K-distribution

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

Moments of Certain Deformed Probability Distributions

Abstract: We consider properties of two classes of discrete probability distributions, namely the so-called Deformed Modified Factorial Series Distributions (DMFSD) and Deformed Modified Power Series Distributions (DMPSD). The formulae for moments and recurrence relations for the moments of these deformed distributions are derived. The results obtained generalize or extend some Theorems given by Janardan (Janardan, K. G. (1984). Moments of certain series distributions and their applications. SIAM J. Appl. Math. 44:854–868) and Gupta (Gupta, R. C. (1974). Modified power series distributions and some of its applications. Sankhya, Ser. B 35:288–298).

A note on realization of decision networks using summation elements

Abstract: Frequently engineering considerations place limitations on the size of decision making systems and on the resources of the system designer. The pertinent high order probability distributions may be unknown and it may not be possible to measure and/or store these distributions in their entirety; some type of approximation is then necessary. One type of approximation that has been studied previously involves measuring and storing several of the lower order component distributions and using these to approximate the high order distribution, using the criterion of maximum entropy. This note considers the related realization problem for binary distributions. By a realization of such an approximation is meant a physical network with the following properties: (1) Its inputs are the variables on which the decision is to be based. (2) Stored within it are the lower order component distributions on which the approximation is to be based. (3) Its outputs (one for each possible decision) are approximations to the high order distributions sufficient to make the decisions. The realization problem for maximum entropy approximations is particularly simple because of their functional form. Maximum entropy distributions are always products of functions of the variables in the given component distributions. Therefore, the logarithms of these distributions are sums of functions of these same variables and hence can be easily realized. It is shown that networks consisting of diodes in the form of “and” gates and resistors in the form of summation elements can realize any probability approximation satisfying the maximum entropy criterion.

Distributions of Runs Revisited

Abstract: Distributions of runs have important applications in many fields, including biological sequence analysis. The generating function (GF) method provides a unified approach to tackle different run-related problems in multistate trials. By utilizing this method, various run-related distributions are derived in a systematic way for both conditional and unconditional models. The GF approach also naturally yields the asymptotic distributions. For all the distributions considered, the limiting distributions are Gaussian, with mean, variance, and covariance linear functions in the size of the system.

Transformation of Bimodal Probability Distributions Into Possibility Distributions

Abstract: At the application level, it is important to be able to define the measurement result as an interval that will contain an important part of the distribution of the measured values, that is, a coverage interval. This practice acknowledged by the International Organization for Standardization (ISO) Guide is a major shift from the probabilistic representation. It can be viewed as a probability/possibility transformation by viewing possibility distributions as encoding coverage intervals. In this paper, we extend previous works on unimodal distributions by proposing a possibility representation of bimodal probability distributions. Indeed, U-shaped distributions or Gaussian mixture distribution are not very rare in the context of physical measurements. Some elements to further propagate such bimodal possibility distributions are also exposed. The proposed method is applied to the case of three independent or positively correlated C-grade resistors in series and compared with the Guide to the Expression of Uncertainty in Measurement (GUM) and Monte Carlo methods.