K-distribution

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

Model selection for environmental data

Abstract: A practical approach is proposed for model selection and discrimination among nested and non-nested probability distributions. Some existing problems with traditional model selection approaches are addressed, including standard testing of a null hypothesis against a more general alternative and the use of some well-known discrimination criteria for non-nested distributions. A generalized information criterion (GIC) is used to choose from two or more model structures or probability distributions. For each set of random samples, all model structures that do not perform significantly worse than other candidates are selected. The two-and three-parameter gamma, Weibull and lognormal distributions are used to compare the discrimination procedures with traditional approaches. Monte Carlo experiments are employed to examine the performances of the criteria and tests over large sets of finite samples. For each distribution, the Monte Carlo procedure is undertaken for various representative sets of parameter values which are encountered in fitting environmental quality data.

The Generation of Correlated Gamma Distributed Random Fields for the Simulation of Synthetic Aperture Radar Images

Abstract: Simulation plays an important role in both the development and analysis of new radar imaging and processing systems and in the analysis of their data. We have developed a synthetic aperture radar (SAR) simulation system, cSAR, that simulates the raw signal data. An important component of this system is the simulation of clutter, or the random spatial fluctuations of backscatter. The prevailing statistical model for clutter is the K distribution. This model is founded on a gamma distributed scattering coefficient. In this paper we present a system for simulating correlated gamma distributed fields of scattering coefficients. Our system starts with the requirement that in radar and other coherent imaging scenarios the locations of elemental scene scatterers must be random to achieve fully developed speckle in the image. We start with a set of scatterers whose spatial location follows a uniform distribution. To generate a correlated random field with this random distribution of scatterers we use the turning ...

Why Mixture of Probability Distributions

Abstract: If we have two random variables ξ1 and ξ2, then we can form their mixture if we take ξ1 with some probability w and ξ2 with the remaining probability 1 − w. The probability density function (pdf) ρ(x) of the mixture is a convex combination of the pdfs of the original variables: ρ(x) = w · ρ1(x) + (1 − w) · ρ2(x). A natural question is: can we use other functions f(ρ1, ρ2) to combine the pdfs, i.e., to produce a new pdf ρ(x) = f(ρ1(x), ρ2(x))? In this paper, we prove that the only combination operations that always lead to a pdf are the operations f(ρ1, ρ2) = w · ρ1 + (1− w) · ρ2 corresponding to mixture. 1 Formulation of the Problem What is mixture. If we have two random variables ξ1 and ξ2, then, for each probability w ∈ [0, 1], we can form a mixture ξ of these variables by selecting ξ1 with probability w and ξ2 with the remaining probability 1− w; see, e.g., [1]. In particular, if we know the probability density function (pdf) ρ1(x) corresponding to the first random variable and the probability density function ρ2(x) corresponding to the second random variable, then the probability density function ρ(x) corresponding to their mixture has the usual form ρ(x) = w · ρ1(x) + (1− w) · ρ2(x). (1) A natural question. A natural question is: are there other combination operations f(ρ1, ρ2) that always transform two probability distributions ρ1(x) and ρ2(x) into a new probability distribution ρ(x) = f(ρ1(x), ρ2(x)). (2)

Some characterizations of distributions of the exponential-type

Abstract: We consider a particular subclass of the two-parameter exponential family with natural parameters γ1, γ2 and characterize those distributions of the family having a ratio of the mean value and the variance that is a linear function of γ1 by the form of the moment generating function. As special cases we find the normal and the gamma distributions.

Fokker-Planck Equation for Fractal Distributions of Probability

Abstract: The Fokker-Planck equation describes the time evolution of the probability density function. It is also known as the Kolmogorov forward equation. The first use of the Fokker-Planck equation was the statistical description of Brownian motion of a particle in a fluid. It is known that the Fokker-Planck equation can be derived from the Chapman-Kolmogorov equation (Gardiner, 1985). We note that the Chapman-Kolmogorov equation is an integral identity relating the joint probability distributions of different sets of coordinates on a stochastic process. In Ref. (Tarasov, 2007), we obtained a fractional generalization of the Chapman-Kolmogorov equation, where integrals of non-integer order (Kilbas et al., 2006) were used. The suggested equation is fractional integral equation (Samko et al., 1993). The fractional Chapman-Kolmogorov equation can be applied to describe fractal distributions of probability in framework of the fractional continuous model. The integrals of fractional order are a powerful tool to study processes in the fractal distributions. Generalized Fokker-Planck equation can be derived (Tarasov, 2005a, 2007) from the fractional Chapman-Kolmogorov equation. The suggested Fokker-Planck equations allow us to describe dynamics of fractal distributions of probability in framework of the fractional continuous model.