Pesudo random numbers for the Landau and Vavilov distributions
type: Item
instance of: scholarly article
title: Pesudo random numbers for the Landau and Vavilov distributions
zbMATH Open document ID: 1012.65003
published in: Computational Statistics
publication date: 2003-03-09T00:00:00Z
review text: The Landau distribution is the distribution with the Laplace transform \(\exp(s\ln(s))\). It is a stable distribution with parameters (1,1). The Vavilov distribution has the Laplace transform \[ \exp(s\ln(s)+\kappa(1-E_2(s/\kappa))+ \kappa\beta^2(\gamma+\ln(s/\kappa)+E_1(s/\kappa))), \] where \(E_p(x)=\int_1^\infty\exp(-x\xi)\xi^{-p} d\xi\), \(p>0\). It is an infinitely divisible distribution. The author considers different methods of pseudo-random number generation with Landau and Vavilov distributions based on the stability and infinite divisibility properties. Special attention is paid to the case where the generator starts from some \(\beta\) and then should continue with a new smaller \(\beta\) (energy decay). The Kölbig-Schorr and Rotondi-Montaga generation methods require costly reinitialization in this case. The author proposes a technique which allows to perform such simulation without reinitialization.
Mathematics Subject Classification ID: 65C10
Mathematics Subject Classification ID: 11K45
Mathematics Subject Classification ID: 60E07
Mathematics Subject Classification ID: 65C50
zbMATH DE Number: 1878603
zbMATH Keywords: Kölbig-Schorr generation method
zbMATH Keywords: infinite divisible distribution
zbMATH Keywords: Laplace transform
zbMATH Keywords: energy decay
zbMATH Keywords: Landau distribution
zbMATH Keywords: Vavilov distribution
zbMATH Keywords: pseudo-random number generation
zbMATH Keywords: stability
zbMATH Keywords: Rotondi-Montaga generation methods
zbMATH Keywords: reinitialization
author: Jean-François Chamayou
MaRDI profile type: Publication
full work available at URL: s001800100055
OpenAlex ID: W1981110862
DOI: 10.1007/S001800100055
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description: scientific article; zbMATH DE number 1878603