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abstract: 'In this article, we proposed a new probability distribution named as power Maxwell distribution (PMaD). It is another extension of Maxwell distribution (MaD) which would lead more flexibility to analyze the data with non-monotone failure rate. Different statistical properties such as reliability characteristics, moments, quantiles, mean deviation, generating function, conditional moments, stochastic ordering, residual lifetime function and various entropy measures have been derived. The estimation of the parameters for the proposed probability distribution has been addressed by maximum likelihood estimation method and Bayes estimation method. The Bayes estimates are obtained under gamma prior using squared error loss function. Lastly, real-life application for the proposed distribution has been illustrated through different lifetime data.'
author:
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    [Abhimanyu Singh Yadav$^{1}$[^1], Hassan S. Bakouch $^2$, Sanjay Kumar Singh$^3$ and Umesh Singh$^3$]{}\
    $^1$[Department of Statistics, Central University of Rajasthan, Ajamer, India]{}\
    $^2$ [Department of Mathematics, Faculty of Science, Tanta University, Tanta, Egypt]{}\
    $^3$[Department of Statistics and DST-CIMS, BHU, Varanasi, India]{}
title: ' **Power Maxwell distribution: Statistical Properties, Estimation and Application**'
---

**Keywords:** Maxwell distribution, Power Maxwell distribution, moments, stochastic order, entropy, Classical and Bayes estimation.

Introduction
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The Maxwell distribution has broad application in statistical physics, physical chemistry, and their related areas. 