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UniformContinuousDistribution Class

Continuous Uniform Distribution.
Inheritance Hierarchy
SystemObject
  Accord.Statistics.DistributionsDistributionBase
    Accord.Statistics.Distributions.UnivariateUnivariateContinuousDistribution
      Accord.Statistics.Distributions.UnivariateUniformContinuousDistribution

Namespace:  Accord.Statistics.Distributions.Univariate
Assembly:  Accord.Statistics (in Accord.Statistics.dll) Version: 3.7.0
Syntax
[SerializableAttribute]
public class UniformContinuousDistribution : UnivariateContinuousDistribution, 
	IFittableDistribution<double, IFittingOptions>, IFittable<double, IFittingOptions>, 
	IFittable<double>, IFittableDistribution<double>, IDistribution<double>, 
	IDistribution, ICloneable, ISampleableDistribution<double>, IRandomNumberGenerator<double>
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The UniformContinuousDistribution type exposes the following members.

Constructors
  NameDescription
Public methodUniformContinuousDistribution
Creates a new uniform distribution defined in the interval [0;1].
Public methodUniformContinuousDistribution(DoubleRange)
Creates a new uniform distribution defined in the interval [min;max].
Public methodUniformContinuousDistribution(Double, Double)
Creates a new uniform distribution defined in the interval [a;b].
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Properties
  NameDescription
Public propertyEntropy
Gets the entropy for this distribution.
(Overrides UnivariateContinuousDistributionEntropy.)
Public propertyLength
Gets the length of the distribution (b-a).
Public propertyMaximum
Gets the maximum value of the distribution (b).
Public propertyMean
Gets the mean for this distribution.
(Overrides UnivariateContinuousDistributionMean.)
Public propertyMedian
Gets the median for this distribution.
(Inherited from UnivariateContinuousDistribution.)
Public propertyMinimum
Gets the minimum value of the distribution (a).
Public propertyMode
Gets the mode for this distribution.
(Overrides UnivariateContinuousDistributionMode.)
Public propertyQuartiles
Gets the Quartiles for this distribution.
(Inherited from UnivariateContinuousDistribution.)
Public propertyStatic memberStandard
Gets the Standard Uniform Distribution, starting at zero and ending at one (a=0, b=1).
Public propertyStandardDeviation
Gets the Standard Deviation (the square root of the variance) for the current distribution.
(Inherited from UnivariateContinuousDistribution.)
Public propertySupport
Gets the support interval for this distribution.
(Overrides UnivariateContinuousDistributionSupport.)
Public propertyVariance
Gets the variance for this distribution.
(Overrides UnivariateContinuousDistributionVariance.)
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Methods
  NameDescription
Public methodClone
Creates a new object that is a copy of the current instance.
(Overrides DistributionBaseClone.)
Public methodComplementaryDistributionFunction
Gets the complementary cumulative distribution function (ccdf) for this distribution evaluated at point x. This function is also known as the Survival function.
(Inherited from UnivariateContinuousDistribution.)
Public methodCumulativeHazardFunction
Gets the cumulative hazard function for this distribution evaluated at point x.
(Inherited from UnivariateContinuousDistribution.)
Public methodDistributionFunction(Double)
Gets the cumulative distribution function (cdf) for this distribution evaluated at point x.
(Inherited from UnivariateContinuousDistribution.)
Public methodDistributionFunction(Double, Double)
Gets the cumulative distribution function (cdf) for this distribution in the semi-closed interval (a; b] given as P(a < X ≤ b).
(Inherited from UnivariateContinuousDistribution.)
Public methodEquals
Determines whether the specified object is equal to the current object.
(Inherited from Object.)
Public methodStatic memberEstimate
Estimates a new uniform distribution from a given set of observations.
Protected methodFinalize
Allows an object to try to free resources and perform other cleanup operations before it is reclaimed by garbage collection.
(Inherited from Object.)
Public methodFit(Double)
Fits the underlying distribution to a given set of observations.
(Inherited from UnivariateContinuousDistribution.)
Public methodFit(Double, IFittingOptions)
Fits the underlying distribution to a given set of observations.
(Inherited from UnivariateContinuousDistribution.)
Public methodFit(Double, Double)
Fits the underlying distribution to a given set of observations.
(Inherited from UnivariateContinuousDistribution.)
Public methodFit(Double, Int32)
Fits the underlying distribution to a given set of observations.
(Inherited from UnivariateContinuousDistribution.)
Public methodFit(Double, Double, IFittingOptions)
Fits the underlying distribution to a given set of observations.
(Overrides UnivariateContinuousDistributionFit(Double, Double, IFittingOptions).)
Public methodFit(Double, Int32, IFittingOptions)
Fits the underlying distribution to a given set of observations.
(Inherited from UnivariateContinuousDistribution.)
Public methodGenerate
Generates a random observation from the current distribution.
(Inherited from UnivariateContinuousDistribution.)
Public methodGenerate(Random)
Generates a random observation from the current distribution.
(Overrides UnivariateContinuousDistributionGenerate(Random).)
Public methodGenerate(Int32)
Generates a random vector of observations from the current distribution.
(Inherited from UnivariateContinuousDistribution.)
Public methodGenerate(Int32, Double)
Generates a random vector of observations from the current distribution.
(Inherited from UnivariateContinuousDistribution.)
Public methodGenerate(Int32, Random)
Generates a random vector of observations from the current distribution.
