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Fabretti, Annalisa; Leorato, Samantha

Random distributions via sequential quantile array. (English) Zbl 1462.60062

Electron. J. Stat. 14, No. 1, 1611-1647 (2020).
Summary: 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 T. Hill and M. Monticino [Ann. Stat. 26, No. 4, 1242–1253 (1998; Zbl 0955.60033)] 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.

MSC:

60G57 Random measures
62G07 Density estimation

Keywords:

quantiles; random probability measures; M-quantiles

Citations:

Zbl 0955.60033
Cite Review PDF
Full Text: DOI Euclid

References:

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