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 of the fractional differences of the structure amplitudes and intensities of two related crystals

Abstract: The probability distributions of the fractional intensities and amplitudes of x-ray reflections from a pair of imperfectly related structures are derived when both the structures satisfy the requirements of a given type of basic Wilson distribution. These two distributions are used to obtain theoretical expressions for 2 new fractional type ofR-indices which are expected to be useful in the final stages of refinement. The theoretical distributions are also used to deduce some theoretical distributions which are useful as tests for centrosymmetry via the random permutation method. The theoretical values of the relevant semi-cumulative functions are also tabulated.

Active sonar clutter classification using higher order moments.

Abstract: The statistics of normalized matched‐filter echoes from an active sonar system operating in a myriad of oceanic environments has been studied extensively for three broad clutter classes including using low‐order cumulants to classify subregions of the data [Gelb et al., Proceedings of the ISURC (2008) and references therein]. That work compared empirical distributions to parametric models (e.g., the K distribution and the generalized Pareto distribution). A report on extensions of this work is presented including studies of the accuracy of analytic parameter estimation methods and the efficacy of using higher order moments in the classification process. For each class, with increasingly heavy non‐Rayleigh distributed tails, comparisons are made of brute force parameter estimation with the use of analytic estimators. Additionally, comparisons of higher order moments (including skew and kurtosis) computed from the data are made with analytic fits to the data. Using a feature‐based classifier, the gains of using increasingly higher order moments are assessed. [Work sponsored by the Office of Naval Research (ONR).]

On a general class of probability distributions and its applications

Abstract: A general class of probability distributions is proposed and its properties examined. The proposed family contains distributions of a wide variety of shapes, such as U shaped, uniform and long-tailed distributions, as well as distributions with supports that have finite limits at one or both endpoints. Due to its great flexibility, this parametric class (which we refer to as the class of UIC distributions) can be routinely used to fit empirical data collected in different experimental or observational studies without the need of specifying in prior the type and form of distributions to be fitted. It is also simple and inexpensive to simulate from the proposed class of distributions, making it particularly attractive in simulation based optimization applications involving stochastic components with distributions empirically determined from historical data. More importantly, it is shown both theoretically and empirically that under fairly general conditions the sampling distribution of a standardized sample statistic is approximately an UIC distribution, which provides a much closer approximation than the normal approximation in small to medium sample sizes. Applications in the bootstrap, such as estimation of the variance of sample quantiles and quantile estimation by the "smoothed" bootstrap are discussed. The Monte Carlo studies conducted show encouraging results, even in cases where the traditional kernel density approximations do not perform well.