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Showing papers on "K-distribution published in 2000"


Book
16 May 2000
TL;DR: In this article, asymptotic quantization for nonsingular probability distributions and singular probability distributions is studied. But quantization of singular distributions is not a special case of the problem of non-singular distributions.
Abstract: General properties of the quantization for probability distributions- Asymptotic quantization for nonsingular probability distributions- Asymptotic quantization for singular probability distributions

814 citations


Journal ArticleDOI
TL;DR: In this article, a simple generalized model based on the Nakagami distribution is proposed to describe the statistics of the envelope of the backscattered echo from an ensemble of scatterers.
Abstract: The backscattered ultrasonic echo from tissue can be described in terms of Rayleigh distribution or K distribution. Even though both generalized K distribution and homodyned K distribution can account for some of the scattering conditions that exist in tissues, the analytical complexity involved with these distributions is significant. A much simpler generalized model based on the Nakagami distribution is proposed here. This model can describe the statistics of the envelope of the backscattered echo from an ensemble of scatterers with varying number densities, varying cross sections, and the presence or absence of regularly spaced scatterers. Computer simulations and experiments on tissue-mimicking phantoms have been undertaken to test the validity of the model. Results clearly show the versatility of the Nakagami distribution and its parameter to model the backscattered envelope from tissues. It is suggested that Nakagami distribution may be a good model for use in tissue characterization because of its simple analytical nature and ability to encompass different scattering conditions.

482 citations


Journal ArticleDOI
TL;DR: In this article, the Gaussian theory is reviewed and nonlinear short-term probability distributions are derived from a narrow band second-order model, which has different impact on different measurement techniques, and this is further demonstrated for wave data from WAVEMOD Crete measurement campaign and laser data from the North Sea.

95 citations


ReportDOI
01 Mar 2000
TL;DR: A collection of computer-generated statistical distributions which are useful for performing Monte Carlo simulations are presented, encapsulated into a C++ class, called "Random", so that they can be used with any C++ program.
Abstract: : This report presents a collection of computer-generated statistical distributions which are useful for performing Monte Carlo simulations. The distributions are encapsulated into a C++ class, called "Random", so that they can be used with any C++ program. The class currently contains 27 continuous distributions, 9 discrete distributions, data-driven distributions, bivariate distributions, and number-theoretic distributions. The class is designed to be flexible and extensible, and this is supported in two ways: (1) a function pointer is provided so that the user-programmer can specify an arbitrary probability density function, and (2) new distributions can be easily added by coding them directly into the class. The format of the report is designed to provide the practitioner of Monte Carlo simulations with a handy reference for generating statistical distributions. However, to be self-contained, various techniques for generating distributions are also discussed, as well as procedures for estimating distribution parameters from data. Since most of these distributions rely upon a good underlying uniform distribution of random numbers, several candidate generators are presented along with selection criteria and test results. Indeed, it is noted that one of the more popular generators is probably overused and under what conditions it should be avoided.

53 citations


Journal ArticleDOI
TL;DR: The standard methods for the calculation of total claim size distributions and ruin probabilities, Panjer recursion and algorithms based on transforms, both apply to lattice-type distributions only and therefore require an initial discretization step if continuous distribution functions are of interest.
Abstract: Abstract The standard methods for the calculation of total claim size distributions and ruin probabilities, Panjer recursion and algorithms based on transforms, both apply to lattice-type distributions only and therefore require an initial discretization step if continuous distribution functions are of interest. We discuss the associated discretization error and show that it can often be reduced substantially by an extrapolation technique.

35 citations


Journal ArticleDOI
TL;DR: For basic discrete probability distributions, − Bernoulli, Pascal, Poisson, hypergeometric, contagious, and uniform, − q-analogs are proposed as discussed by the authors.
Abstract: For basic discrete probability distributions, − Bernoulli, Pascal, Poisson, hypergeometric, contagious, and uniform, − q-analogs are proposed.

