A Tweedie Markov process and its application in fisheries stock assessment

Abstract

The Tweedie distribution is a useful tool to model zero-inflated non-negative continuous data. However, the Tweedie dispersion relationship (DR) is not general enough to cover some important forms such as quadratic dispersion, and an easy and fast-to-implement Tweedie AR(1) model (first-order autoregressive model) needs to be developed for spatio-temporal modelling. In this research we extend the Tweedie distribution to accommodate flexible DRs, and propose a Tweedie Markov process (TMP) with the AR(1) autocorrelation structure. This TMP is simple to implement and requires only the Tweedie probability density function. Simulation studies and real data analysis are conducted to validate our new approach.