Wyniki wyszukiwania - Biblioteka Nauki

1

Power Size Biased Two-Parameter Akash Distribution

100%

Alhyasat K. , Kamarulzaman I. , Al-Omari A. I. , Bakar M. A. A.

Statistics in Transition new series

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2020

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tom 21

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nr 3

73-91

EN

In this paper, the two-parameter Akash distribution is generalized to size-biased two parameter Akash distribution (SBTPAD). A further modification to SBTPAD is introduced, creating the power size-biased two-parameter Akash distribution (PSBTPAD). Several statistical properties of PSBTPAD distribution are proved. These properties include the following: moments, coefficient of variation, coefficient of skewness, coefficient of kurtosis, the maximum likelihood estimation of the distribution parameters, and finally order statistics. Moreover, plots of the density and distribution functions of PSBTPAD are presented and a reliability analysis is considered. The Rényi entropy of PSBTPAD is proved and the application of real data is discussed.

2

Uwagi o wzorze na momenty rozkładu prawdopodobieństwa Pólyi

67%

Gerstenkorn T.

Śląski Przegląd Statystyczny

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2015

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nr 13 (19)

131-135

EN

The probability distribution of a random variable can be characterized by some numbers called parameters of the distribution. The most commonly used parameters are the moments. Our attention is concentrated on the Pólya distribution because it is easily possible to obtain from it some special cases very important in the statistics distri-butions such as binomial, negative binomial and Poisson (in the limit procedure). In 1972 G. Mühlbach introduced very interesting formulae for the moments of the Pólya distribu-tion. The author did not investigate an appreciation of the numerical efficacy of the for-mula for the simple moments. We will show that it is possible to demonstrate this formula in a simpler form. It has a practical significance and importance.

3

Remarks on the generalized doubly truncated gamma distribution

54%

Gerstenkorn T. , Gerstenkorn J. , Tadeusz Gerstenkorn U. o. Ł. , Joanna Gerstenkorn U. o. Ł.

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tom 141

EN

In the present paper we discuss a doubly truncated generalized gamma distribution and give formulae for the moments of this distribution and special cases together with examples of calculations.

4

Application of the Moment Shape Representations to the General Shape Analysis

54%

Frejlichowski D.

Image Processing & Communications

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2016

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tom Vol. 21, no. 4

31--38

EN

The General Shape Analysis (GSA) is a task similar to the shape recognition and retrieval. However, in GSA an object usually does not belong to a template class, but can only be similar to some of them. Moreover, the number of applied templates is limited. Usually, ten most general shapes are used. Hence, the GSA consists in searching for the most universal information about them. This is useful when some general information has to be concluded, e.g. in coarse classification. In this paper the result of the application of three shape descriptors based on the moment theory to the GSA is presented. For this purpose the Moment Invariants, Contour Sequence Moments, and Zernike Moments were selected.

5

Méthodes de réalisation de produit scalaire et de problème de moments avec maximisation d'entropie

54%

Girardin V.

Studia Mathematica

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1997

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tom 124

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nr 3

199-213

EN

We develop several methods of realization of scalar product and generalized moment problems. Constructions are made by use of a Hilbertian method or a fixed point method. The constructed solutions are rational fractions and exponentials of polynomials. They are connected to entropy maximization. We give the general form of the maximizing solution. We show how it is deduced from the maximizing solution of the algebraic moment problem.

6

Korovkin theorem in modular spaces

54%

Bardaro C. , Mantellini I.

Commentationes Mathematicae

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2007

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tom 47

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nr 2

EN

In this paper we obtain an extension of the classical Korovkin theorem in abstract modular spaces. Applications to some discrete and integral operators are discussed.

7

Korovkin theorem in modular spaces

54%

Bardaro C. , Mantellini I.

Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae

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2007

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tom Vol. 47, [Z] 2

239-253

EN

In this paper we obtain an extension of the classical Korovkin theorem in abstract modular spaces. Applications to some discrete and integral operators are discussed.

8

Alternative approach to moments of order statistics from one-parameter Weibull distribution

54%

Rai P. K. , Sirohi A.

