K-distribution

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

A note on the Cauchy-type mixture distributions

Abstract: An interesting class of continuous distributions, called Cauchy-type mixture, with potential applications in modelling erratic phenomena is introduced by Soltani and Tafakori [A class of continuous kernels and Cauchy type heavy tail distributions. Statist Probab Lett. 2013;83:1018–1027]. In this work, we provide more insights into the Cauchy-type mixture distributions, involving certain characterizations, connections with the generalized Linnik distributions and the class of discrete distributions induced by stable laws. We also prove that the Laplace transform of Cauchy-type mixture distributions when normalized by constant terms become as a density functions in terms of distributional conjugate property.

Failure Probability Analysis Based on FRI Model for SCC Growth Introducing Stress Intensity Factor Distribution as Function of Crack Depth

Abstract: Failure probability of welds by stress corrosion cracking (SCC) in austenitic stainless steel piping is analyzed by probabilistic fracture mechanics (PFM) approach based on an electro-chemical crack growth model named FRI model[1] through which a basic equation is derived. Introducing the relation among dK/dt, da/dt and dK/da (K: stress intensity factor, a: crack depth and t: time) into the basic equation, modified basic equation is derived which can give da/dt in explicit form in contrast to the fact that the basic equation is transcendental and can be solved only numerically by iterative method. From numerical evaluation of K distribution at a crack tip under bending stress, it is realized that there exists a relation between a and K and it can be expressed approximately by quadratic function, i.e. K = Km{1−(a−am)2/am2}. By examining K as function of a, am is proved to be a linear function of membrane stress to bending stress ratio. These findings are incorporated into the modified basic equation which is shown to be able to calculate da/dt without instability and needs no iteration. Stratified Monte-Carlo method is introduced which defines two dimensional sampling space composed of a/c (c is crack length at surface) ranging from 0 to 1 and K from 0 to Kw which has to be defined referring to KSCC . Log-normal distributions are anticipated for a/c and K probability distributions. The median of K is decided referring to median of a in Bruckner model. Parameter surveys for cumulative failure probability (CFP) performed with the basic equation and the modified basic equation give very close results. In this study, the residual stress distribution generated by residual stress at welding is anticipated to be tensile on inner surface and compressive on outer surface like bending stress distribution. Therefore the simulation is performed under bending dominative condition. The modified basic equation is proved to need about 1/2 calculation time of needed by the original basic equation in the CFP simulation.© 2011 ASME

Probability distribution of velocity difference in the inertial interval of a turbulence spectrum

Abstract: The statistical turbulence characteristics are analyzed in the inertial interval of a spectrum. An equation is obtained for the probability distribution of the velocity difference at two points. Parameters characterizing the turbulence spectrum in the inertial interval enter into the equation in the role of unknown constants. These constants are calculated from the condition that a solution exists which has a physical meaning.

The p -adic Valued Probability Distributions (Generalized Functions)

Abstract: Unboundedness of the p-adic Gaussian distribution is the strong reason to create a variant of the p-adic theory of probability, where probabilities belong to spaces of distributions (=generalized functions). This chapter is devoted to this problem. This theory is very similar to the ordinary quantum probability (over the field of real numbers). Both these formalisms develop without measure-theoretical constructions.

Nonlinear Filtering of Convex Sets of Probability Distributions.

Abstract: A solution is provided to the problem of computing a convex set of conditional probability distributions that characterize the state of a nonlinear dynamic system as it evolves in time. The estimator uses the Galerkin approximation to solve Kolmogorov's equation for the diffusion of a continuous-time nonlinear system with discrete-time measurement updates. Filtering of the state is accomplished for a convex set of distributions simultaneously, and closed-form representations of the resulting sets of means and covariances are generated.