Displaying similar documents to “Exact laws for sums of ratios of order statistics from the Pareto distribution”

An almost sure limit theorem for moving averages of random variables between the strong law of large numbers and the Erdös-Rényi law

Hartmut Lanzinger (2010)

ESAIM: Probability and Statistics

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We prove a strong law of large numbers for moving averages of independent, identically distributed random variables with certain subexponential distributions. These random variables show a behavior that can be considered intermediate between the classical strong law and the Erdös-Rényi law. We further show that the difference from the classical behavior is due to the influence of extreme terms.

One sided strong laws for random variables with infinite mean

André Adler (2017)

Open Mathematics

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This paper establishes conditions that secure the almost sure upper and lower bounds for a particular normalized weighted sum of independent nonnegative random variables. These random variables do not possess a finite first moment so these results are not typical. These mild conditions allow us to show that the almost sure upper limit is infinity while the almost sure lower bound is one.

Inequalities and limit theorems for random allocations

Istvan Fazekas, Alexey Chuprunov, Jozsef Turi (2011)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

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Random allocations of balls into boxes are considered. Properties of the number of boxes containing a fixed number of balls are studied. A moment inequality is obtained. A merge theorem with Poissonian accompanying laws is proved. It implies an almost sure limit theorem with a mixture of Poissonian laws as limiting distribution. Almost sure versions of the central limit theorem are obtained when the parameters are in the central domain.

Further study on complete convergence for weighted sums of arrays of rowwise asymptotically almost negatively associated random variables

Haiwu Huang, Hanjun Zhang, Qingxia Zhang, Jiangyan Peng (2015)

Kybernetika

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In this paper, the authors further studied the complete convergence for weighted sums of arrays of rowwise asymptotically almost negatively associated (AANA) random variables with non-identical distribution under some mild moment conditions. As an application, the Marcinkiewicz-Zygmund type strong law of large numbers for weighted sums of AANA random variables is obtained. The results not only generalize the corresponding ones of Wang et al. [19], but also partially improve the corresponding...

Inequalities and limit theorems for random allocations

István Fazekas, Alexey Chuprunov, József Túri (2011)

Annales UMCS, Mathematica

Similarity:

Random allocations of balls into boxes are considered. Properties of the number of boxes containing a fixed number of balls are studied. A moment inequality is obtained. A merge theorem with Poissonian accompanying laws is proved. It implies an almost sure limit theorem with a mixture of Poissonian laws as limiting distribution. Almost sure versions of the central limit theorem are obtained when the parameters are in the central domain.

Laws of large numbers for ratios of uniform random variables

André Adler (2015)

Open Mathematics

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Let {Xnn n ≥ 1} and {Yn, n ≥ 1} be two sequences of uniform random variables. We obtain various strong and weak laws of large numbers for the ratio of these two sequences. Even though these are uniform and naturally bounded random variables the ratios are not bounded and have an unusual behaviour creating Exact Strong Laws.