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1
Content available remote On the monotonicity of tail probabilities
Fokkink Robbert, Pelekis Christos, Papavassiliou Symeon
Probability and Mathematical Statistics
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2022
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Vol. 42, Fasc. 1
133--141
EN
Let S and X be independent random variables, assuming values in the set of non-negative integers, and suppose further that both expectations ES and EX are integers satisfying ES>EX. We establish a sufficient condition for the tail probability P(S> ES) to be larger than the tail probability P(S+X> E(S+X)), when the mean of S is equal to the mode.
2
Badanie ruchu generowanego w sieci transmisyjnej przez dane telemetryczne pod kątem zbieżności z rozkładem Poissona
Torbus Sławomir Andrzej, Kreft Joanna, Wałaszewski Maksym, Woźniak Patrycja
Rynek Energii
|
2021
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Nr 3
79--84
PL
W części teoretycznej pracy scharakteryzowano rozkład Poissona oraz nieparametryczny test zgodności chi-kwadrat Pearsona. Przedstawiono również metodę weryfikacji hipotez dotyczących zbieżności dowolnego typu danych stanowiących zmienną losową, w tym wyników pomiarów, z rozkładem Poissona. Praktyczna część pracy polegała na określeniu zbieżności ruchu telekomunikacyjnego generowanego w sieci transmisji bezprzewodowej przez dane telemetryczne z rozkładem Poissona. Przeprowadzono szereg obliczeń dla rzeczywistych wyników uzyskanych podczas pomiarów dziennych, tygodniowych oraz miesięcznych, a następnie dokonano ich analizy i sformułowano wnioski.
EN
In the theoretical part of the work, the Poisson distribution and the nonparametric chi-square compatibility test of Pearson are characterized. A method of verification of hypotheses concerning the convergence of any type of data, including measurement results, which are a random variable with the Poisson distribution, was also presented. The practical part of the work consisted in determining the convergence of telecommunications traffic generated in a wireless transmission network by telemetry data with the Poisson distribution. A series of calculations was carried out for the actual results obtained during daily, weekly and monthly measurements, and then the obtained results were analyzed, and conclusions were formulated.
3
Content available remote Data driven efficient score tests for Poissonity
Inglot Tadeusz
Probability and Mathematical Statistics
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2019
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Vol. 39, Fasc. 1
115--126
EN
New data driven score tests for testing goodness of fit of the Poisson distribution are proposed. They are direct applications of the general construction of data driven goodness-of-fit tests for composite hypotheses developed in Inglot et al. (1997). By a simulation study it is shown that these tests perform almost equally well as the best known solutions for standard alternatives and outperform them for more difficult alternatives.
4
Content available Application of a single sampling plan minimizing the sum of risks in an EOQ model with trade credit
Veerakumari Pradeepa, Harikrishnan Aruna
Operations Research and Decisions
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2019
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Vol. 29, No. 1
121--130
EN
Acceptance sampling by attributes is a universally used statistical tool for quality control. It is a technique that deals with the decision to accept or reject a batch of goods using defined procedures. An attribute single sampling plan designed under the assumption that the number of defects has a Poisson distribution is the optimal plan whenever the chance of a defect occurring in the manufacturing process is low. This study introduces the incorporation of an attribute single sampling plan minimizing the sum of risks with an economic order quantity (EOQ) model taking into account the possibility of trade credit. The plan ensures the effectiveness of the optimal design based on the minimization of costs including the inspection costs, stock holding costs and ordering costs.
5
Content available Model symulacyjny gęstościomierza radiometrycznego
Joostberens J.
Systemy Wspomagania w Inżynierii Produkcji
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2017
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Vol. 6, iss. 2
126--134
PL
Gęstościomierze radiometryczne znajdują zastosowanie w układach monitoringu i sterowania różnych procesów technologicznych, w tym również procesów przeróbki węgla kamiennego takich jak: wzbogacanie w cieczy ciężkiej, wzbogacanie w osadzarce, flotacja węgla. Gęstościomierze te działają na zasadzie absorpcji promieniowania gamma. Głowica pomiarowa gęstościomierza składa się ze źródła promieniowania oraz detektora, zwykle w postaci licznika scyntylacyjnego. Sygnał z detektora promieniowania jest ciągiem impulsów, który jest sygnałem stochastycznym o rozkładzie czasowym Poissona. Impulsy te zliczane są często za pomocą licznika impulsów, stanowiącego rodzaj filtru dolnoprzepustowego. Zależność pomiędzy mierzoną średnią wartością gęstości ośrodka, a średnią częstością zliczanych impulsów ma teoretycznie charakter wykładniczy. W artykule przedstawiono model symulacyjny gęstościomierza radiometrycznego. Opisano metodę pomiarową oraz podano równania modelu gęstościomierza. Przedstawiono również przykładowe wyniki badań symulacyjnych w formie graficznej.
