K-distribution

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

Minimum distance estimators for count data based on the probability generating function with applications

Abstract: This paper studies properties of parameter estimators obtained by minimizing a distance between the empirical probability generating function and the probability generating function of a model for count data. Specifically, it is shown that, under certain not restrictive conditions, the resulting estimators are consistent and, suitably normalized, asymptotically normal. These properties hold even if the model is misspecified. Three applications of the obtained results are considered. First, we revisit the goodness-of-fit problem for count data and propose a weighted bootstrap estimator of the null distribution of test statistics based on the above cited distance. Second, we give a probability generating function version of the model selection test problem for separate, overlapping and nested families of distributions. Finally, we provide an application to the problem of testing for separate families of distributions. All applications are illustrated with numerical examples.

A compound class of Poisson and lifetime distributions

Abstract: A new lifetime class with decreasing failure rate which is obtained by compounding truncated Poisson distribution and a lifetime distribution, where the compounding procedure follows same way that was previously carried out by Adamidis and Loukas(1998). A general form of probability, distribution, survival and hazard rate functions as well as its properties will be presented for such a class. This new class of distributions generalizes several distributions which have been introduced and studied in the literature.

Tutorial : S-system analysis of continuous univariate probability distributions

Abstract: This tutorial describes the numerical analysis of continuous univariate probability functions with S-systems. These are computationally efficient nonlinear ordinary differential equations that contain virtually all ordinary differential equations as special cases. After a brief introduction to S-systems, it is shown how central and noncentral probability distributions, as well as auxiliary functions such as Bessel, Gamma, and Beta functions, can be recast equivalently as S-systems. The representation of distributions as S-systems permits rapid computation of function evaluations over wide ranges of random variables, as well as moments, quantiles, power and inverse power. It also offers transformation methods and various options of approximation. The recasting procedure employs elementary mathematics and needs to be executed only once. The tutorial contains a catalogue of recast S-system representations for nearly all relevant distributions and auxiliary functions, and thus enables the reader to evaluate d...

Statistical scattering model for high-resolution sonar images : characterisation and parameter estimation

Abstract: The statistical mechanism ruling the reverberation from the seabed in high-resolution sonar devices is investigated. The signal received from a sonar cell is assumed to arise from the coherent sum of a random number of independent elementary contributions. Under proper conditions regarding the surface roughness and the incidence angle, the observables can be modelled as compound-Gaussian random variables with a nonuniform distribution of phase. A general expression has been found for evaluating the first- and second-order probability density function of the complex observables, and the case corresponding to a gamma distributed texture is investigated. The authors also propose a technique for estimating parameters of the generalised K distribution based on approximating the design distribution with a neighbouring family. Results have demonstrated that the algorithm achieves good performance within the examined range of parameter values.