{"id":40,"date":"2010-03-03T11:14:29","date_gmt":"2010-03-03T11:14:29","guid":{"rendered":"https:\/\/blog.informationgeometry.org\/?p=40"},"modified":"2021-08-05T00:56:23","modified_gmt":"2021-08-05T00:56:23","slug":"natural-exponential-families-qvf","status":"publish","type":"post","link":"https:\/\/blog.informationgeometry.org\/natural-exponential-families-qvf\/","title":{"rendered":"Natural Exponential Families QVF"},"content":{"rendered":"<div class=\"comment\">\n<p>They are only 6 exponential family distributions that admit variance as a quadratic function (QVF=quadratic variance function) of the parameter. For the multivariate case, it is a bit more complex but well defined and studied:<\/p>\n<p>The $2d+4$ simple quadratic natural exponential families on $R^d$<\/p>\n<p>Frank.<\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>They are only 6 exponential family distributions that admit variance as a quadratic function (QVF=quadratic variance function) of the parameter. For the multivariate case, it is a bit more complex but well defined and studied: The $2d+4$ simple quadratic natural<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[2],"tags":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/blog.informationgeometry.org\/wp-json\/wp\/v2\/posts\/40"}],"collection":[{"href":"https:\/\/blog.informationgeometry.org\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blog.informationgeometry.org\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blog.informationgeometry.org\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/blog.informationgeometry.org\/wp-json\/wp\/v2\/comments?post=40"}],"version-history":[{"count":3,"href":"https:\/\/blog.informationgeometry.org\/wp-json\/wp\/v2\/posts\/40\/revisions"}],"predecessor-version":[{"id":95,"href":"https:\/\/blog.informationgeometry.org\/wp-json\/wp\/v2\/posts\/40\/revisions\/95"}],"wp:attachment":[{"href":"https:\/\/blog.informationgeometry.org\/wp-json\/wp\/v2\/media?parent=40"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.informationgeometry.org\/wp-json\/wp\/v2\/categories?post=40"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.informationgeometry.org\/wp-json\/wp\/v2\/tags?post=40"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}