University of Oulu

Terhi Mäkinen & Lasse Holmström (2017) Modeling probability density through ultraspherical polynomial transformations, Communications in Statistics - Simulation and Computation, 46:8, 5879-5900, DOI: 10.1080/03610918.2016.1186181

Modeling probability density through ultraspherical polynomial transformations

Saved in:
Author: Mäkinen, Terhi1; Holmström, Lasse2
Organizations: 1Finnish Meteorological Institute, Helsinki, Finland
2Department of Mathematical Sciences, University of Oulu, Oulu, Finland
Format: article
Version: accepted version
Access: open
Online Access: PDF Full Text (PDF, 0.4 MB)
Persistent link:
Language: English
Published: Informa, 2017
Publish Date: 2017-11-20


We present a method for fitting parametric probability density models using an integrated square error criterion on a continuum of weighted Lebesgue spaces formed by ultraspherical polynomials. This approach is inherently suitable for creating mixture model representations of complex distributions and allows fully autonomous cluster analysis of high-dimensional datasets. The method is also suitable for extremely large sets, allowing post facto model selection and analysis even in the absence of the original data. Furthermore, the fitting procedure only requires the parametric model to be pointwise evaluable, making it trivial to fit user-defined models through a generic algorithm.

see all

Series: Communications in statistics. B, Simulation and computation
ISSN: 0361-0918
ISSN-E: 1532-4141
ISSN-L: 0361-0918
Volume: 46
Issue: 8
Pages: 5879 - 5900
DOI: 10.1080/03610918.2016.1186181
Type of Publication: A1 Journal article – refereed
Field of Science: 112 Statistics and probability
Funding: Work of LH supported by grant no. 24301034 from the Academy of Finland.
Academy of Finland Grant Number: 250862
Detailed Information: 250862 (Academy of Finland Funding decision)
Copyright information: This is an Accepted Manuscript of an article published by Taylor & Francis in Communications in statistics: simulation and computation on 27 May 2016, available online: