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1
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Goodness-of-fit tests derived from characterizations of continuous distributions

100%
Szynal D.
Banach Center Publications
|
2010
|
tom 90
|
nr 1
203-223
EN
Starting from characterizations of continuous distributions in terms of the expected values of two functions of record values we construct a family of goodness-of-fit tests calculated from U-statistics.
2
Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik
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Review: Dobiesław Bobrowski; Probabilistic in technical applications

100%
Szynal D.
Mathematica Applicanda
|
1983
|
tom 11
|
nr 22
PL
Artykuł nie zawiera streszczenia
EN
The article contains no abstract
3
Content available remote

On functional measures of skewness

64%
Dziubińska R., Szynal D.
Applicationes Mathematicae
|
1995-1996
|
tom 23
|
nr 4
395-403
EN
We introduce a concept of functional measures of skewness which can be used in a wider context than some classical measures of asymmetry. The Hotelling and Solomons theorem is generalized.
4
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Characterizations of uniform and exponential distributions via moments of the kth record values randomly indexed

64%
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.
5
Content available remote

On formulae for central moments of counting distributions

64%
Steliga K., Szynal D.
Applicationes Mathematicae
|
2015
|
tom 42
|
nr 1
111-124
EN
The aim of this article is to give new formulae for central moments of the binomial, negative binomial, Poisson and logarithmic distributions. We show that they can also be derived from the known recurrence formulae for those moments. Central moments for distributions of the Panjer class are also studied. We expect our formulae to be useful in many applications.
6
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On existence and an asymptotic behavior of random solutions of a class of stochastic functional-integral equations

64%
Szynal D., Wędrychowicz S.
Colloquium Mathematicum
|
1987
|
tom 51
|
nr 1
349-364
7
Content available remote

On the compound α(t)-modified Poisson distribution

64%
Steliga K., Szynal D.
Applicationes Mathematicae
|
2015
|
tom 42
|
nr 4
359-377
EN
In this paper we introduce compound α(t)-modified Poisson distributions. We obtain the compound Delaporte distribution as the special case of the compound α(t)-modified Poisson distribution. The characteristics of α(t)-modified Poisson and some compound distributions with gamma, exponential and Panjer summands are presented.
8
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Goodness-of-fit tests based on characterizations of continuous distributions

64%
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].
9
Content available remote

On monotone dependence functions of the quantile type

64%
Krajka A., Szynal D.
Applicationes Mathematicae
|
1995-1996
|
tom 23
|
nr 1
51-72
EN
We introduce the concept of monotone dependence function of bivariate distributions without moment conditions. Our concept gives, among other things, a characterization of independent and positively (negatively) quadrant dependent random variables.
10
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Characterizations of the inverse Weibull distribution and generalized extreme value distributions by moments of kth record values

64%
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.
11
Content available remote

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

64%
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.
12
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The Kalman filter in the case where exists correlation between noises of the plant and meter

64%
Kowalski A., Szynal D.
Mathematica Applicanda
|
1985
|
tom 13
|
nr 26
PL
W pracy sformułujemy i rozwiążemy problem liniowej filtracji z czasem dyskretnym, dopuszczającej w modelu Kalmana istnienie korelacji między szumem obiektu a szumem urządzenia pomiarowego w chwili k oraz między szumem obiektu w chwili k a szumem urządzenia pomiarowego w chwili k+1. Rozpatrywany model pojawia się wtedy, gdy szum urządzenia pomiarowego zniekształca stan układu w chwili pomiaru i wpływa na stan układu w chwili następnej. Ponadto podajemy rozwiązanie problemu dualnego w rozważanym uogólnieniu filtracji Kalmana.
EN
The paper is concerned with a problem of optimal linear filtering in the case where exists correlation between the noises w(k) of the plant and noises v(k) and v(k+1) of the meter. The algorithm obtained contains the classical Kalman's solution and its generalization given by Simkin [5]. The dual problem under these conditions is also considered.
13
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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

64%
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.
14
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On the Bayes estimators of the parameters of inflated modified power series distributions

64%
Murat M., Szynal D.
Discussiones Mathematicae Probability and Statistics
|
2000
|
tom 20
|
nr 2
189-209
EN
In this paper, we study the class of inflated modified power series distributions (IMPSD) where inflation occurs at any of support points. This class includes among others the generalized Poisson,the generalized negative binomial and the lost games distributions. We derive the Bayes estimators of parameters for these distributions when a parameter of inflation is known. First, we take as the prior distribution the uniform, Beta and Gamma distribution. In the second part of this paper, the prior distribution is the generalized Pareto distribution.
15
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On two families of tests for normality with empirical description of their performances

64%
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.
16
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Moments of counting distributions satisfying recurrence relations

64%
Murat M., Szynal D.
Mathematica Applicanda
|
2000
|
tom 28
|
nr 42/01
PL
Artykuł nie zawiera streszczenia
EN
The article contains no abstract
17
Content available remote

On random split of the segment

64%
Bieniek M., Szynal D.
Applicationes Mathematicae
|
2005
|
tom 32
|
nr 3
243-261
EN
We consider a partition of the interval [0,1] by two partition procedures. In the first a chosen piece of [0,1] is split into halves, in the second it is split by uniformly distributed points. Initially, the interval [0,1] is divided either into halves or by a uniformly distributed random variable. Next a piece to be split is chosen either with probability equal to its length or each piece is chosen with equal probability, and then the chosen piece is split by one of the above procedures. These actions are repeated indefinitely. We investigate the probability distribution of the lengths of the consecutive pieces after n splits.
18
Content available remote

Goodness-of-fit tests using characterizations of continuous distributions

64%
Morris K., Szynal D.
Applicationes Mathematicae
|
2001
|
tom 28
|
nr 2
151-168
EN
Using characterization conditions of continuous distributions in terms of moments of order statistics and moments of record values we present new goodness-of-fit techniques.
19
Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik
Content available

La convergence en probabilité et la convergence presque sûre de certaines suites de variables aléatoires dépendantes

63%
Szynal D.
Colloquium Mathematicum
|
1970
|
tom 21
|
nr 2
321-338
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