Showing papers on "K-distribution published in 1981"
TL;DR: In this article, a form of compound distribution is proposed to describe the non-Rayleigh distribution and correlation properties of high-resolution radar sea clutter and a possible physical mechanism is discussed.
Abstract: A proposed form of compound distribution to describe the non-Rayleigh distribution and correlation properties of high resolution radar sea clutter is shown to be a good fit to experimental data. From this model the K distribution is derived, and a possible physical mechanism is discussed.
401 citations
TL;DR: In this paper, various steps involved in the estimation of an extreme design wave are reviewed, including methods of data collection, the use of a plotting formula, selection of a suitable distribution and its parameters, the plotting of confidence bands about the best-fit line, and the selection of the design wave corresponding to a prescribed return period or encounter probability.
Abstract: The various steps involved in the estimation of an extreme design wave are reviewed. These include the following: methods of data collection, the use of a plotting formula, the selection of a suitable distribution and its parameters, the plotting of confidence bands about the best-fit line, and the selection of a design wave corresponding to a prescribed return period or encounter probability. The probability distributions commonly used, including the log-normal and Extremal Types I, II, and III distributions (Gumbel, Fretchet, and Weibull respectively), are described, and their properties are summarized in tabular form for ready reference.
76 citations
TL;DR: In this paper, a general sufficient condition for stochastic ordering of probability distributions is proved and the question of existence of upper and lower bounds in the class of all distributions with given marginals is considered.
Abstract: Some characterizations for the stochastic ordering of probability distributions are given. Especially a general sufficient condition for stochastic ordering is proved and the question of existence of upper and lower bounds in the class of all distributions with given marginals is considered. Stochastic ordering is applied to prove a general theorem on monotonicity of the OC-function of sequential probability ratio tests in stochastic processes.
63 citations
TL;DR: In this paper, the lognormal, Weibull, Pearson type 3, and log Pearson types 3, each a three-parameter distribution, were evaluated in a generalized fashion in terms of the dimensionless variate K (K=X/υ\N\dx, in which X equals randon variable, and υ n = its mean) which has a population mean of unity.
Abstract: The lognormal, Weibull, Pearson type 3, and log Pearson type 3, each a three-parameter distribution, were evaluated in a generalized fashion in terms of the dimensionless variate K (K=X/υ\N\dx, in which X equals randon variable, and υ\N\dn equals its mean) which has a population mean of unity. The bounds of the distributions, areas of the portions of distributions in the negative region of variate when they enter such regions, and the differences in some important quantiles among the four distributions, are presented. The four distributions become less applicable for hydrologic frequency analysis as they deviate more and more from their two-parameter counterparts (lognormal in the case of log Pearson). When they have well-applicable properties, their quantile values differ little for some or all distributions indicating that choice of a distribution makes little difference. Some guidelines are provided for selecting the best applicable distribution for a given hydrologic sample.
13 citations
TL;DR: In this article, the moments of the transformed family of distributions are calculated and the fitting of data to this family is illustrated with a numerical example and the resulting fit is compared with the Johnson's SB distribution fit.
Abstract: The distribution of y=e -1where I is distributed as a gamma random variable is considered(Grassia. 1977). It is shown that this transformed Family of distributions covers a wide region in the (√β1,β2) plane. The moments of this Family of distributions are easily calculated. The fitting of data to this family of distributions is illustrated with a numerical example and the resulting fit is compared with the Johnson's SB distribution fit.
13 citations
01 Jan 1981
TL;DR: In this paper, the joint, marginal, and conditional distributions arising out of (X, Z) are derived via probability generating function techniques, and several ad hoc estimation techniques are discussed.
Abstract: A discrete r.v. X is generalized (compounded) by another discrete r.v. Zi to yield the compound distribution of Z = Z1+ … + ZX. Distributional properties are given concerning the bivariate structure of X and Z. The joint, marginal, and conditional distributions arising out of (X, Z) are derived via probability generating function techniques. Special attention is given to power series distributions (PSD), in particular when Z is a compound Poisson. Recurrences for joint probabilities and cumulants are indicated. Several ad hoc estimation techniques are discussed.
