Showing papers on "K-distribution published in 1974"
TL;DR: In this article, the concept of increasing "conditional mean exceedance" provides a reasonable way of describing the heavy-tail phenomenon, and a family of Pareto distributions is shown to represent distributions for which this parameter is linearly increasing.
Abstract: Distributions with heavier-than-exponential tails are studied for describing empirical phenomena. It is argued that the concept of increasing “conditional mean exceedance” provides a reasonable way of describing the heavy-tail phenomenon, and a family of Pareto distributions is shown to represent distributions for which this parameter is linearly increasing. A test is developed and modified so as to be suitable for testing heavy-tailedness, and some graphical procedures are also suggested.
198 citations
TL;DR: Two distinct versions of the generalized beta distribution of the second kind are considered in this article, and they compare favorably with the commonly used gamma and log normal distributions in their ability to fit selected sets of accumulated streamflow and precipitation amount data.
Abstract: Two distinct versions of the generalized beta distribution of the second kind are considered. These beta-type distributions compare favorably with the commonly used gamma and log normal distributions in their ability to fit selected sets of accumulated streamflow and precipitation amount data. The comparisons are based on empirical results associated with three different goodness of fit criteria. Since the cumulative distribution functions of these beta-type distributions are in closed form, they possess unique computational advantages over the gamma and log normal distributions.
92 citations
TL;DR: In this paper, the authors examined the family whose probability generating functions have the form of the generalized hypergeometric function, pFq [(a); (b); λ(s-1)].
Abstract: This paper examines the family whose probability generating functions have the form of the generalized hypergeometric function, pFq [(a); (b); λ(s-1)] . It includes a number of matching distributions as well as many classic discrete distributions. Properties may be derived from the differential equations satisfied by the various generating functions e.g. useful recurrence formulae for probabilities, cumulants, and moments about an arbitrary point can be obtained.
28 citations
25 citations
18 citations
TL;DR: In this article, the central limit theorem of probability theory and two assumptions within the spirit of weak turbulence theory are used to determine the probability distributions for Fourier components of the electric field.
Abstract: Probability distributions for Fourier components of the electric field, including joint distributions for various Fourier components and multiple time distributions for the same component, are determined using the central limit theorem of probability theory and two assumptions within the spirit of weak turbulence theory. The distributions are all Gaussians or simple integrals of Gaussians. This statistical framework is applied to the special case where the turbulence is dominated by the wave‐particle interaction. In this case, quantities appearing in the distributions as parameters, such as the mean and standard deviation, are determined by quasilinear theory and Dupree's recent theory of phase space granulation, or clumps.
17 citations
29 May 1974
TL;DR: In this article, the idea of sampling from a distribution by majorizing its probability density function is applied to gamma and beta distributions, resulting in sampling algorithms whose performance will not deteriorate when the parameters are increased.
Abstract: : John von Neumann's idea of sampling from a distribution by majorizing its probability density function is applied to gamma and beta distributions. Optimum envelopes are constructed resulting in sampling algorithms whose performance will not deteriorate when the parameters are increased. In some methods the process of acceptance is accelerated. For this the employed test functions are replaced in most cases with simpler bounds which are difficult to derive but easy to apply. The reported computational experience indicates that the new methods can be of considerable practical use. (Author)
10 citations
TL;DR: In this paper, two simulation procedures for arbitrary gamma distributions are compared, and both procedures depend on closed form approximations to the cumulative gamma distributions, but one procedure appears to yield considerably more accurate results than the other.
Abstract: Two simulation procedures for arbitrary gamma distributions are compared. Both procedures depend on closed form approximations to the cumulative gamma distributions, but one procedure appears to yield considerably more accurate results than the other. Tables are given which allow this procedure to be easily applied.
2 citations
01 Jan 1974
TL;DR: In this paper, the authors discuss six discrete distributions or populations, applicable to a variety of sampling situations, which are defined on countable spaces, such as 0 to n, 0 to ∞, or k to n, which when specified, give particular cases.
Abstract: This chapter focuses on discrete probability distributions. It discusses six discrete distributions or populations, applicable to a variety of sampling situations. They are widely useful probability models. They are defined on countable spaces, such as 0 to n , 0 to ∞, or k to ∞ and 1–3 parameters, which when specified, give particular cases.. The chapter also provides information on μ, σ, α 3 , and α 4 in terms of the parameters and shows how to approximate the probability functions p( y ).