ErlangDistribution Class

[SerializableAttribute]
public class ErlangDistribution : GammaDistribution

<SerializableAttribute>
Public Class ErlangDistribution
	Inherits GammaDistribution

[SerializableAttribute]
public ref class ErlangDistribution : public GammaDistribution

[<SerializableAttribute>]
type ErlangDistribution = 
    class
        inherit GammaDistribution
    end

Inheritance

Object  →  Distribution  →  ContinuousDistribution  →  GammaDistribution  →  ErlangDistribution

The Erlang distribution characterizes the distribution of the time it takes for an event to occur n times when the probability per unit time of the event occurring is constant.

The Erlang distribution is a special case of the Gamma distribution with the first parameter being an integer.

When the order equals 1, the Erlang distribution reduces to the Exponential distribution.

The order parameter (an integer) represents the number of events, and the scale parameter (a double) represents the mean time between events.

Applications of the Erlang distribution include modeling the time between arrivals of customers in a queue, the time until a certain number of failures occur in a system, and other processes where events happen at a constant rate.

This example demonstrates how to create an Erlang distribution with non-standard parameters and use its properties and methods.

using System;  
using Numerics.NET.Statistics.Distributions;  

// Create an Erlang distribution with order 3 and scale 2.0  
var erlang = new ErlangDistribution(3, 2.0);  

// Distribution parameters  
Console.WriteLine($"Order: {erlang.ShapeParameter}");  
Console.WriteLine($"Scale: {erlang.ScaleParameter}");  

// Functions  
double pdf = erlang.ProbabilityDensityFunction(1.0);  
double cdf = erlang.DistributionFunction(1.0);  
Console.WriteLine($"PDF at x=1.0: {pdf}");  
Console.WriteLine($"CDF at x=1.0: {cdf}");  

// Moments  
double mean = erlang.Mean;  
double variance = erlang.Variance;  
Console.WriteLine($"Mean: {mean}");  
Console.WriteLine($"Variance: {variance}");  

// Other properties  
double entropy = erlang.Entropy;  
double mode = erlang.Mode;  
Console.WriteLine($"Entropy: {entropy}");  
Console.WriteLine($"Mode: {mode}");

Reference