types in MathNet.Numerics.Distributions

Type Zipf

Namespace MathNet.Numerics.Distributions

Interfaces IDiscreteDistribution

Discrete Univariate Zipf distribution. Zipf's law, an empirical law formulated using mathematical statistics, refers to the fact that many types of data studied in the physical and social sciences can be approximated with a Zipfian distribution, one of a family of related discrete power law probability distributions. For details about this distribution, see.

Constructors

Static Functions

Methods

Properties

Public Constructors

Zipf(double s, int n, Random randomSource)

Initializes a new instance of the Zipf class.
Parameters
double s

The s parameter of the distribution.

int n

The n parameter of the distribution.

Random randomSource

The random number generator which is used to draw random samples.

Zipf(double s, int n)

Initializes a new instance of the Zipf class.
Parameters
double s

The s parameter of the distribution.

int n

The n parameter of the distribution.

Public Static Functions

double CDF(double s, int n, double x)

Computes the cumulative distribution (CDF) of the distribution at x, i.e. P(X ≤ x).
Parameters
double s

The s parameter of the distribution.

int n

The n parameter of the distribution.

double x

The location at which to compute the cumulative distribution function.

Return
double

the cumulative distribution at location x.

bool IsValidParameterSet(double s, int n)

Tests whether the provided values are valid parameters for this distribution.
Parameters
double s

The s parameter of the distribution.

int n

The n parameter of the distribution.

double PMF(double s, int n, int k)

Computes the probability mass (PMF) at k, i.e. P(X = k).
Parameters
double s

The s parameter of the distribution.

int n

The n parameter of the distribution.

int k

The location in the domain where we want to evaluate the probability mass function.

Return
double

the probability mass at location k.

double PMFLn(double s, int n, int k)

Computes the log probability mass (lnPMF) at k, i.e. ln(P(X = k)).
Parameters
double s

The s parameter of the distribution.

int n

The n parameter of the distribution.

int k

The location in the domain where we want to evaluate the log probability mass function.

Return
double

the log probability mass at location k.

int Sample(Random rnd, double s, int n)

Samples a random variable.
Parameters
Random rnd

The random number generator to use.

double s

The s parameter of the distribution.

int n

The n parameter of the distribution.

int Sample(double s, int n)

Samples a random variable.
Parameters
double s

The s parameter of the distribution.

int n

The n parameter of the distribution.

void Samples(Int32[] values, double s, int n)

Fills an array with samples generated from the distribution.
Parameters
Int32[] values

The array to fill with the samples.

double s

The s parameter of the distribution.

int n

The n parameter of the distribution.

void Samples(Random rnd, Int32[] values, double s, int n)

Fills an array with samples generated from the distribution.
Parameters
Random rnd

The random number generator to use.

Int32[] values

The array to fill with the samples.

double s

The s parameter of the distribution.

int n

The n parameter of the distribution.

IEnumerable<int> Samples(Random rnd, double s, int n)

Samples a sequence of this random variable.
Parameters
Random rnd

The random number generator to use.

double s

The s parameter of the distribution.

int n

The n parameter of the distribution.

IEnumerable<int> Samples(double s, int n)

Samples a sequence of this random variable.
Parameters
double s

The s parameter of the distribution.

int n

The n parameter of the distribution.

Public Methods

double CumulativeDistribution(double x)

Computes the cumulative distribution (CDF) of the distribution at x, i.e. P(X ≤ x).
Parameters
double x

The location at which to compute the cumulative distribution function.

Return
double

the cumulative distribution at location x.

bool Equals(object obj)

int GetHashCode()

Type GetType()

double Probability(int k)

Computes the probability mass (PMF) at k, i.e. P(X = k).
Parameters
int k

The location in the domain where we want to evaluate the probability mass function.

Return
double

the probability mass at location k.

double ProbabilityLn(int k)

Computes the log probability mass (lnPMF) at k, i.e. ln(P(X = k)).
Parameters
int k

The location in the domain where we want to evaluate the log probability mass function.

Return
double

the log probability mass at location k.

int Sample()

Draws a random sample from the distribution.
Return
int

a sample from the distribution.

IEnumerable<int> Samples()

Samples an array of zipf distributed random variables.
Return
IEnumerable<int>

a sequence of samples from the distribution.

void Samples(Int32[] values)

Fills an array with samples generated from the distribution.

string ToString()

A string representation of the distribution.
Return
string

a string representation of the distribution.

Public Properties

double Entropy get;

Gets the entropy of the distribution.

int Maximum get;

Gets the largest element in the domain of the distributions which can be represented by an integer.

double Mean get;

Gets the mean of the distribution.

double Median get;

Gets the median of the distribution.

int Minimum get;

Gets the smallest element in the domain of the distributions which can be represented by an integer.

int Mode get;

Gets the mode of the distribution.

int N get;

Gets or sets the n parameter of the distribution.

Random RandomSource get; set;

Gets or sets the random number generator which is used to draw random samples.

double S get;

Gets or sets the s parameter of the distribution.

double Skewness get;

Gets the skewness of the distribution.

double StdDev get;

Gets the standard deviation of the distribution.

double Variance get;

Gets the variance of the distribution.