# Reliability study of proportional odds family of discrete distributions

## TL;DR

This paper investigates the properties of the discrete Marshall-Olkin family of distributions with a fixed tilt parameter, focusing on aging properties and stochastic orderings, supported by multiple examples.

## Contribution

It extends the Marshall-Olkin family to the discrete case and analyzes its aging and stochastic ordering properties, which is a novel contribution.

## Key findings

- Different aging properties are characterized.
- Stochastic orderings are established.
- Several illustrative examples are provided.

## Abstract

The proportional odds model gives a method of generating new family of distributions by adding a parameter, called tilt parameter, to expand an existing family of distributions. The new family of distributions so obtained is known as Marshall-Olkin family of distributions or Marshall-Olkin extended distributions. In this paper, we consider Marshall-Olkin family of distributions in discrete case with fixed tilt parameter. We study different ageing properties, as well as different stochastic orderings of this family of distributions. All the results of this paper are supported by several examples.