(Inherited from UnivariateContinuousDistribution.)
Public methodGenerate(Int32, Double, Random)
Generates a random vector of observations from the current distribution.
(Overrides UnivariateContinuousDistributionGenerate(Int32, Double, Random).)
Public methodGetHashCode
Serves as the default hash function.
(Inherited from Object.)
Public methodGetRange
Gets the distribution range within a given percentile.
(Inherited from UnivariateContinuousDistribution.)
Public methodGetType
Gets the Type of the current instance.
(Inherited from Object.)
Public methodHazardFunction
Gets the hazard function, also known as the failure rate or the conditional failure density function for this distribution evaluated at point x.
(Inherited from UnivariateContinuousDistribution.)
Protected methodInnerComplementaryDistributionFunction
Gets the complementary cumulative distribution function (ccdf) for this distribution evaluated at point x. This function is also known as the Survival function.
(Inherited from UnivariateContinuousDistribution.)
Protected methodInnerDistributionFunction
Gets the cumulative distribution function (cdf) for this distribution evaluated at point x.
(Overrides UnivariateContinuousDistributionInnerDistributionFunction(Double).)
Protected methodInnerInverseDistributionFunction
Gets the inverse of the cumulative distribution function (icdf) for this distribution evaluated at probability p. This function is also known as the Quantile function.
(Inherited from UnivariateContinuousDistribution.)
Protected methodInnerLogProbabilityDensityFunction
Gets the log-probability density function (pdf) for this distribution evaluated at point x.
(Overrides UnivariateContinuousDistributionInnerLogProbabilityDensityFunction(Double).)
Protected methodInnerProbabilityDensityFunction
Gets the probability density function (pdf) for this distribution evaluated at point x.
(Overrides UnivariateContinuousDistributionInnerProbabilityDensityFunction(Double).)
Public methodInverseDistributionFunction
Gets the inverse of the cumulative distribution function (icdf) for this distribution evaluated at probability p. This function is also known as the Quantile function.
(Inherited from UnivariateContinuousDistribution.)
Public methodLogCumulativeHazardFunction
Gets the log of the cumulative hazard function for this distribution evaluated at point x.
(Inherited from UnivariateContinuousDistribution.)
Public methodLogProbabilityDensityFunction
Gets the log-probability density function (pdf) for this distribution evaluated at point x.
(Inherited from UnivariateContinuousDistribution.)
Protected methodMemberwiseClone
Creates a shallow copy of the current Object.
(Inherited from Object.)
Public methodProbabilityDensityFunction
Gets the probability density function (pdf) for this distribution evaluated at point x.
(Inherited from UnivariateContinuousDistribution.)
Public methodQuantileDensityFunction
Gets the first derivative of the inverse distribution function (icdf) for this distribution evaluated at probability p.
(Inherited from UnivariateContinuousDistribution.)
Public methodStatic memberRandom
Generates a random observation from the Uniform distribution defined in the interval 0 and 1.
Public methodStatic memberRandom(Int32)
Generates a random observation from the Uniform distribution defined in the interval 0 and 1.
Public methodStatic memberRandom(Random)
Generates a random observation from the Uniform distribution defined in the interval 0 and 1.
Public methodStatic memberRandom(Double, Double)
Generates a random observation from the Uniform distribution with the given parameters.
Public methodStatic memberRandom(Int32, Double)
Generates a random observation from the Uniform distribution defined in the interval 0 and 1.
Public methodStatic memberRandom(Double, Double, Int32)
Generates a random vector of observations from the Uniform distribution with the given parameters.
Public methodStatic memberRandom(Double, Double, Random)
Generates a random observation from the Uniform distribution with the given parameters.
Public methodStatic memberRandom(Int32, Double, Random)
Generates a random observation from the Uniform distribution defined in the interval 0 and 1.
Public methodStatic memberRandom(Double, Double, Int32, Double)
Generates a random vector of observations from the Uniform distribution with the given parameters.
Public methodStatic memberRandom(Double, Double, Int32, Random)
Generates a random vector of observations from the Uniform distribution with the given parameters.
Public methodStatic memberRandom(Double, Double, Int32, Double, Random)
Generates a random vector of observations from the Uniform distribution with the given parameters.
Public methodToString
Returns a String that represents this instance.
(Inherited from DistributionBase.)
Public methodToString(IFormatProvider)
Returns a String that represents this instance.
(Inherited from DistributionBase.)
Public methodToString(String)
Returns a String that represents this instance.
(Inherited from DistributionBase.)
Public methodToString(String, IFormatProvider)
Returns a String that represents this instance.
(Overrides DistributionBaseToString(String, IFormatProvider).)
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Extension Methods
  NameDescription
Public Extension MethodHasMethod
Checks whether an object implements a method with the given name.
(Defined by ExtensionMethods.)
Public Extension MethodIsEqual
Compares two objects for equality, performing an elementwise comparison if the elements are vectors or matrices.
(Defined by Matrix.)
Public Extension MethodToT
Converts an object into another type, irrespective of whether the conversion can be done at compile time or not. This can be used to convert generic types to numeric types during runtime.
(Defined by ExtensionMethods.)
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Remarks

