LogisticDistribution Class

SystemObject
  Accord.Statistics.DistributionsDistributionBase
    Accord.Statistics.Distributions.UnivariateUnivariateContinuousDistribution
      Accord.Statistics.Distributions.UnivariateLogisticDistribution

[SerializableAttribute]
public class LogisticDistribution : UnivariateContinuousDistribution

<SerializableAttribute>
Public Class LogisticDistribution
	Inherits UnivariateContinuousDistribution

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	Name	Description
	LogisticDistribution	Constructs a Logistic distribution with zero location and unit scale.
	LogisticDistribution(Double)	Constructs a Logistic distribution with given location and unit scale.
	LogisticDistribution(Double, Double)	Constructs a Logistic distribution with given location and scale parameters.

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	Name	Description
	Entropy	Gets the entropy for this distribution. (Overrides UnivariateContinuousDistributionEntropy.)
	Location	Gets the location value μ (mu).
	Mean	Gets the location value μ (mu). (Overrides UnivariateContinuousDistributionMean.)
	Median	Gets the median for this distribution. (Overrides UnivariateContinuousDistributionMedian.)
	Mode	Gets the mode for this distribution. (Overrides UnivariateContinuousDistributionMode.)
	Quartiles	Gets the Quartiles for this distribution. (Inherited from UnivariateContinuousDistribution.)
	Scale	Gets the distribution's scale value (s).
	StandardDeviation	Gets the Standard Deviation (the square root of the variance) for the current distribution. (Inherited from UnivariateContinuousDistribution.)
	Support	Gets the support interval for this distribution. (Overrides UnivariateContinuousDistributionSupport.)
	Variance	Gets the variance for this distribution. (Overrides UnivariateContinuousDistributionVariance.)

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	Name	Description
	Clone	Creates a new object that is a copy of the current instance. (Overrides DistributionBaseClone.)
	ComplementaryDistributionFunction	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.)
	CumulativeHazardFunction	Gets the cumulative hazard function for this distribution evaluated at point x. (Inherited from UnivariateContinuousDistribution.)
	DistributionFunction(Double)	Gets the cumulative distribution function (cdf) for this distribution evaluated at point x. (Inherited from UnivariateContinuousDistribution.)
	DistributionFunction(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.)
	Equals	Determines whether the specified object is equal to the current object. (Inherited from Object.)
	Finalize	Allows an object to try to free resources and perform other cleanup operations before it is reclaimed by garbage collection. (Inherited from Object.)
	Fit(Double)	Fits the underlying distribution to a given set of observations. (Inherited from UnivariateContinuousDistribution.)
	Fit(Double, IFittingOptions)	Fits the underlying distribution to a given set of observations. (Inherited from UnivariateContinuousDistribution.)
	Fit(Double, Double)	Fits the underlying distribution to a given set of observations. (Inherited from UnivariateContinuousDistribution.)
	Fit(Double, Int32)	Fits the underlying distribution to a given set of observations. (Inherited from UnivariateContinuousDistribution.)
	Fit(Double, Double, IFittingOptions)	Fits the underlying distribution to a given set of observations. (Inherited from UnivariateContinuousDistribution.)
	Fit(Double, Int32, IFittingOptions)	Fits the underlying distribution to a given set of observations. (Inherited from UnivariateContinuousDistribution.)
	Generate	Generates a random observation from the current distribution. (Inherited from UnivariateContinuousDistribution.)
	Generate(Int32)	Generates a random vector of observations from the current distribution. (Inherited from UnivariateContinuousDistribution.)
	Generate(Random)	Generates a random observation from the current distribution. (Inherited from UnivariateContinuousDistribution.)
	Generate(Int32, Double)	Generates a random vector of observations from the current distribution. (Inherited from UnivariateContinuousDistribution.)
	Generate(Int32, Random)	Generates a random vector of observations from the current distribution. (Inherited from UnivariateContinuousDistribution.)
	Generate(Int32, Double, Random)	Generates a random vector of observations from the current distribution. (Inherited from UnivariateContinuousDistribution.)
	GetHashCode	Serves as the default hash function. (Inherited from Object.)
	GetRange	Gets the distribution range within a given percentile. (Inherited from UnivariateContinuousDistribution.)
	GetType	Gets the Type of the current instance. (Inherited from Object.)
	HazardFunction	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.)
	InnerComplementaryDistributionFunction	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.)
	InnerDistributionFunction	Gets the cumulative distribution function (cdf) for this distribution evaluated at point x. (Overrides UnivariateContinuousDistributionInnerDistributionFunction(Double).)
	InnerInverseDistributionFunction	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. (Overrides UnivariateContinuousDistributionInnerInverseDistributionFunction(Double).)
	InnerLogProbabilityDensityFunction	Gets the log-probability density function (pdf) for this distribution evaluated at point x. (Overrides UnivariateContinuousDistributionInnerLogProbabilityDensityFunction(Double).)
	InnerProbabilityDensityFunction	Gets the probability density function (pdf) for this distribution evaluated at point x. (Overrides UnivariateContinuousDistributionInnerProbabilityDensityFunction(Double).)
	InverseDistributionFunction	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.)
	LogCumulativeHazardFunction	Gets the log of the cumulative hazard function for this distribution evaluated at point x. (Inherited from UnivariateContinuousDistribution.)
	LogProbabilityDensityFunction	Gets the log-probability density function (pdf) for this distribution evaluated at point x. (Inherited from UnivariateContinuousDistribution.)
	MemberwiseClone	Creates a shallow copy of the current Object. (Inherited from Object.)
	ProbabilityDensityFunction	Gets the probability density function (pdf) for this distribution evaluated at point x. (Inherited from UnivariateContinuousDistribution.)
	QuantileDensityFunction	Gets the first derivative of the inverse distribution function (icdf) for this distribution evaluated at probability p. (Overrides UnivariateContinuousDistributionQuantileDensityFunction(Double).)
	ToString	Returns a String that represents this instance. (Inherited from DistributionBase.)
	ToString(IFormatProvider)	Returns a String that represents this instance. (Inherited from DistributionBase.)
	ToString(String)	Returns a String that represents this instance. (Inherited from DistributionBase.)
	ToString(String, IFormatProvider)	Returns a String that represents this instance. (Overrides DistributionBaseToString(String, IFormatProvider).)

