Extreme Optimization >
User's Guide >
Statistics Library >
Continuous Probability Distributions >
The Erlang Distribution
Extreme Optimization User's Guide
User's Guide
Up: Continuous Probability Distributions Next: The Exponential Distribution Previous: The Chi-Square Distribution Contents
The Erlang Distribution
The Erlang distribution models the waiting time for the
nth occurance of an event with specified waiting time.
The Erlang distribution has two parameters. The first parameter,
the number of occurances n, acts as a shape parameter. The
second parameter, the waiting time θ, is a scale
parameter.
The Erlang distribution is a special case of the Gamma distribution, with location
parameter 0 and the shape parameter restricted to integral values.
When n = 1, the Erlang distribution reduces to the
exponential
distribution.
The probability density function is:
The Erlang distribution is implemented by the ErlangDistribution
class. It has one constructor which takes the number of occurrances
and the waiting time (or the shape and scale parameters) as
parameters. The first parameter must be an integer. The following
constructs an Erlang distribution with n = 10 and waiting
time 7.6: degrees of freedom:
| C# |  Copy Code |
|---|
ErlangDistribution erlang = new ErlangDistribution(10, 7.6); |
| Visual Basic | Copy Code |
|---|
Dim erlang As ErlangDistribution = New ErlangDistribution(10, 7.6) |
The ErlangDistribution class has two specific
properties,
ShapeParameter, which returns the shape parameter of
the distribution, and
ScaleParameter, which returns the scale parameter.
ErlangDistribution has one static (Shared
in Visual Basic) method,
GetRandomVariate, which generates a random variate
using a user-supplied uniform random number generator.
| C# | Copy Code |
|---|
MersenneTwister random = new MersenneTwister();
double variate = ErlangDistribution.GetRandomVariate(random, 10, 7.6); |
| Visual Basic | Copy Code |
|---|
Dim random As MersenneTwister = New MersenneTwister()
Dim variate As Double = ErlangDistribution.GetRandomVariate(random, 10, 7.6) |
The above example uses the Mersenne
Twister to generate uniform random numbers.
For details of the properties and methods common to all
continuous distribution classes, see the topic on ContinuousDistribution
class.
Up: Continuous Probability Distributions Next: The Exponential Distribution Previous: The Chi-Square Distribution Contents
Copyright 2004-2008,
Extreme Optimization. All rights reserved.
Extreme Optimization, Complexity made simple, M#, and M
Sharp are trademarks of ExoAnalytics Inc.
Microsoft, Visual C#, Visual Basic, Visual Studio, Visual
Studio.NET, and the Visual Studio Logo are registered trademarks of Microsoft Corporation