# Gamma Distribution in ST-Sim

Syncrosim Forums ST-Sim & State-and-Transition Simulation Models Gamma Distribution in ST-Sim

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A user recently emailed this question:
I have a question about how a gamma probability distribution is implemented in ST-Sim. A gamma distribution is characterized by two parameters: a shape parameter (k) and a rate parameter (beta). However, ST-Sim only allows input of Mean and Standard Deviation as parameters that characterize a gamma distribution.

Should I:
(1) be substituting k and beta values in for the mean and standard deviation if I want to use a gamma probability distribution? Or…
(2) is ST-Sim converting mean and SD to the shape and rate parameters internally? In other words, I provide the ‘moments’ (mean and SD) and ST-Sim somehow converts these moments to shape and rate. Thanks.

The second option is correct. You provide the mean and standard deviation and the shape and rate parameters are calculated internally according to the following formulas:

``````k = (mu / sigma)^2
θ = sigma^2 / mu
``````

where:

``````k is the Shape;
θ is the Scale;
1/θ is the Rate;
mu is the Mean; and
sigma is the Standard Deviation
``````
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