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Showing papers on "K-distribution published in 1983"


Journal ArticleDOI
TL;DR: In this article, a new procedure based on gaussian quadrature is developed to decrease the error in the approximation to any desired level, which can be used to increase the accuracy.
Abstract: Practical limits on the size of most probabilistic models require that probability distributions be approximated by a few representative values and associated probabilities. This paper demonstrates that methods commonly used to determine discrete approximations of probability distributions systematically underestimate the moments of the original distribution. A new procedure based on gaussian quadrature is developed in this paper. It can be used to decrease the error in the approximation to any desired level.

311 citations


Book ChapterDOI
01 Jan 1983

10 citations



Journal ArticleDOI
TL;DR: In this article, a representation for singular distributions in two dimensions is given, which is used to characterize the types of marginal distributions that members of this class can have, and a representation is given that makes the construction of a class of singular distributions of two dimensions simple to carry out.
Abstract: Singular distributions are seldom covered in undergraduate probability courses, although they are of interest in statistics and, as is shown by example, can easily arise through extending mixed discrete and continuous distributions to two or more dimensions. A representation is given that makes the construction of a class of singular distributions in two dimensions simple to carry out. This representation is also used to characterize the types of marginal distributions that members of this class can have.

3 citations



ReportDOI
01 Aug 1983
TL;DR: In this paper, the informative quantile function IQ(u) = (Qu - Q(0.5)) divided by 2(Q( 0.75) - Q (0.25)) is used to identify probability models for observed data and its use to provide concepts of representative distributions which illustrate the different types of shapes and tail behavior that real distributions can have.
Abstract: : A problem of great importance to statistical data analysts is quick identification of possible probability distributions for observed data, and classification of tail behavior of probability distributions. This paper discusses the informative quantile function IQ(u) = (Q(u) - Q(0.5)) divided by 2(Q(0.75) - Q(0.25)), and its use to identify probability models for observed data and its use to provide concepts of representative distributions which illustrate the different types of shapes and tail behavior that real distributions can have. This paper also discusses estimators of tail exponents; they can be used to identify outlying data values, and more centrally to identify possible distributions to fit to data. (Author)

2 citations


Journal ArticleDOI
01 Jan 1983-Frequenz
TL;DR: In this article, the problem of the numerical NCDA calculation is addressed by a recurrence algorithm developed by Beall which, in contrast with the application of Neyman's original probability formula, allows such calculations to be carried out exactly without approximative constraints.
Abstract: Various CCITT activities initiated since the late seventies and recent publications on research intended to assess the quality of communication channels transmitting digital information have shown that, although further studies are necessary, Neyman's 'contagious' typeprobability distribution-briefly termed NCDA-seems to be an appropriate tool for the mathematical-statistical description of the error performance of such transmission paths on which disturbances frequently give rise to error bursts. Since the NCDA, developed as early as 1939 for the description of certain experimental results obtained in the field of botany, cannot be assumed to be generally known to communication engineers, this report is intended to give some explanations and historical background information mainly based on Neyman's original paper [1] and n on-communication-engineering publications. Moreover, aspects of the computer implementation are discussed for the application of the NCDA. With respect to the problem of the numerical NCDA calculation, attention shall be paid to a recurrence algorithm developed by Beall which-in contrast with the application of Neyman's original probability formula-allows such calculations to be carried out exactly without approximative constraints. Übersicht: Eine Reihe von CCITT-Aktivitäten seit Ende der siebziger Jahre sowie Publikationen aus jüngster Zeit im Zusammenhang mit Untersuchungen über mögliche Qualitätsaussagen für Übertragungswege digitaler Informationen zeigen, daß zur mathematisch statistischen Beschreibung des Fehlerverhaltens dieser Übertragungswege, auf denen sich Störungen oft in Fehlcrbündeln auswirken, die Neyman'sche .ansteckende' Wahrscheinlichkeitsverteilung vom Typ A kurz: NCDA ein geeignetes Mittel zu sein scheint, wenngleich weitere Untersuchungen notwendig sind. Da die NCDA, bereits 1939 für die Beschreibung gewisser Versuchsergebnisse auf dem Gebiet der Botanik entwickelt, in der Nachrichtenübertragungstechnik nicht als allgemein bekannt unterstellt werden darf, ist mit der vorliegenden Arbeit beabsichtigt, einige Erläuterungen und historische Hintergrundinformationen zu geben, die sich im wesentlichen auf die Neyman'sche Originalarbeit [1] sowie auf nicht-nachrichtentechnische Publikationen stützen. Außerdem werden bezüglich der Anwendung der NCDA Aspekte der Rechner-Implementierung diskutiert. Dabei soll zur Frage der numerischen NCDA-Berechnung das Augenmerk auf einen Rekursionsalgorithmus von Bcall gelenkt werden, mit dem derartige Berechnungen im Gegensatz zur Anwendung der originären Neyman'schen Wahrscheinlichkeitsformel exakt ohne approximative Nebenbedingungen durchgeführt werden können. Für die Dokumentation: Mathematische Statistik / Ansteckende Wahrscheinlichkeit / NEYMAN'sche Wahrscheinlichkeitsverteilung / BEALL'scher Rekursionsalgorithmus / Digital-Nachrichtenübertragung / Nachrichtenkanal / Kanalqualität

2 citations



Journal ArticleDOI
TL;DR: In this paper, a necessary and sufficient condition is given for the existence of stationary probability distributions of a non-Markovian model with linear transition rule, which has applications in psychological and biological research, in control theory, and in adaptation theory.

1 citations