K-distribution

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

Algorithmic learning of probability distributions from random data in the limit

Abstract: We study the problem of identifying a probability distribution for some given randomly sampled data in the limit, in the context of algorithmic learning theory as proposed recently by Vinanyi and Chater. We show that there exists a computable partial learner for the computable probability measures, while by Bienvenu, Monin and Shen it is known that there is no computable learner for the computable probability measures. Our main result is the characterization of the oracles that compute explanatory learners for the computable (continuous) probability measures as the high oracles. This provides an analogue of a well-known result of Adleman and Blum in the context of learning computable probability distributions. We also discuss related learning notions such as behaviorally correct learning and orther variations of explanatory learning, in the context of learning probability distributions from data.

Properties and Applications of some Distributions derived from Frullani's integral

Abstract: Frullani’s integral dates from 1821, but a probabilistic interpretation of it has never been made. In this paper, Frullani’s integral formula is shown to result from mixing a lifetime distribution by allowing the logarithm of the scale factor to be uniformly distributed over a finite range. This gives a class of long-tailed distributions related to slash distributions, where the pdf is simply expressed in terms of the survival function of the ‘parent’ distribution. The resulting survival distributions have all moments finite, and can exhibit the bimodal hazard functions sometimes seen in practice. A distribution of this type analogous to the t-distribution is derived, the corresponding multivariate distributions are given, and two skewed versions of this distribution are derived. The use of the mixed distributions for inference is exemplified by fitting them to several datasets. It is expected that there will be many applications, in health, reliability, telecommunications, finance, etc.

Generalized Incomplete Modified Bessel Distributions with Applications to Reliability.

Abstract: : Properties of the generalized incomplete modified Bessel distributions are developed and applications to various problems in systems reliability are given (Author)

Process of random distributions : classification and prediction

Abstract: We define a continuous time stochastic process such that each is a Ferguson-Dirichlet random distribution. The parameter of this process can be the distribution of any usual such as the (multifractional) Brownian motion. We also extend Kraft random distribution to the continuous time case. We give an application in classifiying moving distributions by proving that the above random distributions are generally mutually orthogonal. The proofs hinge on a theorem of Kakutani. Key words and phrases. Bayesian, Clustering, Dirichlet distributions, Dirichlet processes, E.M. algorithm, gamma processes, Kraft processes, mixture, nonparametric estimation, random distributions, S.A.E.M. algorithm, weighted gamma processes