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	Name	Description
	HasMethod	Checks whether an object implements a method with the given name. (Defined by ExtensionMethods.)
	IsEqual	Compares two objects for equality, performing an elementwise comparison if the elements are vectors or matrices. (Defined by Matrix.)
	To(Type)	Overloaded. 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.)
	ToT	Overloaded. 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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In probability theory and statistics, the logistic distribution is a continuous probability distribution. Its cumulative distribution function is the logistic function, which appears in logistic regression and feedforward neural networks. It resembles the normal distribution in shape but has heavier tails (higher kurtosis). The Tukey lambda distribution can be considered a generalization of the logistic distribution since it adds a shape parameter, λ (the Tukey distribution becomes logistic when λ is zero).

References:

Wikipedia, The Free Encyclopedia. Logistic distribution. Available on: http://en.wikipedia.org/wiki/Logistic_distribution

This examples shows how to create a Logistic distribution, compute some of its properties and generate a number of random samples from it.

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// Create a logistic distribution with μ = 0.42 and scale = 3
var log = new LogisticDistribution(location: 0.42, scale: 1.2);

double mean = log.Mean;     // 0.42
double median = log.Median; // 0.42
double mode = log.Mode;     // 0.42
double var = log.Variance;  // 4.737410112522892

double cdf = log.DistributionFunction(x: 1.4); // 0.693528308197921
double pdf = log.ProbabilityDensityFunction(x: 1.4); // 0.17712232827170876
double lpdf = log.LogProbabilityDensityFunction(x: 1.4); // -1.7309146649427332

double ccdf = log.ComplementaryDistributionFunction(x: 1.4); // 0.306471691802079
double icdf = log.InverseDistributionFunction(p: cdf); // 1.3999999999999997

double hf = log.HazardFunction(x: 1.4); // 0.57794025683160088
double chf = log.CumulativeHazardFunction(x: 1.4); // 1.1826298874077226

string str = log.ToString(CultureInfo.InvariantCulture); // Logistic(x; μ = 0.42, scale = 1.2)

Reference

Accord.Statistics.Distributions.Univariate Namespace

Accord.Statistics.Distributions.UnivariateTukeyLambdaDistribution