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2020 Random distributions via Sequential Quantile Array
Annalisa Fabretti, Samantha Leorato
Electron. J. Statist. 14(1): 1611-1647 (2020). DOI: 10.1214/20-EJS1697

Abstract

We propose a method to generate random distributions with known quantile distribution, or, more generally, with known distribution for some form of generalized quantile. The method takes inspiration from the random Sequential Barycenter Array distributions (SBA) proposed by Hill and Monticino (1998) which generates a Random Probability Measure (RPM) with known expected value. We define the Sequential Quantile Array (SQA) and show how to generate a random SQA from which we can derive RPMs. The distribution of the generated SQA-RPM can have full support and the RPMs can be both discrete, continuous and differentiable. We face also the problem of the efficient implementation of the procedure that ensures that the approximation of the SQA-RPM by a finite number of steps stays close to the SQA-RPM obtained theoretically by the procedure. Finally, we compare SQA-RPMs with similar approaches as Polya Tree.

Citation

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Annalisa Fabretti. Samantha Leorato. "Random distributions via Sequential Quantile Array." Electron. J. Statist. 14 (1) 1611 - 1647, 2020. https://doi.org/10.1214/20-EJS1697

Information

Received: 1 November 2018; Published: 2020
First available in Project Euclid: 9 April 2020

zbMATH: 07200238
MathSciNet: MR4082478
Digital Object Identifier: 10.1214/20-EJS1697

Subjects:
Primary: 60G57
Secondary: 62G07

Keywords: M-quantiles , quantiles , random probability measures

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Vol.14 • No. 1 • 2020
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