## Appendix A  
The appendix derives the expression of \(f_{C_{t}}(c)\). Starting from (21), and using the binomial expansion ([35], Equation (1.111)), \(f_{C_{RF}}(c)\) can be rewritten as  
\[f_{C_{RF}}(c)=\frac{\ln 2}{W_{r}\Gamma(mN_{t})}A^{mN_{t}}\sum_{i=0}^{\infty} \sum_{j=0}^{mN_{t}+i-1}\frac{(-A)^{i}}{i!}(-1)^{mN_{t}+i-j-1}\left(2^{c/W_{r} }\right)^{j+1} \tag{11}\]Using the series expansion to \(\left(2^{c/W_{r}}\right)^{i+1}\) given by ([35], Equation (1.211.2)), we can rewrite (A1) as  
\[f_{C_{RF}}(c)=\frac{\ln 2}{W_{r}\Gamma(mN_{t})}A^{mN_{t}}\sum\limits_{i=0}^{ \infty}\sum\limits_{j=0}^{mN_{t}+i-1}\frac{(-A)^{i}}{i!}(-1)^{mN_{t}+i-j-1}\sum \limits_{k=0}^{\infty}\frac{((j+1)\ln 2/W_{r})^{k}}{k!}c^{k}\] (A2)  
Substituting (18) and (A2) into (24), and using the binomial expansion to \((c-x)^{k}\) ([35], Equation (1.111)) along with variable changing \(t=2^{x/W_{f}}-1\), \(f_{C_{t}}(c)\) is expressed as  
\[\begin{split}& f_{C_{t}}(c)=\frac{\xi_{3}{}^{2}\Lambda}{b\Gamma( \alpha_{3})\Gamma(\beta_{3})}\!\int_{0}^{2^{c/W_{f}-1}}t^{-1}\sum\limits_{m_{0} =0}^{k}\!\left(\begin{array}{c}k\\ m_{0}\end{array}\right)(-1)^{k-m_{0}}c^{m_{0}}\\ &\times\left[\frac{W_{f}}{\ln 2}\ln(t+1)\right]^{k-m_{0}}G_{1,3}^{3,0}\!\left[\frac{\alpha_{3}\beta_{3}\xi_{3}{}^{2}+1}{\left(\frac{t}{\tau\mu_{3 }}\right)}\frac{1}{b}\right]\begin{array}{c}\xi_{3}{}^{2}+1\\ \xi_{3}{}^{2},\;\alpha_{3},\;\beta_{3}\end{array}\right]dt\end{split}\] (A3)  
where \(\Lambda\) in (A3) is given by  
\[\Lambda=\frac{\ln 2}{W_{r}\Gamma(mN_{t})}A^{mN_{t}}\sum\limits_{i=0}^{\infty} \sum\limits_{j=0}^{mN_{t}+i-1}\frac{(-A)^{i}}{i!}(-1)^{mN_{t}+i-j-1}\sum \limits_{k=0}^{\infty}\frac{((j+1)\ln 2/W_{r})^{k}}{k!}\] (A4)  
Applying Taylor series expansion around \(t=0\), \(\ln(t+1)\) in (A3) can be expressed as ([15], Equation (30))  
\[\ln(t+1)=\ln(0+1)+\sum\limits_{n=1}^{\infty}\frac{(-1)^{n-1}(t-0)^{n}}{n(0+1 )^{n}}\] (A5)  
After substituting (A5) into (A3) and applying ([28], Equation (07.34.21.0084.01)), \(f_{C_{f}+C_{RF}}(c)\) is derived as  
\[\begin{split}& f_{C_{t}}(c)=\frac{\xi_{3}^{2}\Lambda b^{\alpha_{3}+ \beta_{3}-2}}{\Gamma(\alpha_{3})\Gamma(\beta_{3})(2\pi)^{b-1}}\sum\limits_{m_{ 0}=0}^{k}\!\left(\begin{array}{c}k\\ m_{0}\end{array}\right)\left(\sum\limits_{n=1}^{\infty}\frac{(-1)^{n}}{n} \right)^{k-m_{0}}\!\left(\frac{W_{f}}{\ln 2}\right)^{k-m_{0}}\\ &\times c^{m_{0}}T^{kn-m_{0}n}G_{b+1,3b+1}^{3b}\!\left[\begin{array}{c}D_{ 5}^{3}T\\ \bar{b}^{2b}\mu\tau\end{array}\right]\begin{array}{c}m_{0}n+1-kn,E_{5}\\ E_{6},m_{0}n-kn\end{array}\right]\end{split}\] (A6)  
where \(T=2^{c/W_{f}}-1\). Substituting (A6) into (26) along with changing Integral variable \(y=2^{c/W_{f}}-1\), \(F_{C_{t}}(c)\) can be expressed as  
\[\begin{split}& F_{C_{t}}(c)=\frac{\xi_{3}^{2}\Lambda b^{\alpha+ \beta-2}}{\Gamma(\alpha_{3})\Gamma(\beta_{3})(2\pi)^{b-1}}\sum\limits_{m_{0}=0} ^{k}\!\left(\begin{array}{c}k\\ m_{0}\end{array}\right)\left(\sum\limits_{n=1}^{\infty}\frac{(-1)^{n}}{n} \right)^{k-m_{0}}\sum\limits_{h=0}^{\infty}\frac{(-1)^{h}}{h!}\!\left(\frac{W_{ f}}{\ln 2}\right)^{k+1}\\ &\times\int_{0}^{2^{c/W_{f}-1}}[\ln(y+1)]^{m_{0}+h}y^{kn-m_{0}n}G_{b+1,3b+1}^ {3b,1}\!\left[\begin{array}{c}D_{5}^{3}y\\ \bar{b}^{2b}\mu\tau\end{array}\right]\begin{array}{c}m_{0}n+1-kn,E_{5}\\ E_{6},m_{0}n-kn\end{array}\right]dy\end{split}\] (A7)  
Using Taylor series expansion of \(\ln(y+1)\) around \(x=0\), and then applying ([28], Equation (07.34.21.0084.01)), \(F_{C_{t}}(c)\) can be obtained as shown in (27).