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Dispersion Measure for Symmetric, Stable Probability Distributions by Tyhtila, Jussi I. is a scholarly article available to read on EtoBox.

What is Dispersion Measure for Symmetric, Stable Probability Distributions about?

Stable distributions is an interesting and important class of probability distributions. They were discovered explicitly by Paul L\'{e}vy in 1925 \cite{lk}. They possess many interesting properties, most importantly they are by definiton invariant under addition, up to a scale. Noteworthly they have power-law type of decay and therefore they are an excellent model for modelling many natural phenomena, such as earthquakes, financial returns, and a multitude of social phenomena such as size distributions of cities and firms \cite{scaling}. The major problem concerning them is that they have an infinite variance \cite{GK} and therefore their practical applicability is somewhat limited. Also they generally do not possess a density expressible in an analytic form. This study proposes a dispersion measure for them, drawing ideas from Fisher information, differential geometry and most importantly, the uncertainty principle for Fourier transform pairs \cite{Weyl}. The study begins with a brief discussion on characteristic functions and their relation to Fourier transforms and their properties, proceeds to a brief presentation of stable distributions and accumulates in defining a concept of

Author

Tyhtila, Jussi I.

Published

2007

Language

EN