Stochastic precedence and minima among dependent variables.
| dc.contributor.author | De Santis, Emilio | |
| dc.contributor.author | Malinovsky, Yaakov | |
| dc.contributor.author | Spizzichino, Fabio | |
| dc.date.accessioned | 2019-10-08T15:50:55Z | |
| dc.date.available | 2019-10-08T15:50:55Z | |
| dc.date.issued | 2020-02-14 | |
| dc.description.abstract | Abstract. The notion of stochastic precedence between two random variables emerges as a relevant concept in several fields of applied probability. When one consider a vector of random variables X1, ..., Xn, this notion has a preeminent role in the analysis of minima of the type minj∈A Xj for A ⊂ {1, . . . n}. In such an analysis, however, several apparently controversial aspects can arise (among which phenomena of “nontransitivity”). Here we concentrate attention on vectors of non-negative random variables with absolutely continuous joint distributions, in which a case the set of the multivariate conditional hazard rate functions can be employed as a convenient method to describe different aspects of stochastic dependence. In terms of the m.c.h.r. functions, we first obtain convenient formulas for the probability distributions of the variables minj∈A Xj and for the probability of events {Xi = minj∈A Xj}. Then we detail several aspects of the notion of stochastic precedence. On these bases, we explain some controversial behavior of such variables and give sufficient conditions under which paradoxical aspects can be excluded. On the purpose of stimulating active interest of readers, we present several comments and pertinent examples. | en_US |
| dc.description.uri | https://link.springer.com/article/10.1007/s11009-020-09772-3 | en_US |
| dc.format.extent | 19 pages | en_US |
| dc.genre | journal articles | en_US |
| dc.genre | preprints | |
| dc.identifier | doi:10.13016/m2n39c-etvq | |
| dc.identifier.citation | De Santis, Emilio, Yaakov Malinovsky, and Fabio Spizzichino. “Stochastic Precedence and Minima Among Dependent Variables.” Methodology and Computing in Applied Probability 23, no. 1 (March 1, 2021): 187–205. https://doi.org/10.1007/s11009-020-09772-3. | en_US |
| dc.identifier.uri | http://hdl.handle.net/11603/14982 | |
| dc.identifier.uri | https://doi.org/10.1007/s11009-020-09772-3 | |
| dc.language.iso | en_US | en_US |
| dc.publisher | Springer Nature | |
| dc.relation.isAvailableAt | The University of Maryland, Baltimore County (UMBC) | |
| dc.relation.ispartof | UMBC Mathematics Department Collection | |
| dc.relation.ispartof | UMBC Faculty Collection | |
| dc.rights | This item is likely protected under Title 17 of the U.S. Copyright Law. Unless on a Creative Commons license, for uses protected by Copyright Law, contact the copyright holder or the author. | |
| dc.subject | Non-transitivity | en_US |
| dc.subject | aggregation/marginalization paradoxes | en_US |
| dc.subject | “small” variables | en_US |
| dc.subject | initially time–homogeneous models | en_US |
| dc.subject | time–homogeneous load sharing models | en_US |
| dc.title | Stochastic precedence and minima among dependent variables. | en_US |
| dc.type | Text | en_US |
| dcterms.creator | https://orcid.org/0000-0003-2888-674X |