EN
Radiometric density meters are widely used in the industry to monitor different technological processes also in coal preparation such as: Heavy-media separation, Jigging, Flotation. Operation of the radiometric density meters is based on the method of gamma radiation absorption. The measuring head of the radiometric density meter consists of a radiation source and a detector usually in the form of a scintillation counter. The output signal from the detector is sequence of pulses which is always a stochastic signal with Poisson distribution. These pulses are often counted by a counter being a kind of a low-pass digital filter. The relation between the measured medium density and the mean intensity of registered pulses is theoretically exponential. In the paper there has been presented a simulation model of the radiometric density meter. There have been described the measurement method and given densitometer model equations. Example simulation results have also been presented in a graphic form.
6
Content available remote Forest Fire Models on Configuration Random Graphs
Leri M., Pavlov Y.
Fundamenta Informaticae
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2016
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Vol. 145, nr 3
313--332
EN
We consider a random process of fire propagation over the links of the two configuration graphs with random node degrees. Node degrees follow either the power-law or the Poisson distribution. A comparative analysis of these graph models in terms of the number of nodes remaining after the fire was performed. The conditions under which this number is greater for one or the other node degree distribution were found.
7
Testowanie hipotezy o rozkładzie Poissona w oparciu o statystykę Cramera – von Misesa
Rogowski A.
Logistyka
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2015
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nr 3
4162--4168, CD 1
PL
W pracy przedstawiono zasadnicze wyniki przedstawione przez Spinell’ego w pracy [12] odnośnie wykorzystania statystyki Cramera – von Misesa do testowania hipotezy o rozkładzie Poissona. Zdefiniowano cztery testy podając graniczne wartości krytyczne testów. Porównano moc rozpatrywanych testów i innych znanych testów zgodności do testowania hipotezy o rozkładzie Poissona. Zarekomendowano test Andersona-Darlinga A2 jako uniwersalny test do testowania hipotezy o rozkładzie Poissona wobec dowolnej hipotezy alternatywnej. Podano przykłady wykorzystania omawianych testów do weryfikacji rozkładu liczby statków na torze wodnym w sytuacji, gdy skorzystanie z testu chi-kwadrat jest niemożliwe bądź dyskusyjne ze względów merytorycznych.
EN
The paper presents the basic results reported by Spinelli in the work [12] on the use of statistics Cramer-von Mises for testing for the hypothesis of Poisson distribution. Defines four tests providing asymptotic critical values test. We compared the power of the tests considered and other known compatibility tests for testing for the hypothesis of Poisson distribution. Recommended the Anderson-Darling A2 test as a universal test for testing for the hypothesis of Poisson distribution against any alternative hypothesis. Are examples of the use of these tests to verify the distribution of the number of ships on the fairway where the use of the chi-square test is not possible or doubtful on the merits.
8
Content available remote On elementary characterizations of the α-modified Poisson distribution
Steliga K., Szynal D.
Probability and Mathematical Statistics
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2012
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Vol. 32, Fasc. 2
215--225
EN
In this article we give a characterization of α-modified Poisson distributions extending Chatterji’s result. Moreover, we consider the α-modified Poisson distributions of type j which are known as Delaporte distributions.
9
Content available remote Improved bounds on bell numbers and on moments of sums of random variables
Berend D., Tassa T.
Probability and Mathematical Statistics
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2010
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Vol. 30, Fasc. 2
185--205
EN
We provide bounds for moments of sums of sequences of independent random variables. Concentrating on uniformly bounded nonnegative random variables, we are able to improve upon previous results due to Johnson et al. [10] and Latała [12]. Our basic results provide bounds involving Stirling numbers of the second kind and Bell numbers. By deriving novel effective bounds on Bell numbers and the related Bell function, we are able to translate our moment bounds to explicit ones, which are tighter than previous bounds. The study was motivated by a problem in operation research, in which it was required to estimate the Lp-moments of sums of uniformly bounded non-negative random variables (representing the processing times of jobs that were assigned to some machine) in terms of the expectation of their sum.
10
Content available Funkcja wiodąca strumienia zgłoszeń statków na torze wodnym Szczecin - Świnoujście
Kasyk L.
