DistErlang

class pydsol.core.distributions.DistErlang(stream: StreamInterface, scale: float, k: int)

Bases: DistContinuous

The Erlang distribution is the distribution of a sum of k independent exponential variables with the scale parameter as the mean. The scale parameter is equal to 1/rate or 1/lambda;, giving the entire Erlang distribution a mean of k*scale. For more information on this distribution see https://mathworld.wolfram.com/ErlangDistribution.html.

GAMMATHRESHOLD = 10

the threshold above which we use a gamma function and below we use repeated drawing

__init__(stream: StreamInterface, scale: float, k: int)

Construct a new Erlang distribution with k and a mean (so not k and a rate) as parameters. It is the distribution of a sum of k independent exponential variables with the scale parameter as the mean. The scale parameter is equal to 1/rate or 1/lambda, giving the entire Erlang distribution a mean of k*scale.

Parameters:

• stream (StreamInterface) – the random stream to use for this distribution

• scale (float) – the mean of a single sample from the exponential distribution, of which k are summed. Equal to 1/rate or 1/lambda.

• k (int) – the shape parameter of the Erlang distribution. The shape k is the number of times a drawing is done from the exponential distribution, where the Erlang distribution is the sum of these k independent exponential variables.

Raises:

• TypeError – when stream is not implementing StreamInterface:

• TypeError – when scale is not a float or int:

• TypeError – when k is not an int:

• ValueError – when k <= 0 or scale <= 0:

draw() → float

Draw a value from the Erlang distribution. Based on the algorithm in Law & Kelton, Simulation Modeling and Analysis, 1991.

probability_density(x: float) → float

Returns the probability density value for value x.

property scale: float

Return the parameter value scale

property k: int

Return the parameter value k

property stream: StreamInterface

Return the current random stream for this distribution.