# On a class of distributions generated by stochastic mixture of the extreme order statistics of a sample of size two

## TL;DR

This paper introduces a new family of distributions created by mixing the extreme order statistics of two samples, exploring their properties, extending classical distributions, and considering bivariate cases.

## Contribution

It proposes a novel distribution family based on stochastic mixtures of order statistics, extending exponential and Laplace distributions, with applications to bivariate models.

## Key findings

- Properties of the new distribution family are thoroughly analyzed.
- The model successfully extends classical distributions like exponential and Laplace.
- An extension to bivariate distributions is developed.

## Abstract

This paper considers a family of distributions constructed by a stochastic mixture of the order statistics of a sample of size two. Various properties of the proposed model are studied. We apply the model to extend the exponential and symmetric Laplace distributions. An extension to the bivariate case is considered.