HyperbolicSecantDistribution Class

[SerializableAttribute]
public class HyperbolicSecantDistribution : ContinuousDistribution

<SerializableAttribute>
Public Class HyperbolicSecantDistribution
	Inherits ContinuousDistribution

[SerializableAttribute]
public ref class HyperbolicSecantDistribution : public ContinuousDistribution

[<SerializableAttribute>]
type HyperbolicSecantDistribution = 
    class
        inherit ContinuousDistribution
    end

Inheritance

Object  →  Distribution  →  ContinuousDistribution  →  HyperbolicSecantDistribution

The hyperbolic secant distribution is a continuous probability distribution whose probability density function is proportional to the hyperbolic secant function. Like the normal distribution, it is bell-shaped and symmetric about its mean, but has heavier tails (higher kurtosis).

Common applications include:

• Modeling financial returns with higher kurtosis than the normal distribution
• Signal processing where data exhibits heavier tails
• Statistical modeling of error distributions in physical measurements
• Neuronal firing patterns in neuroscience
• Quantum mechanics where the wave function follows a sech profile

The distribution is parameterized by μ (location parameter) and σ (scale parameter). It has a fixed shape with kurtosis = 5.

The hyperbolic secant distribution is a useful alternative to the normal distribution when modeling data with heavier tails while maintaining symmetry

Reference