K-distribution

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

The wrapped Gamma distribution and wrapped sums and linear combinations of independent Gamma and Laplace distributions

Abstract: In this paper we first obtain an expression for the probability density function of the wrapped or circular Gamma distribution and then we show how it may be seen, both for integer and non-integer shape parameter, as a mixture of truncated Gamma distributions. Some other properties of the wrapped Gamma distribution are studied and it is shown how this distribution and mixtures of these distributions may be much useful tools in modelling directional data in biology and meteorology. Based on the results obtained, namely the ones concerning mixtures, and on some properties of the distributions of the sum of independent Gamma random variables, the wrapped versions of the distributions of such sums, for both integer and non-integer shape parameters are derived. Also the wrapped sum of independent generalized Laplace distributions is introduced as a particular case of a mixture of wrapped Gamma distributions. Among the particular cases of the distributions introduced there are symmetrical, slightly ske...

Stable Distributions as Noise Models for Molecular Communication

Abstract: In this work, we consider diffusion-based molecular communication timing channels. Three different timing channels are presented based on three different modulation techniques, i.e., i) modulation of the release timing of the information particles, ii) modulation on the time between two consecutive information particles of the same type, and iii) modulation on the time between two consecutive information particles of different types. We show that each channel can be represented as an additive noise channel, where the noise follows one of the subclasses of stable distributions. We provide expressions for the probability density function of the noise terms, and numerical evaluations for the probability density function and cumulative density function. We also show that the tails are longer than Gaussian distribution, as expected.

Strong large deviations for composite hypothesis testing

Abstract: A simple hypothesis P is tested against a composite hypothesis Q , j ∈ {1, 2, · · · , k}, each Q being a product of n probability distributions. We consider the set of achievable false-positive error probability vectors for a generalized NeymanPearson test under a constraint on the probability of correct detection under P. Exact asymptotics (as n → ∞) are derived for this set, in particular the set is determined within an O(1) term.

Estimating parameters for discrete distributions via the empirical probability generating function

Abstract: We consider parameter estimation for a family of discrete distributions characterized by probability generating functions (pgf's). Kemp and Kemp (1988) suggest estimators based on the empirical probability generating function (epgf) the methods involve solving estimating equations obtained by equating functionals of the epgf and pgf on a fixed, finite set of values. We derive asymptotic theory for these estimators and consider some examples. Graphical techniques based on the theory are shown to be useful for exploratory analysis