On the Laplace transform of the Fréchet distribution

@article{Penson2014OnTL,
  title={On the Laplace transform of the Fr{\'e}chet distribution},
  author={K. Penson and K. G'orska},
  journal={Journal of Mathematical Physics},
  year={2014},
  volume={55},
  pages={093501}
}
We calculate exactly the Laplace transform of the Frechet distribution in the form γx−(1 + γ)exp (−x−γ), γ > 0, 0 ≤ x < ∞, for arbitrary rational values of the shape parameter γ, i.e. for γ = l/k with l, k = 1, 2, …. The method employs the inverse Mellin transform. The closed form expressions are obtained in terms of Meijer G functions and their graphical illustrations are provided. A rescaled Frechet distribution serves as a kernel of Frechet integral transform. It turns out that the Frechet… Expand
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