K-distribution

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

Conflations of probability distributions

Abstract: The conflation of a finite number of probability distributions P 1 , ..., P n is a consolidation of those distributions into a single probability distribution Q = Q(P 1 , ..., P n ), where intuitively Q is the conditional distribution of independent random variables X 1 , ..., X n with distributions P 1 , ..., P n , respectively, given that X 1 = ··· = X n . Thus, in large classes of distributions the conflation is the distribution determined by the normalized product of the probability density or probability mass functions. Q is shown to be the unique probability distribution that minimizes the loss of Shannon information in consolidating the combined information from P 1 , ..., P n into a single distribution Q, and also to be the optimal consolidation of the distributions with respect to two minimax likelihood-ratio criteria. In that sense, conflation may be viewed as an optimal method for combining the results from several different independent experiments. When P 1 , ..., P n are Gaussian, Q is Gaussian with mean the classical weighted-mean-squares reciprocal of variances. A version of the classical convolution theorem holds for conflations of a large class of a.c. measures.

Statistical measurements of irradiance fluctuations of a multipass laser beam propagated through laboratory-simulated atmospheric turbulence

Abstract: Experimental results are presented for the statistics of 0.6328-microm laser irradiance fluctuations for multiple-pass propagation through a laboratory-simulated atmospheric turbulence of strength C(2)(n) = 2.476 x 10(-11) m(-2/3) and the smallest scale size l(0) = 2.74 mm. The coefficients of variation gamma(0), skewness gamma(1), and excess gamma(2) of irradiance fluctuations are plotted as a function of path length. From the plots of gamma(2) vs gamma(1) for various values of sigma(2)(1) (= 1.23 k(7/6) C(2)(n)L(11/6)) in different regions within the turbulence, the following forms of the probability distribution functions for the irradiance fluctuations are considered: lognormal, Rice-Nakagami, m distribution, gamma (and exponential), and K distribution. We have also demonstrated the characteristic feature of -8/3 power law behavior of power spectrum and the shift of Tatarski's peak frequency in the case of strong turbulence.

Statistics of Distinct Clutter Classes in Midfrequency Active Sonar

Abstract: The empirical distributions of normalized matched-filter echoes from a midfrequency active sonar with hyperbolic frequency-modulated waveforms in a myriad of oceanic environments are studied for three broad clutter (nontarget) classes: bottom structures, diffuse compact clutter, and compact nonstationary (moving) clutter. The distributions are characterized using the K -distribution (KD) and the generalized Pare to distribution (GPD). Methods of parameter estimation are discussed, and parameters are computed for small subregions of the clutter fields. A plot of the Kolmogorov-Smirnov (KS) goodness-of-fit statistic of individual subregions is presented for each model and class to highlight the versatility of the models when applied to large quantities of data. Cumulants are computed from the data and are utilized as features in a classifier to demonstrate separability between the classes. An important aspect of this work is the use of distinct clutter classes as opposed to collectively characterizing all clutter as reverberation. Environmental effects are not considered, as the goal of this work is to determine the utility of local clutter estimation models in practical sonar processing systems where accurate environmental data are unavailable.

Review of Envelope Statistics Models for Quantitative Ultrasound Imaging and Tissue Characterization

Abstract: The homodyned K-distribution and the K-distribution, viewed as a special case, as well as the Rayleigh and the Rice distributions, viewed as limiting cases, are discussed in the context of quantitative ultrasound (QUS) imaging. The Nakagami distribution is presented as an approximation of the homodyned K-distribution. The main assumptions made are: (1) the absence of log-compression or application of non-linear filtering on the echo envelope of the radiofrequency signal; (2) the randomness and independence of the diffuse scatterers. We explain why other available models are less amenable to a physical interpretation of their parameters. We also present the main methods for the estimation of the statistical parameters of these distributions. We explain why we advocate the methods based on the X-statistics for the Rice and the Nakagami distributions, and the K-distribution. The limitations of the proposed models are presented. Several new results are included in the discussion sections, with proofs in the appendix.

Ill-Posed Problems in Probability And Stability of Random Sums

Abstract: The General Form of Quantitative Convergence Criteria Some Important New Classes of Probability Metrics Convergence in Weak and Strong Metrics Convergence to Prescribed Distributions Ill-Posed Problems in Computer Tomography Stable Probabilistic Schemes Central Pre-Limit Theorems Infinitely Divisible and Stable Distributions Geometric Stable Distributions on the Real Line Multivariate Geometric Stable Distributions Geometric Stable Laws on Banach Space Estimation and Empirical Issues for GS Distributions A Generalisation of Stable Laws Characterisations of Distributions in Reliability Index.