Survival functions versus conditional aggregation-based survival functions on~discrete~space

TL;DR

This paper compares conditional aggregation-based survival functions with standard survival functions on discrete spaces, providing conditions under which they are equivalent and characterizing the operators involved.

Contribution

It introduces a comparison framework between new conditional aggregation-based survival functions and classical ones, including necessary and sufficient conditions for their equivalence.

Findings

Identifies conditions where the two survival functions are equal.

Provides a characterization of the family of operators for which the functions coincide.

Enhances understanding of survival functions in discrete spaces.

Abstract

In this paper we deal with conditional aggregation-based survival functions recently introduced by Boczek et al. (2020). The concept is worth to study because of its possible implementation in real-life situations and mathematical theory as well. The aim of this paper is the comparison of this new notion with the standard survival function. We state sufficient and necessary conditions under which the generalized and the standard survival function equal. The main result is the characterization of the family of conditional aggregation operators (on discrete space) for which these functions coincide.