A general statistical model for waiting times until collapse of a system

TL;DR

This paper introduces a statistical model for waiting times until system collapse, modeling the accumulation process with a mixture of gamma distributions, applicable across various scientific disciplines.

Contribution

It proposes a general model where the waiting time distribution is a mixture of gamma distributions, providing a flexible framework for critical event timing analysis.

Findings

Waiting time distribution is a mixture of gamma distributions.

The mixture can be approximated as an effective gamma distribution.

Applicable to diverse systems with threshold-based collapse.

Abstract

The distribution of waiting times until the occurrence of a critical event is a crucial statistical problem across several disciplines in Science. In this work we present a statistical model in which a relevant quantity X accumulates until overcoming a threshold X*, which defines the collapse. The obtained waiting time distribution is a mixture of gamma distributions, which in turn can be approximated as an effective gamma distribution.