is obtained by moments based relations suggested by Pearson and given by; $$\beta_1=\dfrac{\left[ \mu_3^{'}-3\mu_2^{'}\mu_1^{'}+2\left( \mu_1^{'}\right) ^{3}\right] ^{2}}{\left[\mu_2^{'}-\left( \mu_1^{'}\right)^{2} \right]^{3} }$$ and $$\beta_2=\dfrac{\mu_4^{'}-4\mu_3^{'}\mu_1^{'}+6\mu_2^{'}\left( \mu_1^{'}\right) ^{2}-3\left( \mu_1^{'}\right) ^{4}}{\left[\mu_2^{'}-\left( \mu_1^{'}\right)^{2} \right]^{2} }$$ These values are calculated in Table 1 for different combination of model parameters and it is observed that the shape of PMaD is right skewed and almost symmetrical for some choices of $\alpha, \beta$. Also, it can has the nature of platykurtic, mesokurtic and leptokurtic, thus PMaD may be used to model skewed and symmetric data as well.

Coefficient of variation
------------------------

The coefficient of variation (CV) is calculated by $$CV=\dfrac{\sqrt{\mu_2^{'}-\left( \mu_1^{'}\right)^{2}}}{\mu_1^{'}}\times 100$$

Mode and Median
---------------

The mode $(M_0)$ for PMaD $(\alpha,\beta)$ is obtained by solving the following expression $$\dfrac{d}{dx}f(x,\alpha,\beta)|_{M_0}=0$$ which yield $$M_0=\left( \dfrac{3\beta-1}{2\alpha\beta}\right)^{\frac{1}{2\beta}}$$ The median $(M_{d})$ of the proposed distribtuion can be calculated by using the empirical relation amung mean, median and mode. Thus, the median is, $$M_{d}=\frac{1}{3} M_{0}+\frac{2}{3}\mu_1^{'}=\frac{1}{3} \left[ \left( \dfrac{3\beta-1}{2\alpha\beta}\right)^{\frac{1}{2\beta}}+ \dfrac{4}{\sqrt{\pi}}\left( \frac{1}{\alpha}\right) ^{\frac{1}{2\beta}}\Gamma\left( \dfrac{3\beta+1}{2\beta}\right)\right]$$

[ccccccc]{}\
\[0\][\*]{}[$ \alpha,~ \beta $]{} & $\mu_1^{'}$ & $\mu_2$ & $\beta_1$& $\beta_2$ & $x_0$ & CV\
&\
0.5, 0.5 & 3.0008 & 5.9992 & 2.6675 & 7.0010 & 1.0000 & 0.8162\
0.5, 1.0 & 1.5962 & 0.4530 & 0.2384 & 3.1071 & 1.4142 