Modeling the mileage accumulation process with random effects

This article proposes a non stationary Gamma process with power-law shape function to model mileage accumulated processes in presence of heterogeneity in the sample paths. This heterogeneity is assumed to be charged to both the parameters of the shape function and is modeled through a bivariate distribution. Maximum likelihood estimates of the parameters indexing the bivariate distribution and of the scale parameter of the Gamma process, are obtained. The Monte Carlo sampling method is used to estimate the unconditional density function and the unconditional cumulative distribution function of the mileage accumulated by the population of vehicles up to a given age.