# On sequential maxima of exponential sample means, with an application to ruin probability

## TL;DR

This paper derives the distribution of the maximum average of i.i.d. exponential variables, revealing a simple inverse distribution, and applies this to analyze ruin probabilities in risk models.

## Contribution

It provides a closed-form expression for the inverse distribution of the maximal average of exponential samples and applies it to ruin probability analysis.

## Key findings

- Distribution of maximal average derived explicitly
- Inverse distribution admits a simple closed form
- Application to ruin probability in risk models

## Abstract

We obtain the distribution of the maximal average in a sequence of independent identically distributed exponential random variables. Surprisingly enough, it turns out that the inverse distribution admits a simple closed form. An application to ruin probability in a risk-theoretic model is also given.