HyperbolicSecantDistribution Class 
Namespace: Accord.Statistics.Distributions.Univariate
[SerializableAttribute] public class HyperbolicSecantDistribution : UnivariateContinuousDistribution
The HyperbolicSecantDistribution type exposes the following members.
Name  Description  

HyperbolicSecantDistribution 
Constructs a Hyperbolic Secant (Sech) distribution.

Name  Description  

Entropy 
Gets the entropy for this distribution.
(Overrides UnivariateContinuousDistributionEntropy.)  
Mean 
Gets the mean for this distribution (always zero).
(Overrides UnivariateContinuousDistributionMean.)  
Median 
Gets the median for this distribution (always zero).
(Overrides UnivariateContinuousDistributionMedian.)  
Mode 
Gets the mode for this distribution (always zero).
(Overrides UnivariateContinuousDistributionMode.)  
Quartiles 
Gets the Quartiles for this distribution.
(Inherited from UnivariateContinuousDistribution.)  
StandardDeviation 
Gets the Standard Deviation (the square root of
the variance) for the current distribution.
(Overrides UnivariateContinuousDistributionStandardDeviation.)  
Support 
Gets the support interval for this distribution (inf, +inf).
(Overrides UnivariateContinuousDistributionSupport.)  
Variance 
Gets the variance for this distribution (always one).
(Overrides UnivariateContinuousDistributionVariance.) 
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 semiclosed 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.
(Inherited from UnivariateContinuousDistribution.)  
InnerLogProbabilityDensityFunction 
Gets the logprobability density function (pdf) for
this distribution evaluated at point x.
(Inherited from UnivariateContinuousDistribution.)  
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 logprobability 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.
(Inherited from UnivariateContinuousDistribution.)  
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).) 
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.) 
In probability theory and statistics, the hyperbolic secant distribution is a continuous probability distribution whose probability density function and characteristic function are proportional to the hyperbolic secant function. The hyperbolic secant function is equivalent to the inverse hyperbolic cosine, and thus this distribution is also called the inversecosh distribution.
References:
This examples shows how to create a Sech distribution, compute some of its properties and generate a number of random samples from it.
// Create a new hyperbolic secant distribution var sech = new HyperbolicSecantDistribution(); double mean = sech.Mean; // 0.0 double median = sech.Median; // 0.0 double mode = sech.Mode; // 0.0 double var = sech.Variance; // 1.0 double cdf = sech.DistributionFunction(x: 1.4); // 0.92968538268895873 double pdf = sech.ProbabilityDensityFunction(x: 1.4); // 0.10955386512899701 double lpdf = sech.LogProbabilityDensityFunction(x: 1.4); // 2.2113389316917877 double ccdf = sech.ComplementaryDistributionFunction(x: 1.4); // 0.070314617311041272 double icdf = sech.InverseDistributionFunction(p: cdf); // 1.40 double hf = sech.HazardFunction(x: 1.4); // 1.5580524977385339 string str = sech.ToString(); // Sech(x)