## Appendix A The CDF of SIRs \(z_{i}\) is:  
\[ \begin{split} F_{z_{i}}(z_{i})=\int\limits_{0}^{z_{i}}p_{z_{i}}(t)dt= \frac{8\pi\left(\
icefrac{{n_{1}+1}}{{n_{1}}}\right)^{2\
icefrac{{2n_{1}}}{{n_{2} }}}}{\Gamma(\
icefrac{{n_{1}+1}}{{n_{1}}})\Gamma(\
icefrac{{n_{2}+1}}{{n_{2}}} }\right)\sum\limits_{i_{1}=0}^{+\infty}\sum\limits_{i_{2}=0}^{+\infty}\frac{ \left(\
icefrac{{1-{n_{1}}^{2}}}{{n_{1}^{2}}}\right)^{2\
icefrac{{n_{1}}}{{n_{ 1}}}}\left(\
icefrac{{1-{n_{2}}^{2}}}{{n_{1}^{2}+2\
icefrac{{n_{1}}}{{n_{1}}} }}\right)^{2\
icefrac{{n_{2}}}{{n_{2}}}}}{2^{2\
icefrac{{n_{1}}}{{n_{1}}}}+2 \
icefrac{{n_{2}}}{{n_{1}}}\
icefrac{{1-{n_{2}}^{2}}}{{n_{1}^{2}+2\
icefrac{{ n_{1}}}{{n_{1}}}}}}\times\\ \frac{\
icefrac{{\mu_{1}}^{2\
icefrac{{n_{1}}}{{n_{2}}}}+2\
icefrac{{ n_{2}}}{{n_{1}}}}{\Gamma(\
icefrac{{n_{2}}}{{n_{1}}})\Gamma(\
icefrac{{n_{2}}}{{n_{1}}}) }}{\Gamma(\
icefrac{{n_{2}}}{{n_{1}}})\Gamma(\
icefrac{{n_{2}}}{{n_{2}}})}\sum \limits_{i_{1}=0}^{+\infty}\frac{\left(\
icefrac{{1-{n_{1}}^{2}}}{{n_{1}}} \right)^{2\
icefrac{{n_{1}}}{{n_{2}}}}}{2^{2\
icefrac{{n_{1}}}{{n_{1}}}}+2 \
icefrac{{n_{2}}}{{n_{1}}}\left(\
icefrac{{1-{n_{2}}^{2}}}{{n_{1}^{2}+2\
ice {n_{1}}}}\right)^{2\
icefrac{{n_{1}}}{{n_{2}}}}}\times\\ \frac{\mu_{1}^{2\
icefrac{{n_{1}}}{{n_{2}}}}+2\
icefrac{{n_{2}}}{{n_{1}}} \left(\
icefrac{{1-{n_{1}}^{2}}}{{n_{1}}}+2\
icefrac{{n_{2}}}{{n_{1}}}\left( \
icefrac{{1-{n_{1}}^{2}}}{{n_{1}}}\right)^{2}\
icefrac{{n_{1}}}{{n_{2}}}+2 \
icefrac{{n_{1}}}{{n_{1}}}\left(\
icefrac{{1-{n_{1}}^{2}}}{{n_{1}}}\right)^{ 2}\
icefrac{{n_{1}}}{{n_{2}}}}\right)^{2\
icefrac{{n_{1}}}{{n_{2}}}+2 \
icefrac{{n_{1}}}{{n_{1}}}+2\
icefrac{{n_{2}}}{{n_{2}}}}dt\end{split}  \tag{12}\]  
The integral that appears in the previous expression is solved based on [39]:  
\[\begin{split}\int\limits_{0}^{\lambda}\frac{x^{\text{\tiny{m}}}}{ \left(a+bx^{\text{\tiny{m}}}\right)^{\text{\tiny{p}}}}dx&=\frac{ \
icefrac{{x-p}}{{n}}}{\left(\frac{a}{b}\right)}^{\frac{m+1}{n}}B_{\text{\tiny {2}}}\left(\frac{m+1}{n},p-\frac{m+1}{n}\right),\\ z&=\frac{b\lambda^{\text{\tiny{m}}}}{a+b\lambda^{\text{ \tiny{m}}}},\text{\ }a\text{\textgreater{0}},b\text{\textgreater{0}},n\text  
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