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- Gamma_distribution abstract "In probability theory and statistics, the gamma distribution is a two-parameter family of continuous probability distributions. There are three different parametrizations in common use:With a shape parameter k and a scale parameter θ.With a shape parameter α = k and an inverse scale parameter β = 1/θ, called a rate parameter.With a shape parameter k and a mean parameter μ = k/β.In each of these three forms, both parameters are positive real numbers.The parameterization with k and θ appears to be more common in econometrics and certain other applied fields, where e.g. the gamma distribution is frequently used to model waiting times. For instance, in life testing, the waiting time until death is a random variable that is frequently modeled with a gamma distribution.The parameterization with α and β is more common in Bayesian statistics, where the gamma distribution is used as a conjugate prior distribution for various types of inverse scale (aka rate) parameters, such as the λ of an exponential distribution or a Poisson distribution – or for that matter, the β of the gamma distribution itself. (The closely related inverse gamma distribution is used as a conjugate prior for scale parameters, such as the variance of a normal distribution.)If k is an integer, then the distribution represents an Erlang distribution; i.e., the sum of k independent exponentially distributed random variables, each of which has a mean of θ (which is equivalent to a rate parameter of 1/θ).The gamma distribution is the maximum entropy probability distribution for a random variable X for which E[X] = kθ = α/β is fixed and greater than zero, and E[ln(X)] = ψ(k) + ln(θ) = ψ(α) − ln(β) is fixed (ψ is the digamma function).".
- Gamma_distribution thumbnail Gamma_distribution_pdf.svg?width=300.
- Gamma_distribution wikiPageExternalLink File:Gamma-PDF-3D-by-Theta.png.
- Gamma_distribution wikiPageExternalLink File:Gamma-PDF-3D-by-k.png.
- Gamma_distribution wikiPageExternalLink File:Gamma-PDF-3D-by-x.png.
- Gamma_distribution wikiPageExternalLink eda366b.htm.
- Gamma_distribution wikiPageID "207079".
- Gamma_distribution wikiPageRevisionID "606652786".
- Gamma_distribution cdfImage "325".
- Gamma_distribution hasPhotoCollection Gamma_distribution.
- Gamma_distribution id "p/g043300".
- Gamma_distribution median "No simple closed form".
- Gamma_distribution name "Gamma".
- Gamma_distribution parameters "* k > 0 shape * θ > 0 scale".
- Gamma_distribution parameters "* α > 0 shape * β > 0 rate".
- Gamma_distribution pdfImage "325".
- Gamma_distribution title "Gamma distribution".
- Gamma_distribution title "Gamma-distribution".
- Gamma_distribution type "density".
- Gamma_distribution urlname "GammaDistribution".
- Gamma_distribution subject Category:Conjugate_prior_distributions.
- Gamma_distribution subject Category:Continuous_distributions.
- Gamma_distribution subject Category:Exponential_family_distributions.
- Gamma_distribution subject Category:Factorial_and_binomial_topics.
- Gamma_distribution subject Category:Infinitely_divisible_probability_distributions.
- Gamma_distribution subject Category:Probability_distributions.
- Gamma_distribution type Abstraction100002137.
- Gamma_distribution type Arrangement105726596.
- Gamma_distribution type Cognition100023271.
- Gamma_distribution type ConjugatePriorDistributions.
- Gamma_distribution type ContinuousDistributions.
- Gamma_distribution type Distribution105729036.
- Gamma_distribution type PsychologicalFeature100023100.
- Gamma_distribution type Structure105726345.
- Gamma_distribution comment "In probability theory and statistics, the gamma distribution is a two-parameter family of continuous probability distributions.".
- Gamma_distribution label "Distribución gamma".
- Gamma_distribution label "Distribuição gama".
- Gamma_distribution label "Distribuzione Gamma".
- Gamma_distribution label "Gamma distribution".
- Gamma_distribution label "Gamma-verdeling".
- Gamma_distribution label "Gammaverteilung".
- Gamma_distribution label "Loi Gamma".
- Gamma_distribution label "Rozkład gamma".
- Gamma_distribution label "Гамма-распределение".
- Gamma_distribution label "توزيع غاما".
- Gamma_distribution label "ガンマ分布".
- Gamma_distribution label "伽玛分布".
- Gamma_distribution sameAs Gammaverteilung.
- Gamma_distribution sameAs Distribución_gamma.
- Gamma_distribution sameAs Loi_Gamma.
- Gamma_distribution sameAs Distribuzione_Gamma.
- Gamma_distribution sameAs ガンマ分布.
- Gamma_distribution sameAs 감마_분포.
- Gamma_distribution sameAs Gamma-verdeling.
- Gamma_distribution sameAs Rozkład_gamma.
- Gamma_distribution sameAs Distribuição_gama.
- Gamma_distribution sameAs m.01dd8w.
- Gamma_distribution sameAs Q117806.
- Gamma_distribution sameAs Q117806.
- Gamma_distribution sameAs Gamma_distribution.
- Gamma_distribution wasDerivedFrom Gamma_distribution?oldid=606652786.
- Gamma_distribution depiction Gamma_distribution_pdf.svg.
- Gamma_distribution isPrimaryTopicOf Gamma_distribution.