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 Charles Kenneth Tweedie, a statistician and medical physicist at the University of Liverpool, UK, who presented the first thorough study of these distributions in 1984.
Read more about Tweedie Distributions: Examples, Definitions, The Tweedie Convergence Theorem, The Tweedie Models and Taylor’s Power Law, The Double Power Law, Tweedie Convergence and 1/f Noise, The Tweedie Models and Multifractality