- Extreme Optimization
- Documentation
- Statistics Library User's Guide
- Continuous Distributions
- Continuous Distributions
- The Beta Distribution
- The Cauchy Distribution
- The Chi Square Distribution
- The Erlang Distribution
- The Exponential Distribution
- The F Distribution
- The Gamma Distribution
- The Generalized Pareto Distribution
- The Gumbel Distribution
- The Laplace Distribution
- The Logistic Distribution
- Log-Logistic Distribution
- The Lognormal Distribution
- The Non-central Beta Distribution
- The Non-central Chi Square Distribution
- The Non-central F Distribution
- The Non-central Student t distribution
- The Normal Distribution
- The Pareto Distribution
- The Rayleigh Distribution
- Student's t Distribution
- The Transformed Beta Distribution
- The Transformed Gamma Distribution
- The Triangular Distribution
- The Continuous Uniform Distribution
- The Weibull Distribution

- The Erlang Distribution

## The Erlang Distribution | Extreme Optimization Numerical Libraries for .NET Professional |

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 occurrences 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 The Gamma Distribution, with location parameter 0 and the shape parameter restricted to integral values. When n = 1, the Erlang distribution reduces to the 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 occurrences and the waiting time (or the shape and scale parameters) as arguments. The first argument must be an integer. The following constructs an Erlang distribution with n = 10 and waiting time 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, Sample, which generates a random sample using a user-supplied uniform random number generator.

var random = new MersenneTwister(); double sample = ErlangDistribution.Sample(random, 10, 7.6);

The above example uses the MersenneTwister to generate uniform random numbers.

For details of the properties and methods common to all continuous distribution classes, see the topic on Continuous Probability Distributions class.

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