GAMMA
IMPORTANT CONTINUOUS RANDOM VARIABLE
Used to model time required until occurance of event A.
Has probability density function (pdf)
The Gamma RV has different shapes based on the values of alpha and beta.
Click on a button to see an example graph at right.
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In general, the cumulative distribution function (CDF) of an Gamma 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
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PROPERTIES
Mean:
Variance:
rth central moment about the origin:
Moment Generating Function:
- If and then we get an Exponential Random Variable.
- If and then we get a Chi-square Random Variable.
- If is an integer, m, then we get a m-Erlang Random Variable.
- If is an integer, the Gamma CDF is related to the Poisson CDF.
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RELATED
CONCEPTSRandom Variables Probability Density Function Cumulative Distribution Function Important Continuous Random Variables ![]()
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