ERLANG

IMPORTANT CONTINUOUS RANDOM VARIABLE

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The Erlang RV is a special case of the Gamma Random Variable that occurs when the alpha parameter is an integer.

Gamma RV probability density function (pdf)


Erlang RV Probability Density Function (PDF)

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This has many different shapes based on the values of alpha and beta.

Select a button to see an example graph.
gamma pdf pict, alpha=1

In general, the cumulative distribution function (CDF) of an Erlang random variable does not have a closed form expression. For certain special cases of alpha and beta there are closed form solutions.

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CASES OF ALPHA

If see Exponential RV.

If , then the pdf is
and can be illustrated as
Gamma CDF pict
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PROPERTIES

MEAN VARIANCE

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RELATED
CONCEPTS

  Random Variables
Probability Density Function
Cumulative Distribution Function
Important Continuous Random Variables
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