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Polynomial probability distribution estimation using the method of moments
Uppsala University, Disciplinary Domain of Science and Technology, Technology, Department of Engineering Sciences, Solid State Physics. (Built Environment Energy Systems Group)ORCID iD: 0000-0003-0051-4098
Nordita, Stockholms University.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.ORCID iD: 0000-0002-5451-4563
2017 (English)In: PLoS ONE, ISSN 1932-6203, E-ISSN 1932-6203, Vol. 12, no 4, 1-14 p., 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, 1-14 p., e0174573
National Category
Probability Theory and Statistics Engineering and Technology
Identifiers
URN: urn:nbn:se:uu:diva-319998DOI: 10.1371/journal.pone.0174573ISI: 000399954800004PubMedID: 28394949OAI: oai:DiVA.org:uu-319998DiVA: diva2:1088350
Funder
Swedish Energy AgencySwedish Research Council, 2015-04505
Available from: 2017-04-12 Created: 2017-04-12 Last updated: 2017-06-09Bibliographically approved

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