Showing papers on "K-distribution published in 1978"
TL;DR: In this article, it was shown that a class of modified Bessel-function distributions may have special significance in describing the statistics of radiation scattered by media characterized by a wide range of length scales, and that these distributions may be obtained mathematically by applying a limit procedure to the random walk problem with a variable number of steps.
Abstract: Evidence is presented which suggests that a class of modified Bessel-function distributions may have special significance in describing the statistics of radiation scattered by media characterized by a wide range of length scales. It is shown that these distributions may be obtained mathematically by applying a limit procedure to the random-walk problem with a variable number of steps. The choice of distribution for the step-number fluctuations is briefly discussed.
286 citations
TL;DR: A table is given of differential entropies for various continuous probability distributions that are of use in the calculation of rate-distortion functions and in some statistical applications.
Abstract: A table is given of differential entropies for various continuous probability distributions. The formulas, some of which are new, are of use in the calculation of rate-distortion functions and in some statistical applications.
194 citations
TL;DR: The expected statistical distributions of intercept length are derived in terms of geometrical probability density functions pertaining to plates with known thickness penetrated by lines with random orientation to provide arithmetic and graphical solutions for obtaining distributions of membrane thickness and reciprocal membrane thickness from empirical distribution of intercept lengths.
Abstract: SUMMARY
The expected statistical distributions of intercept length are derived in terms of geometrical probability density functions pertaining to plates with known thickness penetrated by lines with random orientation. These expressions provide arithmetic and graphical solutions for obtaining distributions of membrane thickness and reciprocal membrane thickness from empirical distributions of intercept lengths. Furthermore, general relationships between probability density functions of distributions of intercept length and membrane thickness are derived as well as those between their moments.
Examples of the application of the method to biological samples are given, and estimated distributions of glomerular basement membrane thickness are compared to those obtained by an independent, direct method.
Various sources of bias, which in practice may occur due to departures from the sample model, are discussed and the influence of some of them is estimated. The knowledge of the probability density function of reciprocal intercepts makes it possible to perform a correction of the distributions of measured intercept length, which to some extent eliminates bias.
129 citations
TL;DR: The paper concludes with a critical discussion of the correlation of frequency‐rank distributions and offers a new measure‐the transfer coefficient.
Abstract: Frequency, rank, and frequency-rank distributions are distinguished and discussion then focuses on frequency-rank distributions. The key example of frequency-rank distributions is the so-called “law of anomalous numbers” which, modeled as a “very mixed” Poisson process and simulated by computer, provides a means of exploring the stability of ranks in sample frequency-rank distributions. The paper concludes with a critical discussion of the correlation of frequency-rank distributions and offers a new measure-the transfer coefficient.
26 citations
TL;DR: In this paper, the probability distributions of selected consequences of a liquid-metal fast breeder reactor hypothetical core disruptive accident were obtained using response surface techniques, and the results of these consequences were used to generate the coefficients for response surface functions that approximate the consequences in terms of the selected input parameters.
Abstract: Response surface techniques are presented for obtaining the probability distributions of selected consequences of a liquid-metal fast breeder reactor hypothetical core disruptive accident. The uncertainties of the consequences are considered as a variability of the system and model input parameters used in the accident analysis. Probability distributions are assigned to the input parameters, and parameter values are systematically chosen from these distributions. These input parameters are then used in deterministic consequence analyses that are performed by fast-running analogs of the comprehensive mechanistic accident analysis codes. The results of these deterministic consequence analyses are used to generate the coefficients for response surface functions that approximate the consequences in terms of the selected input parameters. These approximating functions are then used to generate the probability distributions of the consequences with random sampling being used to obtain values for the accident parameters from their distributions. Two different schemes are presented for selecting the knot-point values of the input parameters. The first generates a single second-order polynomial for the entire parameter space; the second generates separate polynomials for specified regions of the parameter space. The calculation of conditional distributions of the consequences and the use of these distributions to define importance distributions of themore » input parameters are presented. The use of these procedures is illustrated by applications to a postulated loss-of-flow transient with failure to scram in a Clinch River Breeder-type reactor.« less
16 citations
TL;DR: In this paper, the extreme points of certain compact convex sets of probability measures are determined, and this information is then used to obtain a representation of the characteristic functions of the probability distributions in those classes, in the same manner as Urbanik has proceeded for the class $L$.
Abstract: The subclasses of class $L$ probability distributions recently studied by K. Urbanik are characterized by requiring that certain functions be convex and have derivatives of some fixed order. The extreme points of certain compact convex sets of probability measures are determined, and this information is then used to obtain a representation of the characteristic functions of the probability distributions in those classes, in the same manner as Urbanik has proceeded for the class $L$.
15 citations
TL;DR: In this paper, joint- or complex-gaussian statistics are assumed to apply to the in-phase and quadrature components of an electromagnetic wave which has propagated through a turbulent medium, and the consequences of this assumption are compared to tropospheric, ionospheric and laboratory propagation experiments.
