Bulletin of the
Korean Mathematical Society BKMS

A special class of exponential dispersion models is the class of Tweedie distributions. This class is very significant in statistical modeling as it includes a number of familiar distributions such as Gaussian, Gamma and compound Poisson. A Tweedie distribution has a power parameter $p$, a mean $m$ and a dispersion parameter $\phi$. The value of the power parameter lies in identifying the corresponding distribution of the Tweedie family. The basic objective of this research work resides in investigating the existence of the implicit estimator of the power parameter of the Tweedie distribution. A necessary and sufficient condition on the mean parameter $m$, suggesting that the implicit estimator of the power parameter $p$ exists, was established and we provided some asymptotic properties of this estimator.

Keywords: Tweedie distributions, power parameter, implicit approach, asymptotic normality

MSC numbers: Primary 62F12; Secondary 60E07, 62F15