Positive stable laws and M-scheme
Pestana, Dinis (1981)
Portugaliae mathematica
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Pestana, Dinis (1981)
Portugaliae mathematica
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Héctor M. Ramos Romero, Miguel Angel Sordo Díaz (2001)
Qüestiió
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In this paper, we introduce a new stochastic order between continuous non-negative random variables called the PLR (proportional likelihood ratio) order, which is closely related to the usual likelihood ratio order. The PLR order can be used to characterize random variables whose logarithms have log-concave (log-convex) densities. Many income random variables satisfy this property and they are said to have the IPLR (increasing proportional likelihood ratio) property (DPLR property)....
Janković, Slobodanka (1997)
Publications de l'Institut Mathématique. Nouvelle Série
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M. Fisz (1955)
Colloquium Mathematicae
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Kozubowski, Tomasz, Podgórski, Krzysztof (1999)
Serdica Mathematical Journal
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Let (Xi ) be a sequence of i.i.d. random variables, and let N be a geometric random variable independent of (Xi ). Geometric stable distributions are weak limits of (normalized) geometric compounds, SN = X1 + · · · + XN , when the mean of N converges to infinity. By an appropriate representation of the individual summands in SN we obtain series representation of the limiting geometric stable distribution. In addition, we study...
Brockett, Patrick L. (1978)
International Journal of Mathematics and Mathematical Sciences
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Aleksander Janicki (1999)
Applicationes Mathematicae
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We present a method of numerical approximation for stochastic integrals involving α-stable Lévy motion as an integrator. Constructions of approximate sums are based on the Poissonian series representation of such random measures. The main result gives an estimate of the rate of convergence of finite-dimensional distributions of finite sums approximating such stochastic integrals. Stochastic integrals driven by such measures are of interest in constructions of models for various problems...
Z. Rychlik (1985)
Banach Center Publications
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Klebanov, Lev, Rachev, Svetlozar (1996)
Serdica Mathematical Journal
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* Research supported by NATO GRANT CRG 900 798 and by Humboldt Award for U.S. Scientists. In this paper a general theory of a random number of random variables is constructed. A description of all random variables ν admitting an analog of the Gaussian distribution under ν-summation, that is, the summation of a random number ν of random terms, is given. The v-infinitely divisible distributions are described for these ν-summations and finite estimates of the approximation of ν-sum...
Agnieszka Jurlewicz
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Zakhar Kabluchko, Axel Munk (2009)
ESAIM: Probability and Statistics
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We generalize a theorem of Shao [ (1995) 575–582] on the almost-sure limiting behavior of the maximum of standardized random walk increments to multidimensional arrays of i.i.d. random variables. The main difficulty is the absence of an appropriate strong approximation result in the multidimensional setting. The multiscale statistic under consideration was used recently for the selection of the regularization parameter in a number of statistical algorithms as well...