ContinuousDistribution Class

Represents a continuous probability distribution.

Definition

Namespace: Extreme.Statistics.Distributions
Assembly: Extreme.Numerics (in Extreme.Numerics.dll) Version: 8.1.23
C# 
[SerializableAttribute]
public abstract class ContinuousDistribution : Distribution
Inheritance
Object  →  Distribution  →  ContinuousDistribution
Derived
More

Remarks

The distribution of a variable is a description of the relative numbers of times each possible outcome will occur in a number of trials. The function describing the distribution is called the probability function, and the function describing the cumulative probability that a given value or any value smaller than it will occur is called the distribution function.

A continuous probability distribution is a statistical distribution whose variables can take on any value within a certain interval. This interval may be infinite.

This library contains classes for the most common continuous distributions. They are listed in the table below:

DistributionDefinition
BetaDistributionThe beta distribution.
CauchyDistributionThe Cauchy distribution.
ContinuousUniformDistributionThe continuous uniform distribution.
ErlangDistributionThe Erlang distribution.
ExponentialDistributionThe exponential distribution.
FDistributionThe F distribution.
GammaDistributionThe gamma distribution.
GumbelDistributionThe Gumbel or extreme value distribution.
LaplaceDistributionThe Laplace distribution.
LogisticDistributionThe logistic distribution.
LognormalDistributionThe log-normal distribution.
NormalDistributionThe normal distribution.
ParetoDistributionThe Pareto distribution.
RayleighDistributionThe Rayleigh distribution.
StudentTDistributionThe student-t distribution.
TriangularDistributionThe triangular distribution.
WeibullDistributionThe Weibull distribution.

ContinuousDistribution is an abstract base class that cannot be instantiated. To create a continuous distribution of a specific type, instantiate a class derived from ContinuousDistribution.

Notes to inheritors: When you inherit from ContinuousDistribution, you must override the following members: ProbabilityDensityFunction(Double), DistributionFunction(Double), Mean and Variance. You should also override the following methods: Sample(), Skewness, Kurtosis.

Constructors

ContinuousDistribution Constructs a new ContinuousDistribution object.

Properties

Entropy Gets the entropy of the distribution.
(Inherited from Distribution)
InterQuartileRange Returns the inter-quartile range of this distribution.
IsSymmetrical Gets whether the distribution is known to be symmetrical around the mean.
IsUnimodal Gets whether the distribution has one or more modes.
Kurtosis Gets the kurtosis of the distribution.
(Inherited from Distribution)
Mean Gets the mean or expectation value of the distribution.
(Inherited from Distribution)
Median Gets the median of the distribution.
Mode Gets the mode of the distribution.
NumberOfModes Gets the number of modes of the distribution.
Skewness Gets the skewness of the distribution.
(Inherited from Distribution)
StandardDeviation Gets the standard deviation of the distribution.
(Inherited from Distribution)
StatisticSymbol Gets the common symbol to describe a statistic from the distribution.
(Inherited from Distribution)
Support Gets the support of the distribution.
Variance Gets the variance of the distribution.
(Inherited from Distribution)

Methods

Cdf Evaluates the cumulative distribution function (CDF) of this distribution for the specified value.
DistributionFunction Evaluates the cumulative distribution function (CDF) of this distribution for the specified value.
EqualsDetermines whether the specified object is equal to the current object.
(Inherited from Object)
FinalizeAllows an object to try to free resources and perform other cleanup operations before it is reclaimed by garbage collection.
(Inherited from Object)
GetAllModes Returns an array that contains all the modes of the distribution.
GetExpectationValue(Func<Double, Double>) Returns the expectation value of a function.
GetExpectationValue(Func<Double, Double>, Double, Double) Returns the un-normalized expectation value of a function over the specified interval.
GetExpectedHistogram(Double[], Double) Gets a vector containing a histogram of the expected number of samples for a given total number of samples.
GetExpectedHistogram(IntervalIndex<Double>, Double) Gets a vector containing a histogram of the expected number of samples for a given total number of samples.
GetExpectedHistogram(Double, Double, Int32, Double) Gets a vector whose bins contain the expected number of samples for a given total number of samples.
GetHashCodeServes as the default hash function.
(Inherited from Object)
GetRandomSequence() Returns a sequence of random samples from the distribution.
GetRandomSequence(Random) Returns a sequence of random samples from the distribution.
GetRandomSequence(Random, Int32) Returns a sequence of random samples of the specified length from the distribution.
GetTypeGets the Type of the current instance.
(Inherited from Object)
HazardFunction Returns the probability of failure at the specified value.
InverseCdf Returns the inverse of the DistributionFunction(Double).
InverseDistributionFunction Returns the inverse of the DistributionFunction(Double).
LeftTailProbability Returns the probability that a sample from the distribution is less than the specified value.
LogProbabilityDensityFunction Returns the logarithm of the probability density function (PDF) of this distribution for the specified value.
MemberwiseCloneCreates a shallow copy of the current Object.
(Inherited from Object)
MomentFunction Returns the value of the moment function of the specified order.
Pdf Returns the value of the probability density function (PDF) of this distribution for the specified value.
Probability Returns the probability that a sample taken from the distribution lies inside the specified interval.
ProbabilityDensityFunction Returns the value of the probability density function (PDF) of this distribution for the specified value.
RightTailProbability Returns the probability that a sample from the distribution is larger than the specified value.
Sample() Returns a random sample from the distribution.
Sample(Int32) Returns a vector of random samples from the distribution.
Sample(Random) Returns a random sample from the distribution.
Sample(Int32, Random) Returns a vector of random samples from the distribution.
SampleInto(Random, IList<Double>) Fills a list with random numbers from the distribution.
SampleInto(Random, IList<Double>, Int32, Int32) Fills part of a list with random numbers from the distribution.
SurvivorDistributionFunction Evaluates the survivor distribution function (SDF) of this distribution for the specified value.
ToStringReturns a string that represents the current object.
(Inherited from Object)
TwoTailedProbability Returns the probability that a sample from the distribution deviates from the mean more than the specified value.

See Also