Showing papers on "K-distribution published in 1986"

One-dimensional stable distributions

Abstract: Examples of stable laws in applications Analytic properties of the distributions in the family $\mathfrak S$ Special properties of laws in the class $\mathfrak W$ Estimators of the parameters of stable distributions.

Survival models for heterogeneous populations derived from stable distributions

Abstract: SUMMARY A new three-parameter family of distributions on the positive numbers is proposed. It includes the stable distributions on the positive numbers, the gamma, the degenerate and the inverse Gaussian distributions. The family is characterized by the Laplace transform, from which moments, convolutions, infinite divisibility, unimodality and other properties are derived. The density is complicated, but a simple saddlepoint approximation is provided. Weibull and Gompertz distributions are naturally mixed over some of the distributions. The family is natural exponential in one of the parameters. The distributions are relevant for application as frailty distributions in life table methods for heterogeneous populations. Desirable properties of such distributions are discussed. As an example survival after myocardial infarction is considered.

Mathematical genesis of the I–K distribution for random optical fields

Abstract: The recently developed I–K distribution and its connection with other distributions is examined in the context of optical waves scattered by a turbulent medium. In particular, it is shown how the I–K distribution, K distribution, and homodyned K distribution all evolve as marginal density functions from compound or doubly stochastic Gaussian optical fields. In this setting the genesis of the I–K distribution is very similar to that of the homodyned K distribution, and there is one special case (α = 1) in which the two distributions are identical. Also, both the homodyned K and the I–K distribution are shown to reduce to the K distribution in strong-turbulence regimes. The I–K distribution is further examined as a model for the irradiance when the distribution parameter α is restricted to half-integer values, leading to simpler forms of the distribution. The special case of the I–K distribution corresponding to α = 1/2 shows a particularly good fit with experimental data over a wide range of conditions of atmospheric turbulence.

Lyapounov Function and Stationary Probability Distributions

Abstract: It is shown that the stationary probability distributions of master equations in the leading order of the system-size are the Lyapounov functions of the corresponding kinetic equations and may be candidates of the potentials of the systems far from equilibrium.

An alternative to the kolmogrov-smirnov two-sample test

Abstract: An alternative to the Kolmogorov-Smirnov two-sample test based on the test statistic is suggested, where #{} denotes the cardinality of the set. For the null-hypothesis case the probability distribution and its low-order moments are derived in the exact and in an approximateversion. Based on Monte Carlo estimates the power of the two tests are compared for samples of uniform, normal, and gamma distributions Pure shifts of expectation and variance of one of the sample distributions are considered as well as the case of shifts in both parameters; other situations considered concern samples from different distributions and samples from disturbed distributions. The results indicate that the test based on T is more powerful than the Kolmogorov-Smirnov test for samples of the uniform distribution which differ in the expectation and in the case of disturbed distributions.

Approximation of Discrete Probability Distributions in Spherical Stereology

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).

The application of the principle of minimum cross-entropy to the characterization of the exponential-type probability distributions

Abstract: Systematic and simple characterizations are presented for several familiar distributions in exponential family by means of the principle of minimum cross-entropy (minimum discrimination information). The suitable prior distributions and the appropriate constraints on expected values are given for the underlying distributions.

Modified information criteria for a uniform approximate equivalence of probability distributions

Abstract: Information criteria for two-sided uniform ϕ-equivalence, which is a newly introduced strong approximate equivalence of probability distributions, are proposed. The criteria resort to some modified K-L informations defined on suitable approximate main domains and are presented in the form of systems with double inequalities. They present systematic implements to handle many statistical approximation problems and are useful to evaluate related approximation errors quantitatively. Criteria for asymptotic cases are also derived from the presented inequalities. As applications, necessary and sufficient conditions and error evaluations are given for approximate and/or asymptotic equivalences of the probability distributions on sampling with and without replacement from a finite population and on quasi-extreme order statistics from a continuous distribution.

Decompositions of multivariate probability distributions

Abstract: The divisors of multivariate probability distributions are considered that are decreasing at infinity not more slowly than normal distributions and that satisfy various symmetry conditions (in particular, the condition of spherical symmetry).