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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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35 citations
Book•
01 May 1998
TL;DR: In this paper, the authors introduce the concept of special probability distributions and their application in probabilistic analysis of odd-numbered exercises. But they do not discuss the application of these distributions in decision theory.
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. Estimation: Theory 11. Estimation: Applications 12. Hypothesis Testing: Theory 13. Hypothesis Testing: Applications. 14. Regression and Correlation. 15. Analysis of Variance. 16. Nonparametric Tests. Appendix A. Sums and Products. Appendix B. Special Probability Distributions. Appendix C. Special Probability Densities. Statistical Tables. Answers to Odd-Numbered Exercises. Index.
35 citations
TL;DR: A method that enables incorporation of correlations between images while keeping a good fit to the marginal distributions is proposed, and the joint distributions produced by the transformation method can be used in supervised classification of radar and optical images.
Abstract: With the ever-increasing number and diversity of Earth observation satellites, it steadily becomes more important to be able to analyze compound data sets consisting of different types of images acquired by different sensors. In this paper, we examine different ways of obtaining joint distributions of such images, and we propose a method that enables incorporation of correlations between images while keeping a good fit to the marginal distributions. The approach basically consists of two steps. First, the marginal densities are specified. Based on this specification, each marginal variable is transformed to a normal distributed variable. The joint distribution of the transformed variables is assumed to be multivariate normal. Transforming back to the original scale gives a joint distribution with dependence, where the initial marginal distributions are preserved. The parameters of the new joint distribution can be estimated. The focus is on marginal distributions that are Gamma, K, or Gaussian, although any distribution could be considered. The joint distributions produced by the transformation method can be used in supervised classification of radar and optical images. Results obtained for a set of four-look synthetic aperture radar (SAR) images, as well as a combination of SAR and optical images, are presented.
35 citations
TL;DR: The standard methods for the calculation of total claim size distributions and ruin probabilities, Panjer recursion and algorithms based on transforms, both apply to lattice-type distributions only and therefore require an initial discretization step if continuous distribution functions are of interest.
Abstract: Abstract The standard methods for the calculation of total claim size distributions and ruin probabilities, Panjer recursion and algorithms based on transforms, both apply to lattice-type distributions only and therefore require an initial discretization step if continuous distribution functions are of interest. We discuss the associated discretization error and show that it can often be reduced substantially by an extrapolation technique.
35 citations
TL;DR: In this article, the authors use an approximate method to construct confidence intervals for the quantiles of the two-parameter gamma and three-parameters generalized gamma distributions for estimating flood quantiles.
Abstract: In hydraulic design, one often needs to estimate flood quantiles for use as design values. It is important to assess the estimation error by constructing confidence intervals (CIs) for these quantiles. Fitting probability distributions to hydrologic data is used widely for estimating quantiles of hydrological variables. The two-parameter gamma (G2) is among the distributions commonly used, but the three-parameter generalized gamma (GG3) (also known as Kritsky-Menkel distribution) is an alternative when more shape flexibility is needed to fit the data. We use an approximate method to construct CIs for the quantiles of the G2 and GG3 distributions. This method is shown to be useful for hydrological applications where the data record is short.
34 citations