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.![]()
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
and can be illustrated as
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PROPERTIES
MEAN VARIANCE
- Used to model time required until mth occurance of event A.
- The rth central moment about the origin for a Erlang Random Variable is:
- The Moment Generating Function for a Erlang Random Variable is:
- If and , then we get an Exponential Random Variable.
- The Erlang CDF is related to the Poisson CDF.
- If Xi are m independent Exponential Random Variables each with parameter lambda, and a transformation of random variables is performed by
then Y will be m-Erlang distributed with and .![]()
RELATED
CONCEPTSRandom Variables Probability Density Function Cumulative Distribution Function Important Continuous Random Variables ![]()
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