| dbo:abstract |
In probability theory and statistics, the normal-inverse-gamma distribution (or Gaussian-inverse-gamma distribution) is a four-parameter family of multivariate continuous probability distributions. It is the conjugate prior of a normal distribution with unknown mean and variance. (en) |
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wiki-commons:Special:FilePath/Normal-inverse-gamma.svg?width=300 |
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| dbo:wikiPageWikiLink |
dbr:Probability_distribution dbr:Scalar_(mathematics) dbr:Determinant dbr:Variance dbr:Inverse-gamma_distribution dbr:Matrix_(mathematics) dbr:Mean dbr:Conjugate_prior dbr:Location_parameter dbr:Statistics dbr:Compound_probability_distribution dbr:Multivariate_Student_distribution dbr:Student's_t-distribution dbc:Normal_distribution dbr:Exponential_family dbr:Normal_distribution dbr:Precision_(statistics) dbr:Probability_theory dbr:Invertible_matrix dbc:Continuous_distributions dbc:Multivariate_continuous_distributions dbr:Real_number dbr:Normal-gamma_distribution dbr:Normal-inverse-Wishart_distribution dbr:Inverse_gamma_distribution dbr:Natural_parameter dbr:File:Normal-inverse-gamma.svg |
| dbp:mean |
, for (en) |
| dbp:mode |
(en) |
| dbp:name |
normal-inverse-gamma (en) |
| dbp:parameters |
dbr:Location_parameter (en) |
| dbp:pdfImage |
565 (xsd:integer) |
| dbp:proof |
For probability density function is Marginal distribution over is Except for normalization factor, expression under the integral coincides with Inverse-gamma distribution with , , . Since , and Substituting this expression and factoring dependence on , Shape of generalized Student's t-distribution is . Marginal distribution follows t-distribution with degrees of freedom . (en) |
| dbp:title |
Proof for (en) |
| dbp:type |
density (en) |
| dbp:variance |
, for (en) |
| dbp:wikiPageUsesTemplate |
dbt:Empty_section dbt:ISBN dbt:ProbDistributions dbt:Reflist dbt:Math_proof dbt:Probability_distribution |
| dct:subject |
dbc:Normal_distribution dbc:Continuous_distributions dbc:Multivariate_continuous_distributions |
| rdf:type |
yago:WikicatContinuousDistributions yago:WikicatMultivariateContinuousDistributions yago:Abstraction100002137 yago:Arrangement105726596 yago:Cognition100023271 yago:Distribution105729036 yago:PsychologicalFeature100023100 yago:Structure105726345 yago:WikicatProbabilityDistributions |
| rdfs:comment |
In probability theory and statistics, the normal-inverse-gamma distribution (or Gaussian-inverse-gamma distribution) is a four-parameter family of multivariate continuous probability distributions. It is the conjugate prior of a normal distribution with unknown mean and variance. (en) |
| rdfs:label |
Normal-inverse-gamma distribution (en) |
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freebase:Normal-inverse-gamma distribution yago-res:Normal-inverse-gamma distribution wikidata:Normal-inverse-gamma distribution https://global.dbpedia.org/id/4sVkw |
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