Generalized probability functions
type: Item
instance of: scholarly article
title: Generalized probability functions
zbMATH Open document ID: 1203.82007
DOI: 10.1155/2009/206176
author: Alexandre Souto Martinez
author: Rodrigo Silva González
author: César Augusto Sangaletti Terçariol
published in: Advances in Mathematical Physics
publication date: 2010-11-16T00:00:00Z
review text: Summary: From the integration of nonsymmetrical hyperboles, a one-parameter generalization of the logarithmic function is obtained. Inverting this function, one obtains the generalized exponential function. Motivated by the mathematical curiosity, we show that these generalized functions are suitable to generalize some probability density functions (pdfs). A very reliable rank distribution can be conveniently described by the generalized exponential function. Finally, we turn the attention to the generalization of one- and two-tail stretched exponential functions. We obtain, as particular cases, the generalized error function, the Zipf-Mandelbrot pdf, the generalized Gaussian and Laplace pdf. Their cumulative functions and moments were also obtained analytically.
Mathematics Subject Classification ID: 82B05
zbMATH DE Number: 5816334
zbMATH Keywords: probability density function (PDF)
zbMATH Keywords: Gaussian PDF
zbMATH Keywords: Laplace PDF
zbMATH Keywords: Zipf-Mandelbrot PDF
Wikidata QID: Q58646958
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2009/206176
OpenAlex ID: W2107151300
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description: scientific article; zbMATH DE number 5816334