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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Journal Article•
TL;DR: In this article, a new definition of form-invariance with reference to matrix variate distributions is proposed, which is applicable to the multivariate and univariate distributions, even though not necessarily to all families of probability distributions that exist, but definitely to those that are commonly used in practice.
Abstract: Summary: Form-invariance is the most practical and desired property of weighted distributions. Weighted distributions commonly arise as univariate probability models in many fields of applications, for example, survival data analysis in medical science. However, the explicit global definition of “form-invariance” seems to be absent (to our knowledge) in spite of the fact that there is a growing use of such distributions during the last three decades. Therefore, in this note an effort is made to provide a new definition of form-invariance with reference to the matrix variate distributions. Obviously this definition and related implications are applicable to the multivariate and univariate distributions (as it should be), even though not necessarily to all families of probability distributions that exist, but definitely to those that are commonly used in practice. To demonstrate the validity of the last statement certain results, based on our new definition of form-invariance, are proved as the characterizations of the class of matrix elliptical distributions. Also considered in this note are certain extensions of our results, as may seem appropriate within the scope of the theory of matrix variate distributions. The concept of form-invariance is extended to marginal and conditional structures, as well as to the sum of independent matrix variates from elliptical distributions.
TL;DR: A class of scale mixtured normal distribution with lifetime probability distributions has been proposed and different properties such as moments, characteristic function, shape characteristics of these probability distributions have been mentioned.
Abstract: A class of scale mixtured normal distribution with lifetime probability distributions has been proposed in this article. Different moments, characteristic function and shape characteristics of these proposed probability distributions have also been provided. The scale mixture of normal distribution is extensively used in Biostatistical field. In this article, some new lifetime probability distributions have been proposed which is the scale mixture of normal distribution. Different properties such as moments, characteristic function, shape characteristics of these probability distributions have also been mentioned.
Patent•
14 May 2007
TL;DR: In this paper, robust methods are developed to provide bounds and probability distributions for the locations of objects as well as for associated variables that affect the accuracy of the location such as the positions of stations, the measurements, and errors in the speed of signal propagation.
Abstract: Robust methods are developed to provide bounds and probability distributions for the locations of objects as well as for associated variables that affect the accuracy of the location such as the positions of stations, the measurements, and errors in the speed of signal propagation. Realistic prior probability distributions of pertinent variables are permitted for the locations of stations, the speed of signal propagation, and errors in measurements. Bounds and probability distributions can be obtained without making any assumption of linearity. The sequential methods used for location are applicable in other applications in which a function of the probability distribution is desired for variables that are related to measurements.
TL;DR: This article shows the probability distribution function of the sum of general independent continuous uniform distributions and the key point of the derivation process is the application of convolution formula.
Abstract: This article will show the probability distribution function of the sum of general independent continuous uniform distributions. Although the probability distribution function of the sum of independent continuous uniform distributions over the same interval (0, 1) is known, it cannot be generalized to the probability distribution function of the sum of general independent continuous uniform distributions over unlike intervals. In this article the key point of the derivation process is the application of convolution formula.
01 Jan 2011
TL;DR: In this article, it is shown that the Bose-Einstein and Fermi-Dirac distributions are nothing but the Boltzmann-Gibbs-von Neumann distribution of an ideal quantum gas.
Abstract: Several distributions of statistical mechanics are reviewed. It is shown that the Bose-Einstein and the Fermi-Dirac distributions are nothing but the Boltzmann-Gibbs-von Neumann distribution of an ideal quantum gas. This Chapter can be used as an introduction in a second course of statistical physics, or in a first course for more mathematically oriented students. The contents is fairly traditional, but is usually dispersed over many chapters. By bringing the material together in one chapter the relation between the distinct distributions is clarified.