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 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 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:
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ErlangDistribution erlang = new ErlangDistribution(10, 7.6);
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Dim erlang As ErlangDistribution = New ErlangDistribution(10, 7.6)
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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 variate using a user-supplied uniform random number generator.
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MersenneTwister random = new MersenneTwister();
double variate = ErlangDistribution.GetRandomVariate(random, 10, 7.6);
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Dim random As MersenneTwister = New MersenneTwister()
Dim variate As Double = ErlangDistribution.GetRandomVariate(random, 10, 7.6)
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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
class.