Showing papers on "K-distribution published in 1982"
TL;DR: A seven-parameter family of bivariate probability distributions is developed which allows for any gamma marginal distributions, any associated correlation (positive or negative), and a range of regression curves.
Abstract: A seven-parameter family of bivariate probability distributions is developed which allows for any gamma marginal distributions, any associated correlation (positive or negative), and a range of regression curves. The form of the family, which relies on the reproducibility property of the gamma distribution, is motivated by the search for tractable parameter estimation, general dependency structure, and straightforward computer sampling for simulation modeling. A modification with closed-form parameter estimation, but less general dependency structure, is also given. Finally, the use of these distributions in the form of first order autoregressive time series is discussed.
68 citations
TL;DR: In this article, it was shown that the probability density function of the intensity for a monochromatic, fully developed speckle pattern changes from an exponential distribution at low turbulence levels to a K distribution as the turbulence level increases.
Abstract: It is shown that, because of the effects of the turbulent atmosphere, the probability density function of the intensity for a monochromatic, fully developed speckle pattern changes from an exponential distribution at low turbulence levels to a K distribution as the turbulence level increases. A physical model that leads to the K distribution is proposed, and the parameters of the K distribution are derived in terms of the strength of turbulence, path length, wavelength, and beam size. The work is then extended to polychromatic and partially developed speckle patterns and to speckle with a coherent background. Good agreement is obtained between the theoretical predictions and experimental measurements.
51 citations
TL;DR: In this article, a method for selecting a distributional model for a random variable, given a random sample of observations of it, is studied for various cases, including those of choosing between the Weibull and lognormal distributions, between the Lognormal and gamma distributions, and between the gamma and Weiball distributions, as well as choosing one of the three.
Abstract: A method for selecting a distributional model for a random variable, given a random sample of observations of it, is studied for various cases. The problems considered include those of choosing between the Weibull and lognormal distributions, between the lognormal and gamma distributions, and between the gamma and Weibull distributions, as well as choosing one of the three. Simulation studies were performed to estimate probabilities of correct selection for the method when it is applied to these problems
35 citations
TL;DR: The characteristic feature of -8/3 power law behavior of power spectrum and the shift of Tatarski's peak frequency in the case of strong turbulence is demonstrated.
Abstract: Experimental results are presented for the statistics of 0.6328-microm laser irradiance fluctuations for multiple-pass propagation through a laboratory-simulated atmospheric turbulence of strength C(2)(n) = 2.476 x 10(-11) m(-2/3) and the smallest scale size l(0) = 2.74 mm. The coefficients of variation gamma(0), skewness gamma(1), and excess gamma(2) of irradiance fluctuations are plotted as a function of path length. From the plots of gamma(2) vs gamma(1) for various values of sigma(2)(1) (= 1.23 k(7/6) C(2)(n)L(11/6)) in different regions within the turbulence, the following forms of the probability distribution functions for the irradiance fluctuations are considered: lognormal, Rice-Nakagami, m distribution, gamma (and exponential), and K distribution. We have also demonstrated the characteristic feature of -8/3 power law behavior of power spectrum and the shift of Tatarski's peak frequency in the case of strong turbulence.
30 citations
TL;DR: In this paper, the probability density functions of quotient of order statistics from the Pareto, Power and Weibull distributions were analyzed using the Mellin transform technique, and the distribution of the quotient Z = X/X where X,X(i < j) are the ith and jth order statistics.
Abstract: This paper deals with the probability density functions of quotient of order statistics. We use the Mellin transform technique, to find the distribution of the quotient Z= X/Xwhere X.,X(i < j) are the ith and jth order statistics from the Pareto, Power and Weibull distributions
16 citations
TL;DR: Csiszar's work on the topological properties of ƒ-divergences enables one to identify strong distances and provides a justification for the experimental findings of previous investigators.
15 citations
TL;DR: The mixed gamma density as mentioned in this paper is derived for link lengths by assuming that both the component link length distribution for each relatively homogeneous part of the landscape and the mixing distribution of weights assigned to the various component distributions can be represented by gamma distributions.
Abstract: An investigation of the lengths of exterior and interior links in 12 disparate areas suggests that link length distributions for most, if not all, natural landscapes represent a mixture of link length populations from different parts of the landscape characterized by different ground slope and/or environmental conditions. The mixed gamma density is derived for link lengths by assuming that both the component link length distribution for each relatively homogeneous part of the landscape and the mixing distribution of weights assigned to the various component distributions can be represented by gamma distributions. The mixed gamma density satisfactorily fits 84% of the 70 link length distributions examined, compared with 67% fitted by the log normal and 59% fitted by the gamma density. Deviations from the mixed gamma density are largely ascribed to spatial distributions of slope and environmental conditions which give rise to nongamma-mixing distributions.
9 citations
TL;DR: In this paper, some criteria based on K-L information number and W-divergence are presented for a certain type of uniform approximate equivalence of two probability distributions, and necessary and sufficient conditions are also given for the corresponding uniform asymptotic equivalence for two random sequences.