Statistics in Transition new series

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2020

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tom 21

|

nr 1

169-176

EN

The Weibull distribution is used to describe various observed failures of phenomena and widely used in survival analysis and reliability theory. Sometimes it is very difficult to compute moments of such distributions due to various reasons for e.g. analytical issues, multi parameter cases etc. This study presents the computation of the moments and the expected value of the product of order statistics in the sample from the one-parameter Weibull distribution. An alternative approach in connection to survival function is used to obtain these moments and expected values. In addition the characteristic function of the above distribution is also obtained in the form of gamma functions. Further an illustration is shown to find the first two moments and expected value of the product of order statistics by using this approach.

9

On SαS density function

54%

Mazurkiewicz G.

Discussiones Mathematicae Probability and Statistics

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2005

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tom 25

|

nr 1

91-101

EN

In this paper, we study some analytical properties of the symmetric α-stable density function.

10

A characterization of probability measures by f-moments

54%

Urbanik K.

Studia Mathematica

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1996

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tom 118

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nr 2

185-204

EN

Given a real-valued continuous function ƒ on the half-line [0,∞) we denote by P*(ƒ) the set of all probability measures μ on [0,∞) with finite ƒ-moments $ʃ_{0}^{∞} ƒ(x)μ^{*n}(dx)$ (n = 1,2...). A function ƒ is said to have the identification property} if probability measures from P*(ƒ) are uniquely determined by their ƒ-moments. A function ƒ is said to be a Bernstein function} if it is infinitely differentiable on the open half-line (0,∞) and $(-1)^{n} ƒ^{(n+1)}(x)$ is completely monotone for some nonnegative integer n. The purpose of this paper is to give a necessary and sufficient condition in terms of the representing measures for Bernstein functions to have the identification property.

11

Odd log-logistic generalised Lindley distribution with properties and applications

47%

Ranjbar V. , Eftekharian A. , Kharazmi O. , Alizadeh M.

Statistics in Transition new series

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2023

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tom 24

|

nr 4

71-92

EN

In this paper, a new three-parameter lifetime model, called the odd log-logistic generalised Lindley distribution, is introduced. Some structural properties of the new distribution including ordinary and incomplete moments, quantile and generating functions and order statistics are obtained. The new density function can be expressed as a linear mixture of exponentiated Lindley densities. Different methods are discussed to estimate the model parameters and a simulation study is carried out to show the performance of the new distribution. The importance and flexibility of the new model are also illustrated empirically by means of two real data sets. Finally, Bayesian analysis and Gibbs sampling are performed based on the two real data sets.

12

The application of cumulants to flow routing

47%

Romanowicz R. J. , Doroszkiewicz J.

Meteorology Hydrology and Water Management. Research and Operational Applications

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2019

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tom Vol. 7, Iss. 1

15--21

EN

This paper aims to fill a gap between present and past research approaches to modelling flow in open channels. In particular, a history of the analytical solutions of a linearized St. Venant equation is presented. A solution of the linearized St. Venant equation, describing the response of a river channel to a single impulse forcing, the so called Instantaneous Unit Hydrograph (IUH), can be described using cumulants, defined as the moments of a logarithm of a variable. A comparison of analytical and numerical solutions of flood wave propagation under various flow conditions is given. The river reach of Biała Tarnowska is used as an illustration of both approaches. A practical application of simplified solutions to the emulator of a flood wave propagation is suggested showing a link between theory and practice.

13

Characteristics of bivariate binomial distribution

47%

Wagner W. , Wyższa Szkoła Informatyki i Zarządzania w Rzeszowie; Wydział Turystyki i Nauk o Zdrowiu; Katedra Turystyki i Rekreacji

Acta Universitatis Lodziensis. Folia Oeconomica

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2011

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tom 255

PL

W pracy podano jeden z wielu możliwych sposobów określenia dwuwymiarowego rozkładu dwumianowego. Inne możliwości są wymieniane w pracy Johnsona i in. (1997, s. 31–92). Mają one związek z rozkładem wielomianowym. Podejście proponowane w pracy jest naturalnym rozszerzeniem jednowymiarowego rozkładu zero-jedynkowego i rozkładu dwumianowego. W przypadku dwuwymiarowym proponowana w pracy postać funkcji charakterystycznej w formie rozpisanej i wektorowej pozwoliła na wyprowadzenie wzorów na momenty zwykle i mieszane. Dwuwymiarowy rozkład dwumianowy przy liczbie prób n dążących do nieskończoności przechodzi w dwuwymiarowy rozkład Poissona. a przy pewnych n, p 1 , p 2 przechodzi w graniczny dwuwymiarowy rozkład normalny. Dwuwymiarowy rozkład dwumianowy daje się rozszerzyć na przypadek wielowymiarowy (Johnson i in. 1997. s. 105–113).

