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On univariate and bivariate aging for dependent lifetimes with Archimedean survival copulas

Franco Pellerey (2008)

Kybernetika

Let 𝐗 = ( X , Y ) be a pair of exchangeable lifetimes whose dependence structure is described by an Archimedean survival copula, and let 𝐗 t = [ ( X - t , Y - t ) | X > t , Y > t ] denotes the corresponding pair of residual lifetimes after time t , with t 0 . This note deals with stochastic comparisons between 𝐗 and 𝐗 t : we provide sufficient conditions for their comparison in usual stochastic and lower orthant orders. Some of the results and examples presented here are quite unexpected, since they show that there is not a direct correspondence between univariate...

On useful schema in survival analysis after heart attack

Czesław Stępniak (2014)

Discussiones Mathematicae Probability and Statistics

Recent model of lifetime after a heart attack involves some integer coefficients. Our goal is to get these coefficients in simple way and transparent form. To this aim we construct a schema according to a rule which combines the ideas used in the Pascal triangle and the generalized Fibonacci and Lucas numbers

Optimal mean-variance bounds on order statistics from families determined by star ordering

Tomasz Rychlik (2002)

Applicationes Mathematicae

We present optimal upper bounds for expectations of order statistics from i.i.d. samples with a common distribution function belonging to the restricted family of probability measures that either precede or follow a given one in the star ordering. The bounds for families with monotone failure density and rate on the average are specified. The results are obtained by projecting functions onto convex cones of Hilbert spaces.

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