Modelling Heavy Tailed Phenomena Using a LogNormal Distribution Having a Numerically Verifiable Infinite Variance

Marco Cococcioni (), Francesco Fiorini and Michele Pagano
Additional contact information
Marco Cococcioni: Department of Information Engineering, L.go Lucio Lazzarino, 1-56122 Pisa, Italy
Francesco Fiorini: Department of Information Engineering, L.go Lucio Lazzarino, 1-56122 Pisa, Italy
Michele Pagano: Department of Information Engineering, L.go Lucio Lazzarino, 1-56122 Pisa, Italy

Mathematics, 2023, vol. 11, issue 7, 1-16

Abstract: One-sided heavy tailed distributions have been used in many engineering applications, ranging from teletraffic modelling to financial engineering. In practice, the most interesting heavy tailed distributions are those having a finite mean and a diverging variance. The LogNormal distribution is sometimes discarded from modelling heavy tailed phenomena because it has a finite variance, even when it seems the most appropriate one to fit the data. In this work we provide for the first time a LogNormal distribution having a finite mean and a variance which converges to a well-defined infinite value. This is possible thanks to the use of Non-Standard Analysis. In particular, we have been able to obtain a Non-Standard LogNormal distribution, for which it is possible to numerically and experimentally verify whether the expected mean and variance of a set of generated pseudo-random numbers agree with the theoretical ones. Moreover, such a check would be much more cumbersome (and sometimes even impossible) when considering heavy tailed distributions in the traditional framework of standard analysis.

Keywords: non-standard analysis; alpha-theory; algorithmic numbers; non-archimedean scientific computing; heavy tailed distributions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
https://www.mdpi.com/2227-7390/11/7/1758/pdf (application/pdf)
https://www.mdpi.com/2227-7390/11/7/1758/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:11:y:2023:i:7:p:1758-:d:1117696

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().