K-distribution

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

Heavy-Tailed Distributions: Properties and Tests

Abstract: Distributions with heavier-than-exponential tails are studied for describing empirical phenomena. It is argued that the concept of increasing “conditional mean exceedance” provides a reasonable way of describing the heavy-tail phenomenon, and a family of Pareto distributions is shown to represent distributions for which this parameter is linearly increasing. A test is developed and modified so as to be suitable for testing heavy-tailedness, and some graphical procedures are also suggested.

A statistical description of polarimetric and interferometric synthetic aperture radar data

Abstract: This paper provides a nearly complete analysis of the key distributions encountered in single- and multi-look polarimetric synthetic aperture radar data under the bivariate Gaussian and K -distribution models. It contains new analytic results on the moments of the amplitude and phase difference in single look data and on the moments of the amplitude in multi-look data. As yet no analytic results for the moments of multi-look phase difference have been found, except in limiting cases. The maximum likelihood estimators of the covariance matrix elements of two jointly Gaussian channels are derived, together with their asymptotic variances. The problems in extending this analysis to the bivariate K distribution are also discussed.

On the entropy of continuous probability distributions (Corresp.)

Abstract: A table is given of differential entropies for various continuous probability distributions. The formulas, some of which are new, are of use in the calculation of rate-distortion functions and in some statistical applications.

Sub-optimum coherent radar detection in a mixture of K-distributed and Gaussian clutter

Abstract: The author introduces two suboptimum procedures for the coherent detection of a radar target signal, in the presence of a mixture of K-distributed and Gaussian distributed clutter. As a comparison, the optimum Neyman-Pearson and the whitening matched filter strategies to detect coherent pulse trains against the above mentioned disturbance are also presented. The optimum detection scheme is heavy to implement: it involves a numerical integration with respect to the texture variable of the K distribution. It strongly depends on the parameters of the clutter distribution, thus no predetermined threshold can be assigned to achieve a given probability of false alarm if such parameters are unknown. The preferred sub-optimum approach is based on the estimation of the texture variable, which is then used to determine the likelihood ratio. Applying the maximum likelihood estimate the resulting detection strategy is a linear quadratic functional of the observed vector and is clutter distribution free. The performance of the proposed detector is close to optimal and much better than the whitening matched filter detector; moreover, it guarantees approximately constant false alarm rate behaviour, regardless of the clutter distribution.

An expansion for some second-order probability distributions and its application to noise problems

Abstract: In this paper it is shown that, in general, second-order probability distributions may be expanded in a certain double series involving orthogonal polynomials associated with the corresponding first-order probability distributions. Attention is restricted to those second-order probability distributions which lead to a "diagonal" form for this expansion. When such distributions are joint probability distributions for samples taken from a pair of time series, some interesting results can be demonstrated. For example, it is shown that if one of the time series undergoes an amplitude distortion in a time-varying "instantaneous" nonlinear device, the covariance function after distortion is simply proportional to that before distortion. Some simple results concerning conditional expectations are given and an extension of a theorem, due to Doob, on stationary Markov processes is presented. The relation between the "diagonal" expansion used in this paper and the Mercer expansion of the kernel of a certain linear homogeneous integral equation, is pointed out and in conclusion explicit expansions are given for three specific examples.