scispace - formally typeset
Search or ask a question
Topic

K-distribution

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


Papers
More filters
01 Jan 2013
TL;DR: In this article, the authors used the idea of approximating Normal and Gamma distributions with Burr type XII distribution to find moments of non-identical order statistics in the presence of Gamma and Normal outliers observations.
Abstract: There are some distributions with no simple closed form for distribution functions such as the Normal and Gamma distributions This will be the problem if we want to find moments of nonidentical order statist ics in the presence of Gamma and Normal outliers observations We used the idea of approximating Normal and Gamma distributions with Burr type XII distribution We get single moments for order statistics from sample of independent nonidentically distributed Bu rr XII random variables that contains p-outlier fro m Normal or Gamma distributions Approximating these distributions with Burr XII distribution and then w e compared the results by previous method
Posted Content
TL;DR: In this paper, the authors introduce a new method to add a parameter to a family of distributions, which is completely studied and a full description of its behaviour in the distribution is given.
Abstract: In this paper we introduce a new method to add a parameter to a family of distributions. The additional parameter is completely studied and a full description of its behaviour in the distribution is given. We obtain several mathematical properties of the new class of distributions such as Kullback-Leibler divergence, Shannon entropy, moments, order statistics, estimation of the parameters and inference for large sample. Further, we showed that the new distribution have the reference distribution as special case, and that the usual inference procedures also hold in this case. Furthermore, we applied our method to yield three-parameter extensions of the Weibull and beta distributions. To motivate the use of our class of distributions, we present a successful application to fatigue life data.
DOI
04 May 2013
TL;DR: In this paper, a compound Gaussian model for modeling sea clutter amplitude stochastic distribution is selected as a result of the sources analysis, because it was confirmed by most of researches.
Abstract: Searching of the sea clutter mathematical model is carried out in this paper. It is suitable to create based on it algorithm for small slow moving targets detection by marine radars. The compound Gaussian model for modeling sea clutter amplitude stochastic distribution is selected as a result of the sources analysis, because it was confirmed by most of researches. The discussed in the literature model based on chaos theory is choosen as perspective alternative for stochastic model; its advantage of using it for such problems solution must be definitively proved or denied. It was proposed many different distributions for high resolution sea clutter amplitude data modeling. The most frequently reported in the literature are K, Log-Normal and Weibull distributions. K distribution belonging to a compound-Gaussian model has the most significant theoretical and experimental background. This distribution choice is physically explained basing on the processes taking place when electromagnetic waves scattered from capillarity and gravity sea waves create a composed echo. Signal representing this echo is the product of two random components, called texture and speckle. Texture is the result of scattering from gravity waves, has a Gamma pdf (in case of K distribution) and corresponds to slow-varying large-scale structure. Speckle is the result of scattering from isolated scatterers (capillarity waves), has a Rayleigh pdf and corresponds to rapid varying small-scale structure. So, K distribution envelope is a compound distribution consisting of a locally Rayleigh distribution speckle whose mean is modulated by a gamma distribution texture. All researches consider Rayleigh pdf for speckle. The lognormal, generalized Gaussian, inverse gamma and some other distributions were proposed for the texture. Due to literature analyses it is seen that texture distribution depends on radar range resolution, but strong dependence is not proved. Some scientists modified K distribution to K-A distribution consisting of the Rayleigh, gamma and Poisson distributions to describe better spikes appearence caused by whitecaps and bursts. Using of Weibull-Weibull (WW) and KK distributions was proposed for high grazing angle and high resolution sea clutter. Doppler characteristics of the sea clutter has been investigated by many researchers and now we have well developed theory. It is known empirical behavior of sea clutter doppler spectrum for different conditions – grazing angle, resolution, wind speed, polarisation and others. Lee, Walker and Ward models are used for sea clutter doppler spectrum describing. Fast moving targets can be effectively detected in heavy sea clutter by doppler radars. But existing theory cannot improve detection of slow moving small targets in heavy sea clutter, because slow moving targets have doppler shift compared to doppler shift of sea clutter. Correlation properties of high resolution sea clutter cannot be derived from its doppler spectrum. In alternative to stohastic model, many researches prefer deterministic model and use chaos theory to describe sea clutter. This choise is based on the fact that both hydrodynamic and electromagnetic therory relying on deterministic models only. If deterministic theory usefulness in applying to high resolution see clutter description be proved completely, it can lead to great progress for small targets in heavy sea clutter detection; because in this case sea clutter behavior can be predicted if initial conditions are precisely known. Using chaotic model for high resolution sea clutter description is highly disputed in recent years, and many researches have questioned first results of high resolution sea clutter describing with chaotic theory usage by Haykin. But great possibilities can give deterministic model for small targets detection definitively proving its ability to describe high resolution sea clutter data precisely causes different scientists to return to chaos theory again and again. Promising results in this field was obtained by using multifractal theory, but still there are not strong methodological background of using deterministic models for small slow moving targets in sea clutter detection, so it is required to make research to prove or deny deterministic models usefulness for high resolution sea clutter data description.
Journal ArticleDOI
TL;DR: In this paper, a method for constructing nonstationary model probability distributions for nonlinear dynamic systems related to the Verhulst stochastic equation is proposed, based on the numerical solution of relaxation differential equations for the mean and the variance.
Abstract: We propose a method for constructing nonstationary model probability distributions for nonlinear dynamic systems related to the Verhulst stochastic equation. The proposed procedure is based on the numerical solution of relaxation differential equations for the mean and the variance. The set of the moment equations is closed and the probability density is constructed on the basis of rigorous analytical relations for the stationary probability characteristics. As a result, these distributions have correct stationary asymptotics. We show the possibility of numerical control of the accuracy of the proposed procedure. We consider the examples of relaxation of the probability characteristics of the amplitude of a self-oscillator and a parametric oscillator with a noise pump. The evolution of the amplitude probability distribution is found.

Network Information
Related Topics (5)
Markov chain
51.9K papers, 1.3M citations
80% related
Estimator
97.3K papers, 2.6M citations
78% related
Iterative method
48.8K papers, 1.2M citations
76% related
Wavelet
78K papers, 1.3M citations
76% related
Robustness (computer science)
94.7K papers, 1.6M citations
73% related
Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20232
20228
20213
20207
201914
201816