A weak version of bivariate lack of memory property

作者：Kolev Nikolai^*; Pinto Jayme

来源：Brazilian Journal of Probability and Statistics (Brazilian Stat. Assoc.), 2018, 32(4): 873-906.

DOI：10.1214/17-BJPS371

• Bivariate Marshall-Olkin's exponential distribution
• copula
• closure properties
• failure rate
• lack of memory property
• non-aging and aging performance
• reliability
• stochastic representation
• singularity

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.

• 出版日期2018-11