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Polynomial probability distribution estimation using the method of moments
Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
Number of Authors: 3
2017 (English)In: PLoS ONE, ISSN 1932-6203, E-ISSN 1932-6203, Vol. 12, no 4, e0174573Article in journal (Refereed) Published
Abstract [en]

We suggest a procedure for estimating Nth degree polynomial approximations to unknown (or known) probability density functions (PDFs) based on N statistical moments from each distribution. The procedure is based on the method of moments and is setup algorithmically to aid applicability and to ensure rigor in use. In order to show applicability, polynomial PDF approximations are obtained for the distribution families Normal, Log-Normal, Weibull as well as for a bimodal Weibull distribution and a data set of anonymized household electricity use. The results are compared with results for traditional PDF series expansion methods of Gram-Charlier type. It is concluded that this procedure is a comparatively simple procedure that could be used when traditional distribution families are not applicable or when polynomial expansions of probability distributions might be considered useful approximations. In particular this approach is practical for calculating convolutions of distributions, since such operations become integrals of polynomial expressions. Finally, in order to show an advanced applicability of the method, it is shown to be useful for approximating solutions to the Smoluchowski equation.

Place, publisher, year, edition, pages
2017. Vol. 12, no 4, e0174573
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:su:diva-143594DOI: 10.1371/journal.pone.0174573ISI: 000399954800004PubMedID: 28394949OAI: oai:DiVA.org:su-143594DiVA: diva2:1104057
Available from: 2017-05-31 Created: 2017-05-31 Last updated: 2017-05-31Bibliographically approved

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CiteExportLink to record
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Citation style
  • apa
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