30 citations


Journal ArticleDOI
01 Feb 2000
TL;DR: The single point statistics of some high-resolution low-grazing angle radar sea clutter are examined in this article, where three different distributions are used to model the cumulative density of the data.
Abstract: The single point statistics of some high-resolution low-grazing angle radar sea clutter are examined Three different distributions are used to model the cumulative density of the data The Weibull and the K-distribution both require the addition of a Rayleigh distributed component to give a good fit to the data This Rayleigh distributed component has a mean level significantly higher than the thermal noise level A third model, the 'sinusoidal bound system' (sin S/sub B/) is also developed It performs very well in fitting the extremes of the cumulative distribution, particularly the upper limit, which is not well fitted by the other models

21 citations



Journal ArticleDOI
TL;DR: In this paper, the authors construct goodness-of-fit tests for continuous distributions using their characterizations in terms of moments of order statistics and moments of record values, based on characterizations presented in [2] and [3].
Abstract: 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].

13 citations



Proceedings ArticleDOI
B. W. Stuck1
05 Jun 2000
TL;DR: An historical, personal and idiosyncratic overview of stable probability distributions in signal processing is presented.
Abstract: An historical, personal and idiosyncratic overview of stable probability distributions in signal processing is presented.

Journal ArticleDOI
TL;DR: In this paper, a new Bayesian formulation for the discrete geophysical inverse problem is proposed, which can significantly reduce the cost of the computations by marginalizing the probability distributions.
Abstract: Summary We derive a new Bayesian formulation for the discrete geophysical inverse problem that can significantly reduce the cost of the computations. The Bayesian approach focuses on obtaining a probability distribution (the posterior distribution), assimilating three kinds of information: physical theories (data modelling), observations (data measurements) and prior information on models. Once this goal is achieved, all inferences can be obtained from the posterior by computing statistics relative to individual parameters (e.g. marginal distributions), a daunting computational problem in high dimensions. Our formulation is developed from the working hypothesis that the local (subsurface) prior information on model parameters supercedes any additional information from other parts of the model. Based on this hypothesis, we propose an approximation that permits a reduction of the dimensionality involved in the calculations via marginalization of the probability distributions. The marginalization facilitates the tasks of incorporating diverse prior information and conducting inferences on individual parameters, because the final result is a collection of 1-D posterior distributions. Parameters are considered individually, one at a time. The approximation involves throwing away, at each step, cross-moment information of order higher than two, while preserving all marginal information about the parameter being estimated. The main advantage of the method is allowing for systematic integration of prior information while maintaining practical feasibility. This is achieved by combining (1) probability density estimation methods to derive marginal prior distributions from available local information, and (2) the use of multidimensional Gaussian distributions, which can be marginalized in closed form. Using a six-parameter problem, we illustrate how the proposed methodology works. In the example, the marginal prior distributions are derived from the application of the principle of maximum entropy, which allows one to solve the entire problem analytically. Both random and modelling errors are considered. The uncertainty measure for estimated parameters is provided by 95 per cent probability intervals calculated from the marginal posterior distributions.

Journal ArticleDOI
TL;DR: In this paper, multivariate composite distributions with specified marginal distributions and a specified Pearson product–moment population correlation structure are characterized.

Journal ArticleDOI
TL;DR: A discrete probability model is used to aid in the description of gamma-ray spectroscopic data obtained from a radioactively contaminated territory and is useful for describing spatial vector valued discrete random fields.

Journal ArticleDOI
TL;DR: In this paper, a class of multidimensional absolutely continuous distributions is considered and the focus of their attention is the limiting distributions for this family that appear as the conjugating parameter tends to the boundary of the set.
Abstract: A class of multidimensional absolutely continuous distributions is considered. Each of them has a moment-generating function that is finite in a bounded set S and, therefore, generates a family of so-called conjugate or associated distributions. At the focus of our attention are the limiting distributions for this family that appear as the conjugating parameter tends to the boundary of S. As in the one-dimensional case, each such limiting distribution can be obtained as a consequence of an Abelian theorem.

Journal ArticleDOI
TL;DR: In this paper, a variational method is proposed to describe some families of probability distributions, where the given probability distributions are to be found from the knowledge of the expected values of some variables.
Abstract: We propose a variational method to describe some families of probability distributions. The given probability distributions are to be found from the knowledge of the expected values of some variables. To do that we restate the problem as a constrained linear inverse problem, which we then proceed to solve by the method of maximum entropy on the mean.

