APPROXIMATING PROBABILITY DISTRIBUTION FUNCTIONS WITH FEW MOMENTS

Authors

  • Emilio Wille UTFPR

DOI:

https://doi.org/10.52292/j.laar.2020.132

Keywords:

Moment problem, Sum of RVs, Product of RVs, Piecewise linear functions, Five-parameter logistic function

Abstract

A procedure is presented for approximating a given probability distribution function
or statistical data considering a subset of their moments.
This is done by a method of fitting moments of a piecewise linear function
to the moments of the known data. The approach has many advantages over popular approximation approaches.
The procedure is demonstrated with commonly used cdfs (Exponential, Gamma, Log-Normal, Normal) and
more difficult problems involving sum and product of random variables,
obtaining good agreement between the theoretical/simulation curves and the piecewise linear approximations.

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Published

2019-11-07

Issue

Vol. 50 No. 1 (2020): Latin American Applied Research

Section

Control and Information Processing

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