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K-distribution

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


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Journal ArticleDOI
TL;DR: In this article, a recursive relation was developed to evaluate numerically the photon-counting distributions and their factorial moments with excellent accuracy, together with a generalized method of steepest descent.
Abstract: The K distribution is used in a number of areas of scientific endeavor. In optics, it provides a useful statistical description for fluctuations of the irradiance (and the electric field) of light that has been scattered or transmitted through random media (e.g., the turbulent atmosphere). The Poisson transform of the K distribution describes the photon-counting statistics of light whose irradiance is K distributed. The K-distribution family can be represented in a multiply stochastic (compound) form whereby the mean of a gamma distribution is itself stochastic and is described by a member of the gamma family of distributions. Similarly, the family of Poisson transforms of the K distributions can be represented as a family of negative-binomial transforms of the gamma distributions or as Whittaker distributions. The K distributions have heretofore had their origins in random-walk models; the multiply stochastic representations provide an alternative interpretation of the genesis of these distributions and their Poisson transforms. By multiple compounding, we have developed a new transform pair as a possibly useful addition to the K-distribution family. All these distributions decay slowly and are difficult to calculate accurately by conventional formulas. A recursion relation, together with a generalized method of steepest descent, has been developed to evaluate numerically the photon-counting distributions and their factorial moments with excellent accuracy.

52 citations

Journal ArticleDOI
TL;DR: In this paper, the authors discuss mixed exponential distributions and general scale mixtures with specific consideration the purpose of insurance modeling, and derive results for equilibrium distributions (defined via stop-loss transforms) of mixed distributions.
Abstract: In this article we discuss mixed exponential distributions and, more generally, scale mixtures with specific consideration the purpose of insurance modeling. Results are derived for equilibrium distributions (defined via stop-loss transforms) of mixed distributions. Some recursive relations are identified for the stop-loss transforms and moments of mixed exponential distributions. Explicit expressions are obtained for equilibrium gamma distributions with arbitrary shape parameter.

52 citations

Journal ArticleDOI
TL;DR: In this article, low-resolution polarimetric data gathered by the AirSAR system over the Feltwell U.K. agricultural testsite reveals Gaussian behaviour at C band for all vegetation types, but clear evidence of texture at longer wavelengths.
Abstract: Low resolution polarimetric data gathered by the AirSAR system over the Feltwell U.K. agriculturaltestsite reveals Gaussian behaviour at C band for all vegetation types, but clear evidence of texture at longer wavelengths. The measurements are compared with the predictions of a polarimetric texture model based on a multivariate K distribution (which includes the Gaussian distribution as a special case), from which distributions of the inphase component, amplitude, amplitude ratio, phase difference and real hermitian product between channels are derived. Kolmogorov-Smirnov fits to these marginal distributions verify that C, Land P band observations over a range of vegetation types are consistent with the model, but there is evidence of the model breaking down in cereal fields at P band. The departure from Gaussian behaviour with increasing wavelength is strongest for cereals; less marked trends are observed for root vegetables, while forest appears Gaussian at all wavelengths. These results are un...

51 citations

Book
01 Jan 2003
TL;DR: In this article, the authors introduce the concept of Probability Distributions and Probability Densities, and present a set of test cases for different types of probability distributions, including normal distributions, sampling distributions, and special distributions.
Abstract: 1. Introduction. 2. Probability. 3. Probability Distributions and Probability Densities. 4. Mathematical Expectation. 5. Special Probability Distributions. 6. Special Probability Densities. 7. Functions of Random Variables. 8. Sampling Distributions. 9. Decision Theory. 10. Point Estimation. 11. Interval Estimation. 12. Hypothesis Testing. 13. Tests of Hypotheses Involving Means, Variances, and Proportions. 14. Regression and Correlation. 15. Design and Analysis of Experiments. 16. Nonparametric Tests.

51 citations

Journal ArticleDOI
TL;DR: In this paper, it was shown that the transformation x = y g(x) occurs naturally in the distribution of the number of customers served during a busy period which implies that at least one particular family of these Lagraagian distributions must play a basic role in queueing theory.
Abstract: Several discrete Lagrangian probability distributions have been generated by Consul and Shanton (1972) by using the Lagrange expansion in y of a probability generating function f(x) under the transformation x = y g(x) where g(x) is another pgf. By using probabilistic arguments the authors show that the transformation x = y g(x) occurs naturally in the distribution of the number of customers served during a busy period which implies that at least one particular family of these Lagraagian distributions must play a basic role in queueing theory. It has also been proved that under one set of conditions all discrete Lagrangian distributions approach to the normal density function while under another set of conditions they approach the inverse Gaussiam density function.

51 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20232
20228
20213
20207
201914
201816