GammaDistribution

GammaDistribution[α,β]
represents a gamma distribution with shape parameter α and scale parameter β.

GammaDistribution[α,β,γ,μ]
represents a generalized gamma distribution with shape parameters α and γ, scale parameter β, and location parameter μ.

DetailsDetails

  • The probability density for value in a gamma distribution is proportional to for , and is zero for . »
  • The probability density for value in a generalized gamma distribution is proportional to for , and is zero elsewhere.
  • GammaDistribution allows α, β, and γ to be any positive real numbers and μ to be any real number.
  • GammaDistribution can be used with such functions as Mean, CDF, and RandomVariate. »

ExamplesExamplesopen allclose all

Basic Examples  (8)Basic Examples  (8)

Probability density function of a gamma distribution:

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Cumulative distribution function of a gamma distribution:

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Mean and variance of a gamma distribution:

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Median of a gamma distribution:

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Probability density function of a generalized gamma distribution:

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Cumulative distribution function of a generalized gamma distribution:

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Mean and variance of a generalized gamma distribution:

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Median of a generalized gamma distribution:

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Introduced in 2007
(6.0)
| Updated in 2010
(8.0)