# Generalization of the pairwise stochastic precedence order to the sequence of random variables

## TL;DR

This paper introduces a new sequential precedence order for comparing sequences of independent random variables, extending the stochastic precedence order from pairs to longer sequences, with a focus on its properties and applications.

## Contribution

It generalizes the stochastic precedence order to sequences of variables and develops a new approach called the sequential precedence order, addressing non-transitivity issues.

## Key findings

- A sufficient condition for the sequential precedence order is derived.
- Examples illustrate the application of the new order.
- The order extends stochastic comparison to longer sequences.

## Abstract

We discuss a new stochastic ordering for the sequence of independent random variables. It generalizes the stochastic precedence order that is defined for two random variables to the case $n>2$. All conventional stochastic orders are transitive, whereas the stochastic precedence order is not. Therefore, a new approach to compare the sequence of random variables had to be developed that resulted in the notion of the sequential precedence order. A sufficient condition for this order is derived and some examples are considered.