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November 2018 A weak version of bivariate lack of memory property
Nikolai Kolev, Jayme Pinto
Braz. J. Probab. Stat. 32(4): 873-906 (November 2018). DOI: 10.1214/17-BJPS371

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.

Citation

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Nikolai Kolev. Jayme Pinto. "A weak version of bivariate lack of memory property." Braz. J. Probab. Stat. 32 (4) 873 - 906, November 2018. https://doi.org/10.1214/17-BJPS371

Information

Received: 1 July 2016; Accepted: 1 August 2017; Published: November 2018
First available in Project Euclid: 17 August 2018

zbMATH: 06979605
MathSciNet: MR3845034
Digital Object Identifier: 10.1214/17-BJPS371

Rights: Copyright © 2018 Brazilian Statistical Association

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Vol.32 • No. 4 • November 2018
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