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Showing papers on "K-distribution published in 1992"


Book
06 Aug 1992
TL;DR: In this paper, the authors provide a systematic account of the theory of generalized Gamma convolutions and related classes of probability distributions and densities, and several well-known probability distributions are treated in the accompanying examples.
Abstract: The aim of this monograph is to provide a systematic account of the theory of generalized Gamma convolutions and related classes of probability distributions and densities. Several well-known probability distributions are treated in the accompanying examples.

349 citations


Journal ArticleDOI
TL;DR: In this paper, the authors introduce a new class of probability models which are referred to as distributions of fractional order statistics, and consider the potential efficacies of various member distributions within the class for hydrologic data analysis.
Abstract: A critical issue in parametric methods of frequency analysis, regardless of the phenomenon being modeled, is that of selection of a form of probability distribution to be applied. When one is interested in continuous distributions there exists little theoretical guidance, other than perhaps that provided by the central limit theorem or the (asymptotic) results of extreme value theory, upon which one may base a choice. This paper, in a very general way, introduces a whole new class of probability models which are referred to as distributions of fractional order statistics. The potential efficacies of various member distributions within the class for hydrologic data analysis are also rationalized in a very intuitive way. Considered in some detail is an application of the theory of fractional order statistics to generalize the Gaussian distribution. Monte Carlo results comparing the performance of the generalized distribution with other common hydrologic models are also set forth.

64 citations


Journal ArticleDOI
TL;DR: In this paper, probability distributions in the exponential family can be fitted directly as log linear models, and the usual maximum likelihood estimates of parameters obtained can be used to compare probability distributions within a log linear model.

26 citations


Journal ArticleDOI
TL;DR: In this article, the authors describe the numerical analysis of continuous univariate probability functions with S-systems, which are computationally efficient nonlinear ordinary differential equations that contain virtually all ordinary differential equation as special cases.
Abstract: This tutorial describes the numerical analysis of continuous univariate probability functions with S-systems. These are computationally efficient nonlinear ordinary differential equations that contain virtually all ordinary differential equations as special cases. After a brief introduction to S-systems, it is shown how central and noncentral probability distributions, as well as auxiliary functions such as Bessel, Gamma, and Beta functions, can be recast equivalently as S-systems. The representation of distributions as S-systems permits rapid computation of function evaluations over wide ranges of random variables, as well as moments, quantiles, power and inverse power. It also offers transformation methods and various options of approximation. The recasting procedure employs elementary mathematics and needs to be executed only once. The tutorial contains a catalogue of recast S-system representations for nearly all relevant distributions and auxiliary functions, and thus enables the reader to evaluate d...

18 citations


Journal ArticleDOI
TL;DR: In this paper, a new class of probability distributions is introduced, which accentuates the periodic behaviour of environmental conditions in time and the random occurrence of some events on each period, following the logic of the appearance of random events in the evolution of real-world systems.
Abstract: A new class of probability distributions is introduced. This class accentuates the periodic behaviour of environmental conditions in time and the random occurrence of some events on each period. A constructive approach is used following the logic of the appearance of random events in the evolution of real-world systems. Some physical and probabilistic properties of the new distributions are discussed. Elementary statistical data models are considered and two types of estimations of the attributes of these distributions are offered. Numerical and graphical illustrations with simulated and observed data are used to motivate our suggestions.

12 citations


01 Jan 1992
TL;DR: Numerical results indicate that, for a given fixed burst length, the distributions of the on/off periods have a significant impact on the cell loss probability.
Abstract: In this paper, we study the effect of the distributions of on/off periods (of on/off sources) on the cell loss probability in an ATM network. Most of the previous works assume that the sources are characterized by their peak and average rates and/or their average burst lengths. Based on these parameters, two-state on/off sources, whose on and off periods are exponentially or geometrically dis- tributed, are then constructed. The cell loss probability in a statistical multiplexer with a finite buffer is approximately computed for the constructed two-state source models. In this paper, we assume that the distributions of the on/off periods are general, such as hyper-geometrical, gen- eral with finite support, and mixed geometrical. The buffer capacity is assumed to finite. Exact expressions for the cell loss probability can be derived, but numerical results are difficult to obtain. Decomposition methods and asymptotic analysis are used to derive simple, accurate approximations for the cell loss probability. Numerical results indicate that, for a given fixed burst length, the distributions of the on/off periods have a significant impact on the cell loss probability. The approximate results are verified using simulation results and are found to be very accurate for most cases. We ob- serve that, for a buffer size of 400 cells, the maximum link utilization that the link can achieve subject to a cell loss probability of is only about 50-60%. Therefore, heavy load approximation should be used cautiously. The results presented here can be used in admission control.

9 citations


Journal ArticleDOI
TL;DR: In this article, the Gamma, Beta Type I and Beta Type II matrices are derived from the general ORIARIM class and the probability densities for all of these distributions are obtained.
Abstract: In this paper, we obtain certain matrix distributions, which are derivable from the Gamma, Beta Type I and Beta Type II matrices. These are members of general ORIARIM class, as defined by Khatri, Khattree and Gupta (1991). The probability densities for all of these distributions are obtained. Further, it is shown that these distributions share certain distributional properties with Wishart distribution. Finally, the joint distributions of eigenvalues are obtained. For the sake of readability, the latter two aspects are presented only for Gaussian Hypergeometric distribution.

7 citations


Journal ArticleDOI
TL;DR: In this article, an integral transform of the compounding distribution is used to estimate the moments of a compound distribution in the case of an earthquake, which can then be converted into a statement about the distribution.
Abstract: Compound Poisson process models have been studied earlier for earthquake occurrences, with some arbitrary compounding distributions. It is more meaningful to abstract information about the compounding distribution from the empirical observations on the earthquake sequences. The difinition of a compound distribution can be interpreted as an integral transform of the compounding distribution. The latter distribution can therefore be estimated by inverting the integral transform. Alternatively, from the moments of the observable random variablesviz. (a) the number of earthquakes per unit time or (b) the waiting times for subsequent earthquakes, the moments of the compounding distribution can be obtained. This information can be converted into a statement about the compounding distribution.

6 citations


Journal ArticleDOI
TL;DR: In this article, the indicator approach in spatial data analysis is presented for the determination of probability distributions to characterize the uncertainty about any unknown value, which is done independently of the estimate retained.
Abstract: In this paper the indicator approach in spatial data analysis is presented for the determination of probability distributions to characterize the uncertainty about any unknown value. Such an analysis is non-parametric and is done independently of the estimate retained. These distributions are given through a series of quantile estimates and are not related to any particular prior model or shape. Moreover, determination of these distributions accounts for the data configuration and data values. An application is discussed. Moreover, some properties related to the Gaussian model are presented.

5 citations


Journal ArticleDOI
TL;DR: In this article, the authors exploit use of Mellin transforms in the study of product and quotient distributions by identifying of distributions, derivation of distributions and moment analysis of distributions using approximating functions.
Abstract: SYNOPTIC ABSTRACTThis paper exploits use of Mellin transforms in the study of product and quotient distributions by (a) identification of distributions (b) derivation of distributions (c) moment analysis of distributions (d) use of approximating functions (e) examples.

1 citations