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1
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Compound Poisson approximation for extremes of moving minima in arrays of independent random variables

100%
Dudkiewicz J.
Applicationes Mathematicae
|
1998-1999
|
tom 25
|
nr 1
19-28
EN
We present conditions sufficient for the weak convergence to a compound Poisson distribution of the distributions of the kth order statistics for extremes of moving minima in arrays of independent random variables.
2
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The Beta(p,1) extensions of the random (uniform) Cantor sets

88%
Pestana D., Aleixo S., Leonel Rocha J.
Discussiones Mathematicae Probability and Statistics
|
2009
|
tom 29
|
nr 2
199-221
EN
Starting from the random extension of the Cantor middle set in [0,1], by iteratively removing the central uniform spacing from the intervals remaining in the previous step, we define random Beta(p,1)-Cantor sets, and compute their Hausdorff dimension. Next we define a deterministic counterpart, by iteratively removing the expected value of the spacing defined by the appropriate Beta(p,1) order statistics. We investigate the reasons why the Hausdorff dimension of this deterministic fractal is greater than the Hausdorff dimension of the corresponding random fractals.
3
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Recurrence relations for conditional moment generating functions of order statistics and record values

88%
AL-Hussaini E., Ahmad A. E.-B., El-Boghdady H.
Discussiones Mathematicae Probability and Statistics
|
2005
|
tom 25
|
nr 2
181-205
EN
In this paper, recurrence relations for conditional moment generating functions and conditional moments of order statistics and record values based on random samples drawn from members of a class of doubly truncated distributions Ád are obtained.
4
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Exact laws for sums of ratios of order statistics from the Pareto distribution

75%
Adler A.
Open Mathematics
|
2006
|
tom 4
|
nr 1
1-4
EN
Consider independent and identically distributed random variables {X nk, 1 ≤ k ≤ m, n ≤ 1} from the Pareto distribution. We select two order statistics from each row, X n(i) ≤ X n(j), for 1 ≤ i < j ≤ = m. Then we test to see whether or not Laws of Large Numbers with nonzero limits exist for weighted sums of the random variables R ij = X n(j)/X n(i).
5
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Characterizations of uniform and exponential distributions via moments of the kth record values randomly indexed

75%
Grudzień Z., Szynal D.
Applicationes Mathematicae
|
1996-1997
|
tom 24
|
nr 3
307-314
EN
We characterize uniform and exponential distributions via moments of the kth record statistics. Too and Lin's (1989) results are contained in our approach.
6
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Goodness-of-fit tests based on characterizations of continuous distributions

75%
Morris K., Szynal D.
Applicationes Mathematicae
|
2000
|
tom 27
|
nr 4
475-488
EN
We construct goodness-of-fit tests for continuous distributions using their characterizations in terms of moments of order statistics and moments of record values. Our approach is based on characterizations presented in [2]-[4], [5], [9].
7
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Characterizations of the inverse Weibull distribution and generalized extreme value distributions by moments of kth record values

75%
Pawlas P., Szynal D.
Applicationes Mathematicae
|
2000
|
tom 27
|
nr 2
197-202
EN
We give characterization conditions for the inverse Weibull distribution and generalized extreme value distributions by moments of kth record values.
8
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Recurrence relations for single and product moments of k-th lower record values from the inverse distributions of Pareto's type and characterizations

75%
Pawlas P., Szynal D.
Discussiones Mathematicae Probability and Statistics
|
2000
|
tom 20
|
nr 2
223-231
EN
We give recurrence relations for single and product moments of k-th lower record values from the inverse Pareto, inverse generalized Pareto and inverse Burr distributions. We present also characterization conditions for these distributions.
9
Content available remote

Characterizations of distributions by moments of order statistics when the sample size is random

63%
Grudzień Z., Szynal D.
Applicationes Mathematicae
|
1995-1996
|
tom 23
|
nr 3
305-318
EN
We give characterizations of the uniform distribution in terms of moments of order statistics when the sample size is random. Special cases of a random sample size (logarithmic series, geometrical, binomial, negative binomial, and Poisson distribution) are also considered.
10
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k-th rekord values from Dagum distribution and characterization

63%
Kumar D.
Discussiones Mathematicae Probability and Statistics
|
2016
|
tom 36
|
nr 1-2
25-41
EN
In this study, we gave some new explicit expressions and recurrence relations satisfied by single and product moments of k-th lower record values from Dagum distribution. Next we show that the result for the record values from the Dagum distribution can be derived from our result as special case. Further, using a recurrence relation for single moments and conditional expectation of record values we obtain characterization of Dagum distribution. In addition, we use the established explicit expression of single moment to compute the mean, variance, coefficient of skewness and coefficient of kurtosis. Finally, we suggest two applications.
11
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On two families of tests for normality with empirical description of their performances

63%
Szynal D., Wołyński W.
Discussiones Mathematicae Probability and Statistics
|
2014
|
tom 34
|
nr 1-2
169-185
EN
We discuss two families of tests for normality based on characterizations of continuous distributions via order statistics and record values. Simulations of their powers show that they are competitive to widely recommended tests in the literature.
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