14

Transmuted Kumaraswamy Distribution

47%

Khan M. S. , King R. , Hudson I. L.

Statistics in Transition new series

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2016

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tom 17

|

nr 2

183-210

EN

The Kumaraswamy distribution is the most widely applied statistical distribution in hydrological problems and many natural phenomena. We propose a generalization of the Kumaraswamy distribution referred to as the transmuted Kumaraswamy (T K w) distribution. The new transmuted distribution is developed using the quadratic rank transmutation map studied by Shaw et al. (2009). A comprehensive account of the mathematical properties of the new distribution is provided. Explicit expressions are derived for the moments, moment generating function, entropy, mean deviation, Bonferroni and Lorenz curves, and formulated moments for order statistics. The T K w distribution parameters are estimated by using the method of maximum likelihood. Monte Carlo simulation is performed in order to investigate the performance of MLEs. The flood data and HIV/ AIDS data applications illustrate the usefulness of the proposed model.

15

Axial dispersion models and their basic properties

47%

Bartova D. , Jakes B. , Kukal J.

Archives of Control Sciences

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2009

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tom Vol. 19, no. 1

5-22

EN

The paper is oriented to summary of important basic relations, which characterize behavior of four axial dispersion models (AEO: axial enforced closed-open model, ACO: axial closed-open model, ACC: axial closed-closed model, AOO: axial open-open model) and three referential models (ideal mixed model, plug flow model, cascade of ideal mixers without back-mixing). Selected basic properties (parametric characteristics) of these models can be used for parameter identification of included hydrodynamic flow structure models. Mathematical description of models including initial and boundary conditions, transfer function, model transient response to Dirac impulse as weighting (impulse) function, model transient response to step function as step response are included in this study. There are also included further characteristics of impulse function: raw moments up to 4th order, variance, variation coefficient, skewness , kurtosis, location and value of mode. Complete set of these characteristics for all studied models is collected (model-by-model) in seven tables. The authors declare several properties of weighting function as key ones: value of 1st raw (dimensional) moment, parametric values and mode properties, related to dependence on Peclet number. The plots of parametric values and mode properties vs. Peclet number are mentioned in the paper for four studied axial dispersion models.

16

On pointwise convergence of nets of Mellin-Kantorovich convolution operators

47%

Bardaro C. , Mantellini I.

Commentationes Mathematicae

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2013

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tom Vol. 53, No. 2

65--77

EN

Here we study pointwise approximation and asymptotic formulae for a class of Mellin-Kantorovich type integral operators, both in linear and nonlinear form.

17

Improved bounds on bell numbers and on moments of sums of random variables

41%

Berend D. , Tassa T.

Probability and Mathematical Statistics

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2010

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tom 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.

18

A Two-Parameter Lindley Distribution

41%

Shanker R. , Mishra A.

Statistics in Transition new series

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2013

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tom 14

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nr 1

45-56

EN

A two-parameter Lindley distribution, of which the Lindley distribution (LD) is a particular case, has been introduced. Its moments, failure rate function, mean residual life function and stochastic orderings have been discussed. The maximum likelihood method and the method of moments have been discussed for estimating its parameters. The distribution has been fitted to some data-sets to test its goodness of fit.

19

Recurrence relations for single and product moments of k-th lower record values from the inverse distributions of Pareto's type and characterizations

41%

Pawlas P. , Szynal D.

Discussiones Mathematicae Probability and Statistics

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2000

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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.

20

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

34%

Grudzień Z. , Szynal D.

Applicationes Mathematicae

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1995-1996

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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.