Topic
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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01 Apr 1963
3 citations
TL;DR: In this article, the double gamma distribution on the real line λc with Laplace transform (1−t2)−c and the distributions of the products of independent random variables X,Y1,…,Yp,U1, etc.
3 citations
01 Jan 1994
3 citations
Posted Content•
TL;DR: It is proved that all probability densities proposed here define heavy-tailed distributions, and it is shown that the weighting of distributions regularly varying with extreme-value index $\alpha > 0$ still results in a regular variation distribution with the same index.
Abstract: Given an arbitrary continuous probability density function, it is introduced a conjugated probability density, which is defined through the Shannon information associated with its cumulative distribution function. These new densities are computed from a number of standard distributions, including uniform, normal, exponential, Pareto, logistic, Kumaraswamy, Rayleigh, Cauchy, Weibull, and Maxwell-Boltzmann. The case of joint information-weighted probability distribution is assessed. An additive property is derived in the case of independent variables. One-sided and two-sided information-weighting are considered. The asymptotic behavior of the tail of the new distributions is examined. It is proved that all probability densities proposed here define heavy-tailed distributions. It is shown that the weighting of distributions regularly varying with extreme-value index $\alpha > 0$ still results in a regular variation distribution with the same index. This approach can be particularly valuable in applications where the tails of the distribution play a major role.
3 citations
01 Jan 1986
TL;DR: In this paper, the backward Euler method converges in the L1-norm for spherical stereology, where the distribution function is a linear combination of Heaviside functions superimposed on a Lipschitz continuous background.
Abstract: If in spherical stereology the actual radius of spheres obeys a discrete probability distribution with unknown jump points the solution of the relevant Abel integral equation is not continuous, and hence the supremum norm is inappropriate for estimating the error of an approximation. We show that the backward Euler method converges in the L1-norm, also in the more general case that the distribution function is a linear combination of Heaviside functions superimposed on a Lipschitz-continuous background. We treat both cases:
(a)
cutting plane (first kind integral equation),
(b)
cutting slice (second kind integral equation).
3 citations