Models with Accelerated Failure Conditionals

TL;DR

This paper extends the accelerated failure conditionals model to include skewed and unimodal distributions, providing closed-form moments and demonstrating improved data fit over previous models with monotonic marginals.

Contribution

The study generalizes the dependence framework to broader distributional families with non-monotonic marginals, enhancing model flexibility and applicability.

Findings

Models with flexible marginals fit skewed, unimodal data better.

Closed-form moments facilitate practical implementation.

Simulation methods include copula and Metropolis-Hastings algorithms.

Abstract

Arnold and Arvanitis (2020) introduced a novel bivariate conditionally specified distribution, a distribution in which dependence between two random variables is established by defining the distribution of one variable conditional on the other. This novel conditioning regime was achieved through the use of survival functions, and the approach was termed the accelerated failure conditionals model. In their work, the conditioning framework was constructed using the exponential distribution. Although further generalization was proposed, challenges emerged in deriving the necessary and sufficient conditions for valid joint survival functions. The present study achieves such generalization, extending the conditioning framework to encompass distributional families whose marginal densities may exhibit unimodality and skewness, moving beyond distributional families whose marginal densities are non-increasing. The resulting models are fully specified through closed-form expressions for their moments, with simulations implemented using either a copula-based procedure or the Metropolis-Hastings algorithm. Empirical applications to two datasets, each featuring variables which are unimodal and skewed, demonstrate that the models with flexible, non-monotonic marginal densities yield a superior fit relative to those models with marginal densities restricted to monotonically decaying forms.