Zeszyty Naukowe / Akademia Morska w Szczecinie
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2006
|
nr 11 (83)
123-130
PL
W artykule przedstawiono postać dyskretną funkcji wiodącej strumienia zgłoszeń jednostek torowych w trzech ujęciach czasowych: wielotygodniowym, tygodniowym i dobowym. Dla tego ostatniego ujęcia wyznaczono również postać ciągłą funkcji wiodącej. Wykorzystano dane dotyczące jednostek mijających linię raportową "Police", systemu VTS na torze wodnym Szczecin - Świnoujście.
EN
In this paper the leading function of a stream of fairway vessel reports has been determined. The discrete form of the leading function has been determined for three variants: "multiweekly", weekly and daily. For the latter the reports of ships passing the VTS reporting line "Police" on the Szczecin - Świnoujście fairway have been utilized.
11
Content available remote Analysis of Short Latencies In Industrial Network Environments
Morawski M.
Journal of Applied Computer Science
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2006
|
Vol. 14, nr 2
65-77
EN
The bibliography shows the typical shape of probability density function (PDF) that describe network latencies. The paper presents the results of the measurements of the PDF of Round Trip Time (RTT) in real network environments. The results show, that the appropriate PDFs are significantly differentiated and depend on the kind of the network, its load, peers load, logic of applications, etc. The PDF measurments is focused on industrial network control programs transmissions, where only loses and short delays are important.
12
An M/G/1 queue with Bernoulli schedules and Coxian-2 server vacations
Madan K.C., Jahromi M.M.J.
Systems Science
|
2003
|
Vol. 29, nr 4
69-83
EN
We study the time-dependent and the steady state behaviour of an M/G/1 queue with Bernoulli schedules and Coxian-2 server vacations. Customers arrive one by one at the system in a Poisson stream. The service time of a customer is assumed to be general (arbitrary). At each service completion epoch, the server may opt to take a vacation with probability p or else may continue to be available in the system. The vacation period of the server is assumed to have a Coxian-2 distribution. We obtain time-dependent probability generating functions for the queue size and the system size. The corresponding steady state results including the stability condition have been derived in explicit and closed forms. Some particular cases of interest including known results of the M/G/1 queue have been derived.
13
Computer modelling of operating processes for both simulational and experimental investigation of fracture problems
Čačko J.
Zeszyty Naukowe. Mechanika / Politechnika Opolska
|
2001
|
z. 67
7-26
EN
The problem of evaluation and computer modelling of operational processes with both continuous and discontinuous nature is presented in the paper. We suppose the knowledge of statistical characteristics of the continuous component in the frame of correlation theory - frequency probability density function of the distribution and power spectral density or autocorrelation function respectively. A simulation model is based on modelling of time-series with application for gaussian and nongaussian processes. Discontinuous events are assumed as a sequence of various impacts with Poissonian distribution, and they are superimposed to a continuous component. A cumulative damage is continuously evaluated regarding to a closed hysteresis loops counting. A fatigue damage mechanism is represented either by rainflow matrix or by a fatigue damage function. The function is specified using some hypothesis of a fatigue cumulative damage and fatigue failure criteria.
14
Content available remote Discontinuous metal films on dielectric substrates, their optical and electrical properties, structures and statistical descriptions
Dobierzewska-Mozrzymas E., Biegański P., Pieciul E.
Optica Applicata
|
2001
|
Vol. 31, nr 1
53-81
EN
A brief survey of some results concerning optical and electrical properties of discontinuous metal films on dielectric substrates and their statistical description is given. Optical properties (transmittance and imaginary part of dielectric permittivity spectra) of Al, Cu and Mn discontinuous films are presented and interpreted in terms of effective medium theories; modified Maxwell-Garnett and Bruggeman. The ranges of dielectric properties, the percolation threshold, and the range of metallic properties are determined for optical and electrical properties of the film examined. The considerations concerning electrical properties include such conduction mechanisms as metal conduction, substrate conduction, quantum tunneling, thermally activated tunneling and hopping. Real structures of the films are examined making use of electron microscope. Also the computer model for determining the contribution of the fundamental conduction mechanisms in discontinuous films is introduced. The inverse power law is used to describe the structure and the statistical distributions of inhomogeneous films of Au, Cu and Mn on dielectric substrates. To this end, the rank of an island is connected with its area for the films with different coverage coefficients (metal content). The dependencies of the island areas on the rank orders in a double-logarithmic plot are straight lines according to the Mandelbrot law. The slope of the straight line characterises the ranges of the distributions of the islands: (i) the log-normal or the Gaussian one (with two parameters of statistical distribution-the mean value and the variance), (ii) the Poisson distribution (with one parameter-the mean value), (iii) Levy stable distribution (the parameters of distribution are infinite). The correlation between optical and electrical properties of discontinuous metal films and their structures and statistical description is found.
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