## 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. [more]