## Nadarajah and Kotz (2007) On the convolution of Pareto and gamma distributions (ComNet(51))

It is well-accepted that Pareto (heavy-tailed) and Gamma (short-tailed) distributions can be used to model the on-off time of a bursty traffic. If $X$ is Pareto, i.e. $X\sim\dfrac{ac^a}{(x+c)^{a+1}}$, and $Y$ is Gamma, i.e. $Y\sim\dfrac{y^{\alpha-1}e^{-y/\lambda}}{\lambda^\alpha\Gamma(\alpha)}$, then $R=X+Y$ models the time between successive on-off cycles.
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