along with the real-life application.\
A random variable $Z$ follows Maxwell distribution with scale parameter $\alpha$, denoted as $Z \sim
MaD(\alpha )$, if its probability density function (pdf) and cumulative distribution function (cdf) are given by $$f(z,\alpha)=\dfrac{4}{\sqrt{\pi}} \alpha^{\frac{3}{2}} z^{2}e^{-\alpha z^{2}}~~~~z\ge 0,\alpha>0$$ and $$F(z,\alpha)=\dfrac{2}{\sqrt{\pi}}\Gamma\left( \frac{3}{2},\alpha z^{2}\right)$$ respectively, where $\Gamma (a, z) =\int_{0}^{z}p^{a-1}e^{-p}dp$ is the incomplete gamma function.\
In this article, we proposed PMaD as a new generalization of the Maxwell distribution and discussed its various statistical properties and application. The objective of this article is to study the statistical properties of the PMaD distribution, and then estimate the unknown parameters using classical and Bayes estimation methods. Other motivations regarding advantages of the PMaD distribution comes from its flexibility to model the data with nono-monotone failure rate. Thus, it can be taken as an excellent alternative to several inverted families of distributions. The uniqueness of this study comes from the fact that we provide a comprehensive description of mathematical and statistical properties of this distribution with the hope that it will attract more extensive applications in biology, medicine, economics, reliability, engineering, and other areas of research.\
The rest of the paper has been shaped in the following manner. The introduction of the 