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See detailComputing system signatures through reliability functions
Marichal, Jean-Luc; Mathonet, Pierre ULg

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 ▲]

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See detailFurther comments on the representation problem for stationary processes
Laurent, Stéphane ULg

in Statistics & Probability Letters (2010), 80

We comment on some points about the coding of stochastic processes by sequences of independent random variables. The most interesting question has to do with the standardness property of the filtration ... [more ▼]

We comment on some points about the coding of stochastic processes by sequences of independent random variables. The most interesting question has to do with the standardness property of the filtration generated by the process, in the framework of Vershik's theory of filtrations. Non-standardness indicates the presence of long memory in a purely probabilistic sense. We aim to provide a short, non-technical presentation of Vershik's theory of filtrations. [less ▲]

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See detailImproved rank-based dependence measures for categorical data
Vandenhende, François; Lambert, Philippe ULg

in Statistics & Probability Letters (2003), 63

We extend rank-based dependence measures like Spearman's rho to categorical data so that the same ±1 limits are always reached under complete dependence. A goodness-of-fit procedure is derived for ... [more ▼]

We extend rank-based dependence measures like Spearman's rho to categorical data so that the same ±1 limits are always reached under complete dependence. A goodness-of-fit procedure is derived for dependence models using copulas. [less ▲]

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See detailThe breakdown behavior of the maximum likelihood estimator in the logistic regression model
Croux, C.; Flandre, C.; Haesbroeck, Gentiane ULg

in Statistics & Probability Letters (2002), 60(4), 377-386

In this note we discuss the breakdown behavior of the maximum likelihood (ML) estimator in the logistic regression model. We formally prove that the ML-estimator never explodes to infinity, but rather ... [more ▼]

In this note we discuss the breakdown behavior of the maximum likelihood (ML) estimator in the logistic regression model. We formally prove that the ML-estimator never explodes to infinity, but rather breaks down to zero when adding severe outliers to a data set. An example confirms this behavior. (C) 2002 Published by Elsevier Science B.V. [less ▲]

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