K-distribution

About: K-distribution is a research topic. Over the lifetime, 1281 publications have been published within this topic receiving 51774 citations.

Probability distributions for Poisson processes with pile-up

Abstract: In this paper, two parametric probability distributions capable to describe the statistics of X-ray photon detection by a CCD are presented. They are formulated from simple models that account for the pile-up phenomenon, in which two or more photons are counted as one. These models are based on the Poisson process, but they have an extra parameter which includes all the detailed mechanisms of the pile-up process that must be fitted to the data statistics simultaneously with the rate parameter. The new probability distributions, one for number of counts per time bins (Poisson-like), and the other for waiting times (exponential-like) are tested fitting them to statistics of real data, and between them through numerical simulations, and their results are analyzed and compared. The probability distributions presented here can be used as background statistical models to derive likelihood functions for statistical methods in signal analysis.

Probability Distributions II: Examples

Abstract: This chapter builds on the work of Chapter 3 and applies the concepts and definitions given there to a number of practical distributions frequently met in physical science. These are: the uniform, exponential, Cauchy, binomial, multinomial, Poisson and normal (Gaussian) distributions. Because of the great importance of the normal distribution, this is discussed in some detail for both the single variate and the multivariate cases, with a separate section on the bivariate case. The basic features and properties of these various distributions, and any relations between them, are derived.

Construction of a gamma-distribution probability paper for straightening discharge probability curves

Abstract: The Hazen probability paper presently being used for plotting discharge probability curves makes it possible to represent the probability curve as a straight line only in the case of a normal distribution of the series. In the case of a skew distribution of the series the probability curve has a bend. In such cases a special gamma-distribution probability paper should be used for skew distributions. The use of such a graph paper permits representing the probability curve as a straight line for any values of the coefficients of variation and skewness.

Average Sample Number Function for Pareto Heavy Tailed Distributions

Abstract: The main purpose of this work is shortly to give the average sample number function after a sequential probability ratio test on the index parameter alpha of stable densities, which we give a mean of the number of data required to take decision in the case , we use the fact that the tails of Levy-stable distributions are asymptotically equivalent to a Pareto law for large data. Stable distributions are a rich class of probability distributions that allow skewness and heavy tails and have many intriguing mathematical properties. The lack of closed formulas for densities and distribution functions for all has been a major drawback to the use of stable distributions by practitioners, but few stable distributions have the analytical formula of their densities functions which are Gauss, Levy, and Cauchy.