Showing papers on "K-distribution published in 1990"

L-Moments: Analysis and Estimation of Distributions Using Linear Combinations of Order Statistics

Abstract: L-moments are expectations of certain linear combinations of order statistics. They can be defined for any random variable whose mean exists and form the basis of a general theory which covers the summarization and description of theoretical probability distributions, the summarization and description of observed data samples, estimation of parameters and quantiles of probability distributions, and hypothesis tests for probability distributions. The theory involves such established procedures as the use of order statistics and Gini's mean difference statistic, and gives rise to some promising innovations such as the measures of skewness and kurtosis and new methods of parameter estimation

Radar sea-clutter at low grazing angles

Abstract: An analysis of sea-clutter data obtained in conditions typical of sea state 2 at X-, S-, L- bands, UHF and VHF is presented. Results show that sea-clutter exhibits very different spectral characteristics at higher frequencies compared to those at low frequencies. Experimental sea-clutter coefficients as a function of grazing angle at various frequency bands were obtained for upswell and cross-swell conditions. Most sea-clutter models use the radar look direction relative to the wind direction as an input parameter (e.g. upwind, crosswind, etc.). Hence a direct comparison of sea-clutter magnitude with values calculated from models under different wind conditions was not made. Instead, these results were contrasted with those calculated from two sea-clutter (the GIT and Sittrop) models, assuming an upwind and a crosswind condition. The data were quite dissimilar in the low-grazing-angle regions to those predicted by the two models. Further research on sea-clutter in the low-grazing-angle regions is needed to ascertain and explain the observed differences. Sea-clutter amplitude statistics were found to fit the K-distribution best in the important low probability of false alarm region. The distribution approached that of a Rayleigh model for vertical polarisation and low-resolution waveforms. Non-Rayleigh statistics were frequently observed even for relatively low resolution and vertical polarisation waveforms. For horizontal polarisation and/or high resolution waveforms, the statistics approached those of a lognormal model. The statistical results provided further evidence that the K-distribution can serve as a limiting distribution for sea-clutter. The results of this paper are pertinent to shipboard radar applications where the grazing angle is low. They also provide additional information for sea-clutter modelling in the low-angle region, particu larly at the lower frequency bands.

Models for Distributions on Permutations

Abstract: A parametric distribution on permutations of k objects is derived from gamma random variables. The probability of a permutation is set equal to the probability that k independent gamma random variables with common shape parameter and different scale parameters are ranked according to that permutation. This distribution is motivated by considering a competition in which k players, scoring points according to independent Poisson processes, are ranked according to the time until r points are scored. The distributions obtained in this way include the popular Luce-Plackett and Thurstone-Mosteller-Daniels ranking models. These gamma-based distributions can serve as alternatives to the null ranking model in which all permutations are equally likely. Here, the gamma models are used to estimate the probability distribution of the order of finish in a horse race when only the probability of finishing first is given for each horse. Gamma models with shape parameters larger than 1 are found to be superior to...

Applications of the gb2 family of distributions in modeling insurance loss processes

Abstract: This paper investigates the use of a four parameter family of probability distributions, the generalized beta of the second kind (GB2), for modeling insurance loss processes. The GB2 family includes many commonly used distributions such as the lognormal, gamma and Weibull. The GB2 also includes the Burr and generalized gamma distributions. Members of this family and their inverse distributions have significant potential for improving the distributional fit in many applications involving thin or heavy-tailed distributions. Members of the GB2 family can be generated as mixtures of well-known distributions and provide a model for heterogeneity in claims distributions. Examples are presented which consider models of the distribution of individual and of aggregate losses. The results suggest that seemingly slight differences in modeling the tails can result in large differences in reinsurance premiums and quantiles for the distribution of total insurance losses.

On a family of counting distributions and recursions for related compound distributions

Abstract: Willmot & Sundt (1989) have considered compound Delaporte distributions and have developed a recursive algorithm to evaluate their counting densities in the case with integer-valued severities. An important point in the derivation is the fact that the Delaporte distributions represent compound Poisson distributions. This leads to a kind of twofold Panjer-type algorithm, cf. Panjer (1981).

New class of location-parameter discrete probability distributions and their characterizations

Abstract: A new class of location-parameter discrete probability distributions (LDPD) has been defined where the population mean is the location parameter. It has been shown that some single parameter discrete distributions do not belong to this class and all discrete probability distributions belonging to this class can be characterized by their variances only. Expressions are given for the first four central moments and a recurrence formula for higher central moments has been obtained. Eight theorems are given to characterize the various distributions in the LDPD class.

