Topic
K-distribution
About: K-distribution is a research topic. Over the lifetime, 1281 publications have been published within this topic receiving 51774 citations.
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01 Jan 2016
TL;DR: In this article, various continuous distributions encountered on a daily basis are discussed: the simplest uniform distribution, the exponential distribution characterizing the decay of unstable atoms and nuclei, the ubiquitous normal (Gauss) distribution in both its general and standardized form, the Maxwell velocity distribution in its vector and scalar form, power-law distribution, and the Cauchy (Lorentz, Breit-Wigner) distribution suitable for describing spectral line shapes and resonances.
Abstract: Particular continuous distributions encountered on a daily basis are discussed: the simplest uniform distribution, the exponential distribution characterizing the decay of unstable atoms and nuclei, the ubiquitous normal (Gauss) distribution in both its general and standardized form, the Maxwell velocity distribution in its vector and scalar form, the Pareto (power-law) distribution, and the Cauchy (Lorentz, Breit–Wigner) distribution suitable for describing spectral line shapes and resonances. Three further distributions are introduced (\(\chi ^2\)-, Student’s t- and F-distributions), predominantly used in problems of statistical inference based on samples. Generalizations of the exponential law to hypo- and hyper-exponential distributions are presented.
2 citations
29 Sep 2014
TL;DR: In this article, the authors define a mixture distribution of logarithmic series distributions with two parameters, and show that if one parameter is larger than zero, the distribution is reduced to trigamma distributions, which are close to zeta distributions or Zipf's law.
Abstract: Digamma distributions are mixture distributions* of logarithmic series distributions*, and hence heavy-tailed distributions*, which have two parameters. The distributions vary widely with the parameter values; if one parameter is larger, the distribution is close to the logarithmic series distributions*. If this parameter is near zero, the distribution is reduced to trigamma distributions, which are close to zeta distributions* or Zipf's law*.
Keywords:
discrete distributions;
heavy-tailed distributions;
polygamma functions
2 citations
TL;DR: In this paper, a mean-value representation of information improvement for generalized probability distributions is given and some interesting properties are also studied, and the concept is extended to bivariate distributions by extending the concept to include information improvement.
Abstract: Theil [1967] has introduced a quantity known as ‘Information-Improvement’ widely used in economic analysis. In this paper a mean-value representation of this measure for generalized probability distributions is given and some of its interesting properties are also studied. Finally the concept is extended to bivariate distributions.
2 citations
01 Jul 1990
TL;DR: It is shown how to make inferences about the probabilities of the various qualitative behaviors a model could exhibit, when partial quantitative information in the form of intervals or probability distributions is given about values (such as initial values) of model variables.
Abstract: Research on nding the di erent behaviors that an incompletely speci ed model can exhibit has concentrated on nding the plausible behaviors, and ruling out implausible ones. However, it would also be useful to estimate the probabilities of di erent behaviors. That is the goal of the present work. We show how to make inferences about the probabilities of the various qualitative behaviors a model could exhibit, when partial quantitative information in the form of intervals or probability distributions is given about values (such as initial values) of model variables. This work has taken place in the Qualitative Reasoning Group at the Arti cial Intelligence Laboratory, The University of Texas at Austin. Research of the Qualitative Reasoning Group is supported in part by NSF grants IRI-8905494 and IRI-8904454; by NASA grant NAG 2-507; by the Texas Advanced Research Program under grant no. 003658-175; and by the Jet Propulsion Laboratory, California Institute of Technology, sponsored by the National Aeronautics and Space Administration. Reference herein to any speci c commercial product, process, or service by trade name, trademark, manufacturer, or otherwise, does not constitute or imply its endorsement by any of its sponsors or the University of Texas.
2 citations
01 May 2015
2 citations