The stochastic Weibull diffusion process: Computational aspects and simulation

摘要

This paper presents a new stochastic diffusion process, in which the mean function is proportional to the density function of the Weibull distribution. This is considered a useful model for survival populations, reliability studies and life-testing experiments. The main features of the process are analysed, including the transition probability density function and conditional and non-conditional mean functions. The parameters of the process are estimated by maximum likelihood using discrete sampling. Newton-Raphson and simulated annealing numerical methods are proposed to solve the likelihood equations, and are compared using a simulation example.