Abstract: In this paper joint- or complex-gaussian statistics are assumed to apply to the in-phase and quadrature components of an electromagnetic wave which has propagated through a turbulent medium, and the consequences of this assumption are compared to tropospheric, ionospheric, and laboratory propagation experiments. New curves for the cumulative probability distribution of intensity and for the variance of intensity versus the variance of the logarithm of intensity are presented. Joint-gaussian statistics are shown to fit the total set of turbulence propagation results better than the log-normal, Rice-Nakagami, or Nakagami-m distributions. However, a major feature of optical observations cannot be fit by joint-gaussian statistics: the straight-line cumulative intensity distributions in the saturation regime that reflect a large probability of occurrence of high intensity spikes.
14 citations
01 May 1978
11 citations
TL;DR: In this article, a general method for approximating tail areas is developed through an extension of the methodology of Andrews, which is applied to both continuous and discrete distributions, and examples of the approximations are given for the standard normal, $t$, and chi-square distributions in the continuous case and for the Poisson and binomial distribution in the discrete case.
Abstract: A general method for approximating tail areas is developed through an extension of the methodology of Andrews. This extension is applied to both continuous and discrete distributions. Examples of the approximations are given for the standard normal, $t$, and chi-square distributions in the continuous case and for the Poisson and binomial distributions in the discrete case. Errors of the approximations are considered. The generality of the method shown indicates that extension is possible to other distributions.
9 citations
TL;DR: In this paper, the distributions of Hadamard coefficient for blocks of size 8 × 1 picture elements in six 625-line television pictures were obtained, and the data were well approximated by gamma distributions.
Abstract: The distributions of Hadamard coefficient for blocks of size 8 × 1 picture elements in six 625-line television pictures were obtained. The data were well approximated by gamma distributions. Low-sequency components were best fitted by choosing ?(n) with n in the range 1/2?2/3, and high-sequency components by n = 1 (equivalent to the negative exponential distribution).
TL;DR: In this paper, a simple formal result concerning joint probability distributions in quantum mechanics is obtained and it is shown that some relatively weak properties of the joint distributions cannot be satisfied in the scope of standard quantum mechanics.
Abstract: A simple formal result concerning joint probability distributions in quantum mechanics is obtained. It is shown that some relatively weak properties of the joint distributions cannot be satisfied in the scope of standard quantum mechanics.
TL;DR: The second sequence of nested neighborhoods of the two-phase structure seminvariant ϕ12 - ϕh1kl2-ϕh 1kl2 in the space group P21 is defined, and conditional probability distributions associated with the first four neighborhoods derived as mentioned in this paper.
Abstract: The second sequence of nested neighborhoods of the two-phase structure seminvariant ϕ12 - ϕh1kl2 - ϕh1kl2 in the space group P21 is defined, and conditional probability distributions associated with the first four neighborhoods derived. In the favorable case that the variance of a distribution happens to be small, the distribution yields a particular reliable value for ϕ12. The most reliable estimates are obtained when ϕ12 ≃ ± π/2, thus facilitating enantiomorph specification in this space group.
01 Jan 1978
TL;DR: In this article, a unified and an extended structure of the above classes of distributions as well as their many applications are given. And the behaviour of these families is investigated under most commonly occurring functional operations such as closure under convolution, a passage to a limit in the weak sense, reversal and mixing properties.
Abstract: The objective of this paper is to give a unified and an extended structure of the above classes of distributions as well as their many applications. The behaviour of these families is investigated under most commonly occurring functional operations such as closure under convolution, a passage to a limit in the weak sense, reversal and mixing properties. The useful and smooth properties of unimodality, strong unimodality and their variants are found to hold for some subclasses of these applicable probability distributions.
01 Jun 1978
TL;DR: Techniques for probabilistic response-surface analysis have been developed to obtain the probability distributions of the consequences of postulated nuclear-reactor accidents and are illustrated in conjunction with the fast-running accident-analysis code SACO to provide probability studies of LMFBR hypothetical core-disruptive accidents.
Abstract: Techniques for probabilistic response-surface analysis have been developed to obtain the probability distributions of the consequences of postulated nuclear-reactor accidents. The uncertainties of the consequences are caused by the variability of the system and model input parameters used in the accident analysis. Probability distributions are assigned to the input parameters, and parameter values are systematically chosen from these distributions. These input parameters are then used in deterministic consequence analyses performed by mechanistic accident-analysis codes. The results of these deterministic consequence analyses are used to generate the coefficients for analytical functions that approximate the consequences in terms of the selected input parameters. These approximating functions are used to generate the probability distributions of the consequences with random sampling being used to obtain values for the accident parameters from their distributions. A computer code PROSA has been developed for implementing the probabilistic response-surface technique. Special features of the code generate or treat sensitivities, statistical moments of the input and output variables, region-wise response surfaces, correlated input parameters, and conditional distributions. The code can also be used for calculating important distributions of the input parameters. The use of the code is illustrated in conjunction with the fast-running accident-analysis code SACO to provide probability studies of LMFBR hypothetical core-disruptive accidents. However, the methods and the programming are general and not limited to such applications.