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In probability and statistics, the Tweedie distributions are a family of probability distributions which include the purely continuous normal and gamma distributions, the purely discrete scaled Poisson distribution, and the class of mixed compound Poisson–gamma distributions which have positive mass at zero, but are otherwise continuous. For any random variable ''Y'' that obeys a Tweedie distribution, the variance var(''Y'') relates to the mean E(''Y'') by the power law, : where ''a'' and ''p'' are positive constants. The Tweedie distributions were named by Bent Jørgensen after Maurice Tweedie, a statistician and medical physicist at the University of Liverpool, UK, who presented the first thorough study of these distributions in 1984.〔 ==Examples== The Tweedie distributions include a number of familiar distributions as well as some unusual ones, each being specified by the domain of the index parameter. We have the *normal distribution, ''p'' = 0, *Poisson distribution, ''p'' = 1, *compound Poisson–gamma distribution, 1 < ''p'' < 2, *gamma distribution, ''p'' = 2, *positive stable distributions, 2 < ''p'' < 3, *inverse Gaussian distribution, ''p'' = 3, *positive stable distributions, ''p'' > 3, and *extreme stable distributions, ''p'' = . For 0 < ''p'' < 1 no Tweedie model exists. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Tweedie distribution」の詳細全文を読む スポンサード リンク
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