11 citations
TL;DR: The class of Lagrangian probability distributions (LPD) given by the expansion of a probability generating function f t under the transformation u = t/g t where g t is also a p.g. f as discussed by the authors has been substantially widened by removing the restriction that the defining functions g t and f t be probability generating functions.
Abstract: The class of Lagrangian probability distributions ‘LPD’, given by the expansion of a probability generating function f‘t’ under the transformation u = t/g‘t’ where g ‘t’ is also a p.g.f., has been substantially widened by removing the restriction that the defining functions g ‘t’ and f‘t’ be probability generating functions. The class of modified power series distributions defined by Gupta ‘1974’ has been shown to be a sub-class of the wider class of LPDs
7 citations
TL;DR: In this paper, a solution for the theoretical first-order probability density function of laser speckle measured with a finite aperture is presented, which involves the solution of an eigenvalue problem.
Abstract: We present a solution for the theoretical first-order probability density function of laser speckle measured with a finite aperture. A two-dimensional Kac-Siegert analysis is made. This involves the solution of an eigenvalue problem. For the spatial speckle correlation function and the spatial profile of the detector we assume gaussian models. The eigenvalues are then exactly expressed by simple formulae, and the probability density is calculated for slit apertures and a two-dimensional aperture. Experimental results are presented, and they agree well with the theory.
5 citations
4 citations
TL;DR: In this paper, the representation of probability distribution functions by Walsh series expansions is discussed, and the resulting expansions are consequently utilized in the derivation of useful expressions for the moments of corresponding probability distributions.
Abstract: This paper discusses the representation of probability distribution functions by Walsh series expansions. Generally, such expansions may be employed for the representation of multivariate distributions. However, we confine attention here to univariate and bivariate distributions. The resulting expansions are consequently utilized in the derivation of useful expressions for the moments of corresponding probability distributions. Applications of Walsh expansions of probability distributions are further illustrated by computing output moments for some general classes of nonlinear systems.
TL;DR: In this paper, the extended-Poisson, general-gamma, Weibull, and mixture-of-Weibull distributions are derived, which allow n dependent, Poisson-type processes to be going on simultaneously.
Abstract: SYNOPTIC ABSTRACTProbability distributions are derived which allow (two related types of) dependence to exist among any finite number of simple events. The extended-Poisson, general-gamma, Weibull, and mixture-of-Weibull distributions are special cases of the most general form obtained. Two basic models, which give rise to these distributions, are discussed. Applications in the areas of back up systems and complexes composed of interrelated parts are given. The applications follow naturally in that the derived distributions allow n dependent, Poisson-type processes to be going on simultaneously.
TL;DR: In this article, selected percentiles, the terminus and the mode of the four-parameter generalized gamma distribution (g.g.d.) are tabulated and tables are also provided which display the Pearson shape parameters 3, and 3? as functions of the basic g.d. shape parameters and vice-versa.
Abstract: Selected percentiles, the terminus and the mode of the four-parameter generalized gamma distribution (g.g.d.) are tabulated. Tables are also provided which display the Pearson shape parameters 3, and 3? as functions of the basic g.g.d. shape parameters and vice-versa. Charts are provided which facilitate a comparison of the g.g.d. with distributions of the Pearson system
01 Jan 1981
TL;DR: In this paper, the authors studied the monotonicity properties of distributions in order to obtain inequalities useful in statistical inference, and showed that some of these properties are well known and have proved to be very useful.
Abstract: It is very important to study the monotonicity properties of distributions in order to obtain inequalities useful in statistical inference. Some monotonicity properties of distributions are well known and have proved to be very useful. During the last decade, more concepts have been introduced and used by several authors in multiple decision problems.
TL;DR: Algorithms, based on the method of superposition and which are effective for large values of the parameters of the distributions simulated, are indicated for the simulation of important discrete distributions.
Abstract: Algorithms, based on the method of superposition and which are effective for large values of the parameters of the distributions simulated, are indicated for the simulation of important discrete distributions.