Extending the Accelerated Failure Conditionals Model to Location-Scale Families

TL;DR

This paper extends the accelerated failure conditionals model to include location-scale families, allowing for more flexible dependence structures and accommodating real-line marginals, with theoretical and simulation-based validation.

Contribution

It introduces a new conditional survival model based on location-scale distributions, expanding the dependence framework and providing closed-form moments and practical applications.

Findings

Model characterized by closed-form moments.

Simulations demonstrate the model's flexibility.

Application to real data shows effective dependence modeling.

Abstract

Arnold and Arvanitis (2020) introduced a novel class of bivariate conditionally specified distributions, in which dependence between two random variables is established by defining the distribution of one variable conditional on the other. This conditioning regime was formulated through survival functions and termed the accelerated failure conditionals model. Subsequently, Lakhani (2025) extended this conditioning framework to encompass distributional families whose marginal densities may exhibit unimodality and skewness, thereby moving beyond families with non-increasing densities. The present study builds on this line of work by proposing a conditional survival specification derived from a location-scale distributional family, where the dependence between $X$ and $Y$ arises not only through the acceleration function but also via a location function. An illustrative example of this new specification is developed using a Weibull marginal for $X$. The resulting models are fully characterized by closed-form expressions for their moments, and simulations are implemented using the Metropolis-Hastings algorithm. Finally, the model is applied to a dataset in which the empirical distribution of $Y$ lies on the real line, demonstrating the models' capacity to accommodate $Y$ marginals defined over $\mathbb{R}$.