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1
Content available remote Laws of large numbers for two tailed Pareto random variables
100%
Adler A.
Probability and Mathematical Statistics
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2008
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tom Vol. 28, Fasc. 1
121--128
EN
We sample m random variables from a two tailed Pareto distribution. A two tailed Pareto distribution is a random variable whose right tail is px−2 and whose left tail is qx−2, where p + q = 1. Next, we look at the largest of these random variables and establish various Weak and Strong Laws that can be obtained with weighted sums of these random variables. The case of m = 1 is completely different from m > 1.
2
Content available remote Complete exact laws
100%
Adler A.
Probability and Mathematical Statistics
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2000
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tom Vol. 20, Fasc. 1
215--222
EN
Consider independent and identically distributed random variables {X,Xn, n ≥ 1} with xP{X > x} ~α(log x)α, where α > −1 and P{X < −x} = o(P{X > x}). Even though the mean does not exist, we establish Laws of Large Numbers of the form [formula].. for all ε > 0 and a particular nonsummable sequence {cn, n ≥ 1}, where L ≠ 0.
3
Content available remote A generalized Law of the Iterated Logarithm for the largest observation of a triangular array
100%
Adler A.
Probability and Mathematical Statistics
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2001
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tom Vol. 21, Fasc. 1
149--157
EN
Consider independent and identically distributed random variables {X, Xkj1≤j≤k, k≥1} from a particular distribution with EX=∞.Weshow that there exists an unusual generalized Law of the Iterated Logarithm involving max 1≤j≤kXkj.
4
Content available remote Limit theorems for arrays of maximal order statistics
100%
Adler A.
Probability and Mathematical Statistics
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2002
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tom Vol. 22, Fasc. 2
211--220
EN
Let {X, Xnj,1≤j≤mn, n≥1} be independent and identically distributed random variables with the Pareto distribution. Let Xn(k) be the k-th largestorder statistic from then-th row of our array. This paper establishes unusual limit theorems involving weighted sums for the sequence {Xn(k), n≥1}.
5
Content available remote On exact strong laws for sums of multidimensionally indexed random variables
63%
Adler A. , Qi Y.
Probability and Mathematical Statistics
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2003
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tom Vol. 23, Fasc. 2
305--313
EN
Let {X, Xn, n ∈ Zd+} be independent and identically distributed random variables satisfying xP (|X| > x) ≈ L(x) with either EX = 0 or E|X| = ∞, where L(x) is slowly varying at infinity. This paper proves that there always exist sequencesof constants {an} and {BN} such that an Exact Strong Law holds, that is [wzór] an Xn/BN → 1 almost surely as N → ∞.
6
Content available remote On exact strong laws of large numbers under general dependence conditions
63%
Adler A. , Matuła P.
Probability and Mathematical Statistics
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2018
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tom Vol. 38, Fasc. 1
103--121
EN
We study the almost sure convergence of weighted sums of dependent random variables to a positive and finite constant, in the case when the random variables have either mean zero or no mean at all. These are not typical strong laws and they are called exact strong laws of large numbers. We do not assume any particular type of dependence and furthermore consider sequences which are not necessarily identically distributed. The obtained results may be applied to sequences of negatively associated random variables.
7
Charakterystyka wartosci przemialowej i wypiekowej wybranych odmian orkiszu
51%
Makowska A. , Obuchowski W. , Adler A. , Sulewska H.
Fragmenta Agronomica
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2008
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tom 25
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nr 1
228-239
8
Content available remote Exact strong laws of large numbers for independent random fields
51%
Kurasiński P. , Matuła P. , Adler A.
Bulletin of the Polish Academy of Sciences. Mathematics
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2018
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tom Vol. 66, no. 2
179--188
EN
Let {Xṉ, ṉ ϵ Nd} be a family of independent random variables with multidimensional indices (a random field) with the same distribution as the r.v. X. A necessary and sufficient condition for the strong law of large numbers in this setting is E|X| logd-1+|X| < ∞. Our goal is to study the almost sure convergence of normalized or weighted sums in the case when this moment condition is not satisfied.
9
Moniliformin in durum wheat [Triticum durum]
51%
Adler A. , Lew H. , Edinger W. , Oberforster M.
Hodowla Roślin, Aklimatyzacja i Nasiennictwo
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1993
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tom 37
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nr 1-2
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