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The asymptotic hazard rate of sums of discrete random variables Arts, Joachim ; ; in Statistics & Probability Letters (2017), 125 Detailed reference viewed: 49 (7 UL)Computing subsignatures of systems with exchangeable component lifetimes Marichal, Jean-Luc in Statistics & Probability Letters (2014), 94 The subsignatures of a system with continuous and exchangeable component lifetimes form a class of indexes ranging from the Samaniego signature to the Barlow-Proschan importance index. These indexes can ... [more ▼] The subsignatures of a system with continuous and exchangeable component lifetimes form a class of indexes ranging from the Samaniego signature to the Barlow-Proschan importance index. These indexes can be computed through explicit linear expressions involving the values of the structure function of the system. We show how the subsignatures can be computed more efficiently from the reliability function of the system via identifications of variables, differentiations, and integrations. [less ▲] Detailed reference viewed: 104 (9 UL)Necessary and sufficient conditions for Hölder continuity of Gaussian processes Azmoodeh, Ehsan ; ; et al in Statistics & Probability Letters (2014), 94 The continuity of Gaussian processes is an extensively studied topic and it culminates in Talagrand’s notion of majorizing measures that gives complicated necessary and sufficient conditions. In this note ... [more ▼] The continuity of Gaussian processes is an extensively studied topic and it culminates in Talagrand’s notion of majorizing measures that gives complicated necessary and sufficient conditions. In this note we study the Hölder continuity of Gaussian processes. It turns out that necessary and sufficient conditions can be stated in a simple form that is a variant of the celebrated Kolmogorov–Čentsov condition. [less ▲] Detailed reference viewed: 40 (0 UL)Ito's formula for Walsh's Brownian motion and applications Hajri, Hatem ; in Statistics & Probability Letters (2014) Detailed reference viewed: 168 (31 UL)Computing system signatures through reliability functions Marichal, Jean-Luc ; Mathonet, Pierre in Statistics & Probability Letters (2013), 83(3), 710-717 It is known that the Barlow-Proschan index of a system with i.i.d. component lifetimes coincides with the Shapley value, a concept introduced earlier in cooperative game theory. Due to a result by Owen ... [more ▼] It is known that the Barlow-Proschan index of a system with i.i.d. component lifetimes coincides with the Shapley value, a concept introduced earlier in cooperative game theory. Due to a result by Owen, this index can be computed efficiently by integrating the first derivatives of the reliability function of the system along the main diagonal of the unit hypercube. The Samaniego signature of such a system is another important index that can be computed for instance by Boland's formula, which requires the knowledge of every value of the associated structure function. We show how the signature can be computed more efficiently from the diagonal section of the reliability function via derivatives. We then apply our method to the computation of signatures for systems partitioned into disjoint modules with known signatures. [less ▲] Detailed reference viewed: 117 (21 UL)Distribution functions of linear combinations of lattice polynomials from the uniform distribution Marichal, Jean-Luc ; in Statistics & Probability Letters (2008), 78(8), 985-991 We give the distribution functions, the expected values, and the moments of linear combinations of lattice polynomials from the uniform distribution. Linear combinations of lattice polynomials, which ... [more ▼] We give the distribution functions, the expected values, and the moments of linear combinations of lattice polynomials from the uniform distribution. Linear combinations of lattice polynomials, which include weighted sums, linear combinations of order statistics, and lattice polynomials, are actually those continuous functions that reduce to linear functions on each simplex of the standard triangulation of the unit cube. They are mainly used in aggregation theory, combinatorial optimization, and game theory, where they are known as discrete Choquet integrals and Lovász extensions. [less ▲] Detailed reference viewed: 37 (2 UL)Cumulative distribution functions and moments of lattice polynomials Marichal, Jean-Luc in Statistics & Probability Letters (2006), 76(12), 1273-1279 We give the cumulative distribution functions, the expected values, and the moments of lattice polynomials when regarded as real functions. Since lattice polynomial functions include order statistics, our ... [more ▼] We give the cumulative distribution functions, the expected values, and the moments of lattice polynomials when regarded as real functions. Since lattice polynomial functions include order statistics, our results encompass the corresponding formulas for order statistics. [less ▲] Detailed reference viewed: 64 (3 UL) |
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