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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

A weak version of bivariate lack of memory property

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Author(s):
Kolev, Nikolai [1] ; Pinto, Jayme [1]
Total Authors: 2
Affiliation:
[1] Univ Sao Paulo, Dept Stat, Rua Matao 1010, BR-05508090 Sao Paulo - Brazil
Total Affiliations: 1
Document type: Journal article
Source: BRAZILIAN JOURNAL OF PROBABILITY AND STATISTICS; v. 32, n. 4, p. 873-906, NOV 2018.
Web of Science Citations: 1
Abstract

We suggest a modification of the classical Marshall-Olkin's bivariate exponential distribution considering a possibility of a singularity contribution along arbitrary line through the origin. It serves as a base of a new weaker version of the bivariate lack of memory property, which might be both ``aging{''} and ``non-aging{''} depending on the additional inclination parameter. The corresponding copula is obtained and we establish its disagreement with Lancaster's phenomena. Characterizations and properties of the novel bivariate memory-less notion are obtained and its applications are discussed. We characterize associated weak multivariate version. The weak bivariate lack of memory property implies restrictions on the marginal distributions. Starting from pre-specified marginals we propose a procedure to build bivariate distributions possessing a weak bivariate lack of memory property and illustrate it by examples. We complement the methodology with closure properties of the new class. We finish with a discussion and suggest several related problems for future research. (AU)

FAPESP's process: 13/07375-0 - CeMEAI - Center for Mathematical Sciences Applied to Industry
Grantee:Francisco Louzada Neto
Support Opportunities: Research Grants - Research, Innovation and Dissemination Centers - RIDC