logo SBA

ETD

Archivio digitale delle tesi discusse presso l’Università di Pisa

Tesi etd-05082023-232719


Tipo di tesi
Tesi di laurea magistrale
Autore
FIORINI, FRANCESCO
URN
etd-05082023-232719
Titolo
Heavy Tailed Distributions in Telecommunications: Statistical Modelling through Alpha-Theory
Dipartimento
INGEGNERIA DELL'INFORMAZIONE
Corso di studi
INGEGNERIA DELLE TELECOMUNICAZIONI
Relatori
relatore Prof. Pagano, Michele
relatore Prof. Cococcioni, Marco
Parole chiave
  • Algorithmic Numbers
  • Alpha-Theory
  • Heavy Tail Probability Distributions
  • Heavy tailed distributions
  • Infinitesimal Probabilities
  • LogNormal distribution
  • Non-Archimedean Scientific Computing
  • Non-Standard Analysis
  • Pareto distribution
  • Probability Density Fitting
  • Teletraffic modelling
Data inizio appello
06/07/2023
Consultabilità
Non consultabile
Data di rilascio
06/07/2093
Riassunto
In this Master thesis we will focus on the peculiar statistical properties of heavy tailed distributions and we will show some of their important engineering applications in the telecommunications world.
In practice, the most relevant heavy tailed distributions are those with finite mean and divergent variance. The LogNormal distribution, although it appears to be an accurate model for the data, is often discarded for modelling heavy tailed phenomena because, in its standard version, it has finite variance.
Using the main theoretical foundations of Alpha-Theory, an advancement in Non-Standard Analysis, introduced by Vieri Benci in late nineties, we will show how to create an Euclidean version of the LogNormal distribution, with well-defined infinite variance (i.e. a numerical value, not a potential diverging infinity, as expressed by the symbol lemniscate). Through experimental tests in Matlab, we will also be able to generate samples that follow this distribution and subsequently verify numerically that the sample values of mean and variance are consistent with the theoretical values, obtaining a convincing result.
File