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- Scaled_inverse_chi-squared_distribution abstract "The scaled inverse chi-squared distribution is the distribution for x = 1/s2, where s2 is a sample mean of the squares of ν independent normal random variables that have mean 0 and inverse variance 1/σ2 = τ2. The distribution is therefore parametrised by the two quantities ν and τ2, referred to as the number of chi-squared degrees of freedom and the scaling parameter, respectively.This family of scaled inverse chi-squared distributions is closely related to two other distribution families, those of the inverse-chi-squared distribution and the inverse gamma distribution. Compared to the inverse-chi-squared distribution, the scaled distribution has an extra parameter τ2, which scales the distribution horizontally and vertically, representing the inverse-variance of the original underlying process. Also, the scale inverse chi-squared distribution is presented as the distribution for the inverse of the mean of ν squared deviates, rather than the inverse of their sum. The two distributions thus have the relation that if then Compared to the inverse gamma distribution, the scaled inverse chi-squared distribution describes the same data distribution, but using a different parametrization, which may be more convenient in some circumstances. Specifically, if then Either form may be used to represent the maximum entropy distribution for a fixed first inverse moment and first logarithmic moment .The scaled inverse chi-squared distribution also has a particular use in Bayesian statistics, somewhat unrelated to its use as a predictive distribution for x = 1/s2. Specifically, the scaled inverse chi-squared distribution can be used as a conjugate prior for the variance parameter of a normal distribution. In this context the scaling parameter is denoted by σ02 rather than by τ2, and has a different interpretation. The application has been more usually presented using the inverse gamma distribution formulation instead; however, some authors, following in particular Gelman et al. (1995/2004) argue that the inverse chi-squared parametrisation is more intuitive.".
- Scaled_inverse_chi-squared_distribution thumbnail Scaled_inverse_chi_squared.svg?width=300.
- Scaled_inverse_chi-squared_distribution wikiPageID "1653682".
- Scaled_inverse_chi-squared_distribution wikiPageRevisionID "604895156".
- Scaled_inverse_chi-squared_distribution cdfImage "250".
- Scaled_inverse_chi-squared_distribution hasPhotoCollection Scaled_inverse_chi-squared_distribution.
- Scaled_inverse_chi-squared_distribution kurtosis "for".
- Scaled_inverse_chi-squared_distribution mean "for".
- Scaled_inverse_chi-squared_distribution name "Scaled inverse chi-squared".
- Scaled_inverse_chi-squared_distribution pdfImage "250".
- Scaled_inverse_chi-squared_distribution skewness "for".
- Scaled_inverse_chi-squared_distribution type "density".
- Scaled_inverse_chi-squared_distribution variance "for".
- Scaled_inverse_chi-squared_distribution subject Category:Continuous_distributions.
- Scaled_inverse_chi-squared_distribution subject Category:Exponential_family_distributions.
- Scaled_inverse_chi-squared_distribution subject Category:Probability_distributions.
- Scaled_inverse_chi-squared_distribution comment "The scaled inverse chi-squared distribution is the distribution for x = 1/s2, where s2 is a sample mean of the squares of ν independent normal random variables that have mean 0 and inverse variance 1/σ2 = τ2.".
- Scaled_inverse_chi-squared_distribution label "Scaled inverse chi-squared distribution".
- Scaled_inverse_chi-squared_distribution sameAs m.05ky2j.
- Scaled_inverse_chi-squared_distribution sameAs Q7429744.
- Scaled_inverse_chi-squared_distribution sameAs Q7429744.
- Scaled_inverse_chi-squared_distribution wasDerivedFrom Scaled_inverse_chi-squared_distribution?oldid=604895156.
- Scaled_inverse_chi-squared_distribution depiction Scaled_inverse_chi_squared.svg.
- Scaled_inverse_chi-squared_distribution isPrimaryTopicOf Scaled_inverse_chi-squared_distribution.