A new semi-parametric family of probability distributions for survival analysis

TL;DR

This paper generalizes the Marshall-Olkin method by introducing multi-parameter families of survival distributions, providing explicit moments for Log-logistic cases and methods for sampling from these new distributions.

Contribution

It extends the Marshall-Olkin approach to include multiple parameters, creating more flexible survival distributions with calculable moments and sampling techniques.

Findings

Introduction of multi-parameter survival families

Explicit moments for Log-logistic distributions

Sampling methods for the new distributions

Abstract

In the context of survival analysis, Marshall and Olkin (1997) introduced families of distributions by adding a scalar parameter to a given survival function, parameterized or not. In that paper, we generalize their approach. We show how it is possible to add more than a single parameter to a given distribution. We then introduce very flexible families of distributions for which we calculate some moments. Notably, we give some tractable expressions of these moments when the given baseline distribution is Log-logistic. Finally, we demonstrate how to generate sample from these new families.