Showing papers on "K-distribution published in 1977"

Exponentially Decreasing Distributions for the Logarithm of Particle Size

Abstract: The family of continuous type distributions such that the logarithm of the probability (density) function is a hyperbola (or, in several dimensions, a hyperboloid) is introduced and investigated. It is, among other things, shown that a distribution of this kind is a mixture of normal distributions. As to applications, the paper focuses on the mass-size distribution of aeolian sand deposits, with particular reference to the findings of R. A. Bagnold. The distribution family seems, however, to be of some potential usefulness in other concrete contexts too.

A Versatile Four Parameter Family of Probability Distributions Suitable for Simulation

Abstract: Methods are well-known for generating random values from many common statistical distributions. These common distributions are sometimes used in simulation studies due to the lack of convenient methods of generating random values from distributions having more arbitrary shapes. A family of distributions is presented here which assumes many shapes, including those of the exponential, Bernoulli and uniform distributions. Any given first four moments may be obtained through manipulation of four parameters. The inverse cdf exists in closed form, allowing straightforward generation of random values given a source of U(0,1) values. Properties of the distribution and methods of parameter determination are developed.

Stochastic Models and Fluctuations in Reversal Time of Ambiguous Figures

Abstract: Five probability distributions for the description of temporal fluctuations in the perception of ambiguous figures were fitted to previously obtained experimental results and classified according to their efficiency in describing the data. The gamma, Wiener, and Capocelli-Riciardi distributions showed the highest efficiency, while the chi2 and Taylor-Aldridge distributions showed a very low effiency. Therefore the underlying process may be described either by a simple Poisson model or by a random-walk model. For the gamma distribution there was a strong correlation between the parameters, while for the Wiener distribution this correlation was lower.

Methods for modelling and generating probabilistic components in digital computer simulation when the standard distributions are not adequate: A survey

Abstract: Methods of modelling probabilistic components which are not adequately represented by the standard continuous distributions (such as normal, gamma, and Weibull) are surveyed. The methods are categorized as systems of distributions, approximations to the cumulative distribution function, and four-parameter distributions. Emphasis is on generality, determination of appropriate parameter values, and random variate generation.

Non‐Gaussian probability distributions for a vortex fluid

Abstract: A system of N two‐dimensional vortices interacting in a bounded region can be described by the statistics of the coordinates of the vortices or by the statistics of the Fourier coefficients of the vorticity field. It is shown that both descriptions give equivalent results. A high energy expression for the probability distribution function of the Fourier coefficients is derived and shown to be non‐Gaussian; it has at least two, and in some cases a continuum of, equal height maximum points corresponding to distinct, but equally probable, equilibrium states. Other stationary points previously thought to be metastable states are shown to be saddle points of the distribution function and hence unstable.

A family of bivariate life distributions

Abstract: . A characteristic function equation and an equivalent compounding scheme are studied. The equation arises from a model for a compartmental system and the compounding scheme arises from a shock model. The class of distributions satisfying the equation and the scheme contain the bivariate exponential distributions of Marshall and Olkin, Downton, Hawkes, and Paulson, as well as the bivariate geometric distributions of Hawkes, Paulson and Uppuluri, Esary and Marshall, and Arnold. The scheme is shown to generalize the univariate shock model of Esary, Marshall and Proschan. Properties of the distributions are derived by studying the equation and the compounding scheme which they satisfy.

Stationary Probability Distributions for Linear Time-Invariant Systems

Abstract: Existence and properties of stationary probability distributions for the output vector of linear time-invariant systems perturbed by white noise are examined. It is shown that a necessary and suffi...

On the galton-watson branching process: application of a method of moments and recursive determination for certain distributions

Abstract: The Galton-Watson branching process is investigated for certain distributions including members of the Poisson, binomial, geometric, and uniform families. Use of moments and application of the Pearson system of frequency distributions are considered. In addition, recursive determination of exact probability distributions is studied.

Probability distribution of velocity difference in the inertial interval of a turbulence spectrum

Abstract: The statistical turbulence characteristics are analyzed in the inertial interval of a spectrum. An equation is obtained for the probability distribution of the velocity difference at two points. Parameters characterizing the turbulence spectrum in the inertial interval enter into the equation in the role of unknown constants. These constants are calculated from the condition that a solution exists which has a physical meaning.

Probability distributions of the fractional differences of the structure amplitudes and intensities of two related crystals

Abstract: The probability distributions of the fractional intensities and amplitudes of x-ray reflections from a pair of imperfectly related structures are derived when both the structures satisfy the requirements of a given type of basic Wilson distribution. These two distributions are used to obtain theoretical expressions for 2 new fractional type ofR-indices which are expected to be useful in the final stages of refinement. The theoretical distributions are also used to deduce some theoretical distributions which are useful as tests for centrosymmetry via the random permutation method. The theoretical values of the relevant semi-cumulative functions are also tabulated.