# On the Laplace transform of the Fr\\'{e}chet distribution

Source: [On the Laplace transform of the Fr\\'{e}chet distribution](<https://www.sota2.com/research/paper/68fa51fd1e209131ce97794d>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-25T11:40:11.924Z

Authors: K. A. Penson, K. G\\'orska

Published: 2014-03-10T19:37:49.000Z

## Abstract

We calculate exactly the Laplace transform of the Fr\\'{e}chet distribution in the form $\\gamma x^{-(1+\\gamma)} \\exp(-x^{-\\gamma})$, $\\gamma \> 0$, $0 \\leq x \< \\infty$, for arbitrary rational values of the shape parameter $\\gamma$, i.e. for $\\gamma = l/k$ with $l, k = 1,2, \\ldots$. 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 Fr\\'{e}chet distribution serves as a kernel of Fr\\'{e}chet integral transform. It turns out that the Fr\\'{e}chet transform of one-sided L\\'{e}vy law reproduces the Fr\\'{e}chet distribution.

## Recorded benchmark results

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1403.2361>)

[PDF](<https://arxiv.org/pdf/1403.2361.pdf>)