K-distribution

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

Testing the Fit of Gamma Distributions Using the Empirical Moment Generating Function

Abstract: This article presents goodness-of-fit tests for two and three-parameter gamma distributions that are based on minimum quadratic forms of standardized logarithmic differences of values of the moment generating function and its empirical counterpart. The test statistics can be computed without reliance to special functions and have asymptotic chi-squared distributions. Monte Carlo simulations are used to compare the proposed test for the two-parameter gamma distribution with goodness-of-fit tests employing empirical distribution function or spacing statistics. Two data sets are used to illustrate the various tests.

Size-biased distributions in the generalized beta distribution family, with applications to forestry

Abstract: Size-biased distributions arise in many forestry applications, as well as other environmental, econometric, and biomedical sampling problems. We examine the size-biased versions of the generalized beta of the first kind, generalized beta of the second kind and generalized gamma distributions. These distributions include, as special cases, the Dagum (Burr Type III), Singh-Maddala (Burr Type XII) and Fisk distributions as well as better-studied distributions such as the Weibull, lognormal, beta (of the first and second kind), gamma and exponential. Our results indicate that specification and estimation of the size-biased forms of these distributions can be viewed within a unified framework. This should facilitate broader application of size-biased distributions in forestry sampling, modeling and analysis.

Pseudospectral time-domain modeling of non-Rayleigh reverberation: synthesis and statistical analysis of a sidescan sonar image of sand ripples

Abstract: The pseudospectral time-domain (PSTD) method is an accurate and efficient scheme for solving the acoustic wave equation numerically. It provides a good basis for a general sonar simulation model because all of the fundamental processes on which sonar depend occur as natural consequences of solving the wave equation. Propagation, interference, and spreading and absorption losses are intrinsic to this solution; reflection and scattering are governed by the distribution of materials within the simulated environment. These processes are analogous to those in the physical system being modeled. The method generates the full spatial and temporal evolution of the acoustic field for a specified model environment. This paper presents the application of a PSTD model to the simulation of a sidescan sonar system operating in deep water. Synthetic sidescan images of sand ripples are simulated using a directional fractal surface as the model sea bed. Different forms of time-varying gain are applied to the received signals to investigate its effects on the statistics of the resulting images. These images are visually realistic and have significantly non-Rayleigh histograms. Rayleigh distribution, Rayleigh mixtures with up to four modes, and K distribution fits to these histograms demonstrate that the form of the applied time-varying gain has a substantial effect both on the derived distribution parameters and on the probability that the data are drawn from that distribution. They also demonstrate that, with a greater chi-square test probability and with fewer fitting parameters, the K distribution provides the more appropriate description of the reverberation from the simulated sand-ripple sea bed generated with the model sonar system.

L p -Nested Symmetric Distributions

Abstract: In this paper, we introduce a new family of probability densities called Lp-nested symmetric distributions. The common property, shared by all members of the new class, is the same functional form ρ(x) = ~ρ(f(x)), where f is a nested cascade of Lp-norms ||x||p = (∑ |xi|p)1/p. Lp-nested symmetric distributions thereby are a special case of ν-spherical distributions for which f is only required to be positively homogeneous of degree one. While both, ν-spherical and Lp-nested symmetric distributions, contain many widely used families of probability models such as the Gaussian, spherically and elliptically symmetric distributions, Lp-spherically symmetric distributions, and certain types of independent component analysis (ICA) and independent subspace analysis (ISA) models, ν-spherical distributions are usually computationally intractable. Here we demonstrate that Lp-nested symmetric distributions are still computationally feasible by deriving an analytic expression for its normalization constant, gradients for maximum likelihood estimation, analytic expressions for certain types of marginals, as well as an exact and efficient sampling algorithm. We discuss the tight links of Lp-nested symmetric distributions to well known machine learning methods such as ICA, ISA and mixed norm regularizers, and introduce the nested radial factorization algorithm (NRF), which is a form of non-linear ICA that transforms any linearly mixed, non-factorial Lp-nested symmetric source into statistically independent signals. As a corollary, we also introduce the uniform distribution on the Lp-nested unit sphere.