Abstract: Some criteria based on K-L information number andW-divergence are presented for a certain type of uniform approximate equivalence of two probability distributions. As applications, some necessary and sufficient conditions are also given for the corresponding uniform asymptotic equivalence of two random sequences.
7 citations
01 Jan 1982
TL;DR: In this article, an analogous problem was considered by compounding a binomial distribution and a generalized beta one given in [8] by T.G.Środka.
Abstract: In paper [6] J.G. Skellam gave a distribution which grew out of a compound of a binomial distribution and a beta one. In the present paper we consider an analogous problem by compounding a binomial distribution and a generalized beta one given in [8] by T. Środka. The distribution obtained yields interesting special as well as limit cases constituting compounds of the binomial distribution and those most frequently encountered in statistical practice.
6 citations
TL;DR: Probability generating functions evaluated on finite difference operators were used systematically to derive formulas for moments of discrete distributions in this article, where they were used to derive probability generating functions for moments in discrete distributions.
Abstract: Probability generating functions evaluated on finite difference operators are used systematically to derive formulas for moments of discrete distributions.
5 citations
TL;DR: The results of a Monte Carlo calculation of the probability distribution of the far-field irradiance produced by a thin turbulent layer placed in front of a finite-aperture transmitter show that Rice-Nakagami and other well-known distributions are inapplicable to this problem.
Abstract: The results of a Monte Carlo calculation of the probability distribution of the far-field irradiance produced by a thin turbulent layer placed in front of a finite-aperture transmitter are discussed. These results clearly show that Rice-Nakagami and other well-known distributions such as the lognormal distribution are inapplicable to this problem.
TL;DR: This paper reports theoretical probability density and cumulative distribution functions for glint and speckle target returns in a compact coherent laser radar.
Abstract: This paper reports theoretical probability density and cumulative distribution functions for glint and speckle target returns in a compact coherent laser radar Calculator programs are given to facilitate use of these results
06 Dec 1982
TL;DR: This paper presents a three-activity approach to fitting distributions to data and highlights the capabilities of UNIFIT which allow the analyst to perform these activities in a thorough and timely manner.
Abstract: An important problem which occurs in many different disciplines is that of determining a probability distribution which is a good representation of an observed data set. For example, in building a simulation model of a manufacturing process or of a computer system, one needs to determine appropriate probability distributions for the input random variables. A common solution to this problem is to fit standard distributions (e.g., normal or gamma) to observed system data. However, since this fitting process is rather complicated and time consuming when done by hand, it is often performed in a superficial and incorrect manner. The net effect is, of course, that the selected distributions may not be good representations of the observed data.UNIFIT is a state-of-the-art, interactive computer package for fitting probability distributions to observed data. By combining the latest statistical techniques with graphical displays, the package allows one to perform a comprehensive analysis of a data set in significantly less time than would otherwise be possible. It employs a there-activity approach for determining an appropriate distribution. The first activity involves using heuristic techniques such as histograms or sample moments to hypothesize one or more families of distributions which might be representative of the observed data. For example, if our data are continuous and if a histogram of the data indicates that the density function of the underlying distribution is skewed to the right, then we might hypothesize that a gamma, lognormal, or Weibull distribution is an appropriate model for our observed data. However, each of these families of distributions has several parameters which must be specified in order to have a completely determined distribution. Therefore, the second activity typically involves estimating the parameters of each hypothesized family from the data, thereby specifying a number of particular distributions. In the third activity we determine which of the fitted distributions, if any, is the best representation for the data using both heuristic techniques and goodness-of-fit tests. An example of a heuristic technique provided by UNIFIT is the frequency comparison, which is a graphical display showing both the observed proportion of observations and the expected proportion of observations from a particular fitted distribution for each histogram interval. The frequency comparison is particularly useful for visually determining how well a selected probability model represents the underlying distribution for the data. In addition to heuristic techniques, UNIFIT makes available to an analyst the chi-square, the Kolmogorov-Smirnov, and the Anderson-Darling goodness-of-fit tests. These tests can be considered to be a formal approach for detecting gross discrepancies between the fitted distribution and the observed data.
TL;DR: In this article, the authors present trigonometric functions and cdmblnations from probability distributions and apply them to the problem of statistical computing and simulation in the context of statistical computer vision.
Abstract: (1982). C132. Trigonometric functions and cdmblnations from probability distributions. Journal of Statistical Computation and Simulation: Vol. 15, No. 2-3, pp. 233-237.
TL;DR: In this paper, a recursive algorithm is presented to compute the lead time aggregate demand distribution from the arrival distributions of each order size, without first fitting the data frequencies to standard distributions.
Abstract: This paper presents a recursive algorithm to compute the lead time aggregate demand distribution from the arrival distributions of each order size. This algorithm can compute the aggregate demand distribution directly from numerical data of arrival frequencies without first fitting the data frequencies to standard distributions. When the arrival distributions do follow certain standard distributions, the aggregate demand distribution can be computed explicitly. The cases of Poisson distributions and negative binomial distributions are demonstrated as examples.