Discrete Distribution for a Wiener Process Range and its Properties

TL;DR

This paper introduces a new discrete distribution based on the Wiener process range, explores its properties including a truncated version, and demonstrates its effectiveness with real data.

Contribution

It presents the first study of the discrete distribution of a Wiener process range and analyzes its properties and a truncated version.

Findings

Properties of the distribution are derived.

The truncated distribution's characteristics are examined.

Effectiveness is demonstrated using a real data set.

Abstract

We introduce the discrete distribution of a Wiener process range. Rather than finding some basic distributional properties including hazard rate function, moments, Stress-strength parameter and order statistics of this distribution, this work studies some basic properties of the truncated version of this distribution. The effectiveness of this distribution is established using a data set.