The continuous uniform distribution or rectangular distribution is a family of symmetric probability distributions such that for each member of the family, all intervals of the same length on the distribution's support are equally probable. The support is defined by the two parameters, a and b, which are its minimum and maximum values. The distribution is often abbreviated U(a,b). It is the maximum entropy probability distribution for a random variate X under no constraint other than that it is contained in the distribution's support.

References:

Examples

The following example demonstrates how to create an uniform distribution defined over the interval [0.42, 1.1].

// Create a new uniform continuous distribution from 0.42 to 1.1
var uniform = new UniformContinuousDistribution(a: 0.42, b: 1.1);

// Common measures
double mean = uniform.Mean;     // 0.76
double median = uniform.Median; // 0.76
double var = uniform.Variance;  // 0.03853333333333335

// Cumulative distribution functions
double cdf = uniform.DistributionFunction(x: 0.9);               // 0.70588235294117641
double ccdf = uniform.ComplementaryDistributionFunction(x: 0.9); // 0.29411764705882359
double icdf = uniform.InverseDistributionFunction(p: cdf);       // 0.9

// Probability density functions
double pdf = uniform.ProbabilityDensityFunction(x: 0.9);     // 1.4705882352941173
double lpdf = uniform.LogProbabilityDensityFunction(x: 0.9); // 0.38566248081198445

// Hazard (failure rate) functions
double hf = uniform.HazardFunction(x: 0.9); // 4.9999999999999973
double chf = uniform.CumulativeHazardFunction(x: 0.9); // 1.2237754316221154

// String representation
string str = uniform.ToString(CultureInfo.InvariantCulture); // "U(x; a = 0.42, b = 1.1)"
See Also