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Meta.Numerics.Statistics.Distributions.DiscreteUniformDistribution Class Reference

Describes a discrete uniform distribution. More...

+ Inheritance diagram for Meta.Numerics.Statistics.Distributions.DiscreteUniformDistribution:
+ Collaboration diagram for Meta.Numerics.Statistics.Distributions.DiscreteUniformDistribution:

Public Member Functions

 DiscreteUniformDistribution (int a, int b)
 Instantiates a new discrete uniform distribution with the given endpoints. More...
 
override double ProbabilityMass (int k)
 Returns the probability of the obtaining the given value.
Parameters
kThe value.
Returns
The probability of obtaining the value.
More...
 
override double LeftExclusiveProbability (int k)
 Computes the probability of obtaining a value less than the given value.
Parameters
kThe value.
Returns
The total probability of obtaining a value strictly less than k .
See also
RightExclusiveProbability
More...
 
override double RightExclusiveProbability (int k)
 Computes the probability of obtaining a value greater than the given value.
Parameters
kThe value.
Returns
The total probability of obtaining a value strictly greater than k .
See also
LeftExclusiveProbability
More...
 
override int InverseLeftProbability (double P)
 Computes the value corresponding to the given percentile.
Parameters
PThe percentile.
Returns
The value.
More...
 
override double MomentAboutMean (int r)
 Gets a central moment of the distribution.
Parameters
rThe order of the moment.
Returns
The central moment Cr.
More...
 
override double Cumulant (int r)
 Computes a cumulant of the distribution.
Parameters
rThe index of the cumulant to compute.
Returns
The rth cumulant of the distribution.
More...
 
- Public Member Functions inherited from Meta.Numerics.Statistics.Distributions.DiscreteDistribution
virtual double LeftInclusiveProbability (int k)
 Computes the probability of obtaining a value less than or equal to the given value. More...
 
virtual double ExpectationValue (Func< int, double > f)
 Computes the expectation value of an artibrary function. More...
 
override double Moment (int r)
 Gets a raw moment of the distribution. More...
 
virtual int GetRandomValue (Random rng)
 Produces a random integer drawn from the distribution. More...
 

Properties

override int Minimum [get]
 
override int Maximum [get]
 
override double Mean [get]
 
override double Variance [get]
 
override double Skewness [get]
 
- Properties inherited from Meta.Numerics.Statistics.Distributions.DiscreteDistribution
abstract int Minimum [get]
 Gets the smallest value in the distribution. More...
 
abstract int Maximum [get]
 Gets the largest value in the distribution. More...
 
override double Mean [get]
 Gets the mean of the distribution. More...
 
- Properties inherited from Meta.Numerics.Statistics.Distributions.UnivariateDistribution
virtual double Mean [get]
 Gets the mean of the distribution. More...
 
virtual double Variance [get]
 Gets the variance of the distribution. More...
 
virtual double StandardDeviation [get]
 Gets the standard deviation of the distribution. More...
 
virtual double Skewness [get]
 Gets the skewness of the distribution. More...
 
virtual double ExcessKurtosis [get]
 Gets the excess kurtosis of the distribution. More...
 

Private Attributes

int a
 
int b
 
int n
 

Detailed Description

Describes a discrete uniform distribution.

In a discrete uniform distribution, each integer in the allowed range is equally probable.

For example, the distribution of results for one roll of a fair die is DiscreteUniformDistribution(1,6).

Constructor & Destructor Documentation

Meta.Numerics.Statistics.Distributions.DiscreteUniformDistribution.DiscreteUniformDistribution ( int  a,
int  b 
)
inline

Instantiates a new discrete uniform distribution with the given endpoints.

Parameters
aOne end-point.
bThe other end-point.

Member Function Documentation

override double Meta.Numerics.Statistics.Distributions.DiscreteUniformDistribution.ProbabilityMass ( int  k)
inlinevirtual

Returns the probability of the obtaining the given value.

Parameters
kThe value.
Returns
The probability of obtaining the value.

Implements Meta.Numerics.Statistics.Distributions.DiscreteDistribution.

override double Meta.Numerics.Statistics.Distributions.DiscreteUniformDistribution.LeftExclusiveProbability ( int  k)
inlinevirtual

Computes the probability of obtaining a value less than the given value.

Parameters
kThe value.
Returns
The total probability of obtaining a value strictly less than k .
See also
RightExclusiveProbability

Reimplemented from Meta.Numerics.Statistics.Distributions.DiscreteDistribution.

override double Meta.Numerics.Statistics.Distributions.DiscreteUniformDistribution.RightExclusiveProbability ( int  k)
inlinevirtual

Computes the probability of obtaining a value greater than the given value.

Parameters
kThe value.
Returns
The total probability of obtaining a value strictly greater than k .
See also
LeftExclusiveProbability

Reimplemented from Meta.Numerics.Statistics.Distributions.DiscreteDistribution.

override int Meta.Numerics.Statistics.Distributions.DiscreteUniformDistribution.InverseLeftProbability ( double  P)
inlinevirtual

Computes the value corresponding to the given percentile.

Parameters
PThe percentile.
Returns
The value.

Reimplemented from Meta.Numerics.Statistics.Distributions.DiscreteDistribution.

override double Meta.Numerics.Statistics.Distributions.DiscreteUniformDistribution.MomentAboutMean ( int  r)
inlinevirtual

Gets a central moment of the distribution.

Parameters
rThe order of the moment.
Returns
The central moment Cr.

Reimplemented from Meta.Numerics.Statistics.Distributions.DiscreteDistribution.

override double Meta.Numerics.Statistics.Distributions.DiscreteUniformDistribution.Cumulant ( int  r)
inlinevirtual

Computes a cumulant of the distribution.

Parameters
rThe index of the cumulant to compute.
Returns
The rth cumulant of the distribution.

Reimplemented from Meta.Numerics.Statistics.Distributions.UnivariateDistribution.

References Meta.Numerics.Functions.AdvancedIntegerMath.BernoulliNumber(), and Meta.Numerics.MoreMath.Pow().

Member Data Documentation

int Meta.Numerics.Statistics.Distributions.DiscreteUniformDistribution.a
private
int Meta.Numerics.Statistics.Distributions.DiscreteUniformDistribution.b
private
int Meta.Numerics.Statistics.Distributions.DiscreteUniformDistribution.n
private

Property Documentation

override int Meta.Numerics.Statistics.Distributions.DiscreteUniformDistribution.Minimum
get

override int Meta.Numerics.Statistics.Distributions.DiscreteUniformDistribution.Maximum
get

override double Meta.Numerics.Statistics.Distributions.DiscreteUniformDistribution.Mean
get

override double Meta.Numerics.Statistics.Distributions.DiscreteUniformDistribution.Variance
get

override double Meta.Numerics.Statistics.Distributions.DiscreteUniformDistribution.Skewness
get


The documentation for this class was generated from the following file: