MathLiveGamma distribution probability density function
This gives the probability density of a continuous random variable following a gamma distribution with shape alpha and scale beta. It is used to model positive, skewed quantities such as waiting times, rainfall totals, and insurance claim sizes.
f(x) = \frac{x^{\alpha - 1} e^{-x/\beta}}{\beta^{\alpha} \Gamma(\alpha)}, \quad x > 0, \ \alpha > 0, \ \beta > 0What the symbols mean
| probability density at x | |
| value of the random variable, x > 0 | |
| shape parameter, \alpha > 0 | |
| scale parameter, \beta > 0 | |
| gamma function evaluated at \alpha | |
| Euler's number, base of the natural logarithm |
About this formula
- FieldStatistics
- TopicProbability distributions
- LevelUniversity
- Also calledgamma distribution pdf, gamma density function, gamma distribution formula, shape scale gamma density, gamma pdf, probability density gamma distribution
- SourceWikidata Q117806
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