Proceedings ArticleDOI
12 Dec 2000
TL;DR: In this paper, the authors considered the probability of stability for an uncertain polynomial which has as coefficients multilinear functions of real, random, independent parameters q/sub i/.
Abstract: Considers the probability of stability for an uncertain polynomial which has as coefficients multilinear functions of real, random, independent parameters q/sub i/. The result requires little a priori information about the probability distributions of these uncertain parameters. We only require that the distributions are symmetric about zero, non-increasing as |q/sub i/| increases, and supported on a given interval [-r/sub i/,r/sub i/]. The probability estimate is sharp in the sense that the estimated probability of stability is p/spl circ/*=1 when the uncertainty bounds r/sub i/ are below the deterministic robustness radius r/sub map/ obtained with the Mapping Theorem. To obtain the probabilistic estimate, we recast the problem so that the following characterization of stability is applicable: if the Nyquist curve for a proper plant lies to the right of a frequency-dependent separating line through -1+j0 at each frequency, then stability is guaranteed. The result is applied in a numerical example, illustrating a common amplification phenomenon: even when the magnitude of uncertainty is significantly greater than the deterministic robustness bound, the risk of instability is small.

Journal ArticleDOI
TL;DR: In this article, a direct potential surface inversion algorithm for multidimensional quantum systems based on combining probability density and energy spectral data is presented, and the algorithm expresses the probability density as a function of energy spectral properties.
Abstract: This paper presents a direct potential surface inversion algorithm for multidimensional quantum systems based on combining probability density and energy spectral data. The algorithm expresses the ...

Journal ArticleDOI
TL;DR: In this article, the global extremality criteria for interval functionals on probability distributions are obtained, and monotonic set contraction methods are considered for the solution of extremal problems on probability distribution.

Journal ArticleDOI
TL;DR: In this paper, it was proved by method of Azlarov that order statistics satisfying a certain e-regression condition also have finite moments of all orders, and the stability problem is considered by the properties of independence of statistics in this characterization.
Abstract: Zinger characterization describes a class of probability distributions that have finite moments of all orders. The stability problem is considered by the properties of independence of statistics in this characterization. It was proved by method of Azlarov that order statistics satisfying a certain e-regression condition also have finite moments of all orders.


Journal ArticleDOI
TL;DR: In this article, the construction of isomorphisms between semigroups of probability distributions (with convolution as group operation) is described, in particular between the set of all probability distributions on a nonnegative axis and a subset of distributions on nonnegative integers.
Abstract: Some methods permitting the construction of isomorphisms between semigroups of probability distributions (with convolution as group operation) are described, in particular, between the set of all probability distributions on a nonnegative axis and a subset of distributions on nonnegative integers. Analogous isomorphisms for the vector case and for sets of distributions corresponding to nondecreasing processes with independent increments are also described.

Posted Content
TL;DR: In this paper, an analytic study of the reaction probability integrals corresponding to various forms of the slowly varying cross-section factor $S(E)$ is attempted, expressed in terms of the extended gamma functions.
Abstract: An analytic study of the reaction probability integrals corresponding to the various forms of the slowly varying cross-section factor $S(E)$ is attempted. Exact expressions for reaction probability integrals are expressed in terms of the extended gamma functions.

Journal ArticleDOI
TL;DR: In this paper, a method for constructing nonstationary model probability distributions for nonlinear dynamic systems related to the Verhulst stochastic equation is proposed, based on the numerical solution of relaxation differential equations for the mean and the variance.
Abstract: We propose a method for constructing nonstationary model probability distributions for nonlinear dynamic systems related to the Verhulst stochastic equation. The proposed procedure is based on the numerical solution of relaxation differential equations for the mean and the variance. The set of the moment equations is closed and the probability density is constructed on the basis of rigorous analytical relations for the stationary probability characteristics. As a result, these distributions have correct stationary asymptotics. We show the possibility of numerical control of the accuracy of the proposed procedure. We consider the examples of relaxation of the probability characteristics of the amplitude of a self-oscillator and a parametric oscillator with a noise pump. The evolution of the amplitude probability distribution is found.