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IfX1, ...,Xnare random variables we denote byX(1)[less-than-or-equals, slant]X(2)[less-than-or-equals, slant]...[less-than-or-equals, slant]X(n)their respective order statistics. In the case where the random variables are independent and identically distributed, one may demonstrate very strong...
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Let N(t) be a non-homogeneous Poisson process with mean value function [Lambda](t) and rate of occurrence [lambda](t). We propose a conditional test of the hypothesis that the process is homogeneous, versus alternatives for which the mean value function is superadditive. Specific models leading...
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Several relativistic extensions of the Maxwell–Boltzmann distribution have been proposed, but they do not explain observed lognormal tail-behavior in the flux distribution of various astrophysical sources. Motivated by this question, extensions of classical central limit theorems are developed...
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A weighted least squares estimator is used to estimate the hazard functions in Aalen's additive risk model from grouped (and possibly censored) survival data. Counting process techniques are applied to derive a functional central limit theorem for the integrated estimator.
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