Empirical models for detection prediction in K-distribution radar sea clutter

Abstract: Simple empirical models are described which enable the radar designer to determine single-scan detection probabilities from the signal-to-clutter ratio and false alarm probability, for the compound K-distribution clutter model. The method to apply these results is discussed in detail, and the variability of the clutter rejection coefficient is briefly reviewed. Results covering the following are presented: the average clutter reflectivity, the shape parameter for the K-distributed clutter amplitude distribution, detection performance for targets in clutter, and evaluation of performance in clutter and noise. >

Comparing distributions of alcohol consumption: empirical probability plots.

Abstract: Summary Parametric approaches to the problem of the distribution of alcohol consumption have not been very successful. In this article, it is shown that regularity in distribution can be studied without making assumptions about a distribution model underlying the data. For this purpose, a method u used with which distributions are compared graphically in so-called probability plots. It appears that, up to a proper linear transformation on a logarithmic scale, a surprisingly large regularity over time can be observed between distributions taken from Dutch samples in 1970, 1981 and 1985. Equally, distributions from male and female sub-samples do not appear to differ up to a linear shift. The finding of a relative equality in distributional form is in accordance with the Ledermann model. However, the difference with the Ledermann's model is that no assumptions about the exact shape of the distributions are being made.

A classification of the main probability distributions by minimizing the weighted logarithmic measure of deviation

Abstract: The paper reanalyzes the following nonlinear program: Find the most similar probability distribution to a given reference measure subject to constraints expressed by mean values by minimizing the weighted logarithmic deviation. The main probability distributions are examined from this point of view and the results are summarized in a table.

Empirical models for detection prediction in K-distribution radar sea clutter

Abstract: Simple empirical models are described which enable the radar designer to determine single-scan detection probabilities from the signal-to-clutter ratio and false alarm probability, for the compound K-distribution clutter model. The method to apply these results is discussed in detail, and the variability of the clutter rejection coefficient is briefly reviewed. Results covering the following are presented: the average clutter reflectivity, the shape parameter for the K-distributed clutter amplitude distribution, detection performance for targets in clutter, and evaluation of performance in clutter and noise. >

Extremal properties of likelihood-ratio quantizers

Abstract: The paper concerns a situation in which there are M hypotheses H/sub 1/,. . ., H/sub M/, and in which Y is a random variable taking values in a set Y', with a different probability distribution under each hypothesis. A quantizer gamma :Y' to (1,. . ., D) is applied to form a quantized random variable gamma (Y). The extreme points of the set of possible probability distributions of gamma (Y) are characterized as gamma ranges over all quantizers. Optimality properties of likelihood-ratio quantizers are then established for a very broad class of quantization problems, including problems involving the maximization of a distance measure as discussed by S.M. Ali and S.D. Silvey(1966). >

Underlying probability distributions of the canonical ensemble

Abstract: The canonical distributions are chi-square distributions which are derived from parent distributions for nonconjugate fluctuating thermodynamic variables. The probability distributions are generated by discrete random variables which are the number of degrees of freedom and the number of particles. Randomized sampling of the total number of degrees of freedom and total number of particles gives rise, respectively, to fluctuations in the energy and volume.

Probabilities of Qualitative Behaviors from Probability Distributions onInputs

Abstract: Research on nding the di erent behaviors that an incompletely speci ed model can exhibit has concentrated on nding the plausible behaviors, and ruling out implausible ones. However, it would also be useful to estimate the probabilities of di erent behaviors. That is the goal of the present work. We show how to make inferences about the probabilities of the various qualitative behaviors a model could exhibit, when partial quantitative information in the form of intervals or probability distributions is given about values (such as initial values) of model variables. This work has taken place in the Qualitative Reasoning Group at the Arti cial Intelligence Laboratory, The University of Texas at Austin. Research of the Qualitative Reasoning Group is supported in part by NSF grants IRI-8905494 and IRI-8904454; by NASA grant NAG 2-507; by the Texas Advanced Research Program under grant no. 003658-175; and by the Jet Propulsion Laboratory, California Institute of Technology, sponsored by the National Aeronautics and Space Administration. Reference herein to any speci c commercial product, process, or service by trade name, trademark, manufacturer, or otherwise, does not constitute or imply its endorsement by any of its sponsors or the University of Texas.

Inverse invariant distributions

Abstract: The probability density function associated with a random variable Z is inverse-invariant if it is identical to the density function associated with the inverse of Z. An intuitive method of finding inverse-invariant density functions is presented, with examples and notes on where these distributions arise. Specific parameter estimation algorithms which produce estimates having inverse-invariant distributions are discussed. >

Proximity between life distributions and exponential distributions (I)

Abstract: This paper is a continuation of the foregoing one [1]. In this paper, we study the proximity between exponential distributions and life distributions in variousW-type classes, whereW-type classes indicate DFR, DFRA, NWU, NWUE, IMRL and HNWUE.

Generalized geometric stable distributions

Abstract: A class of probability distributions is indicated, which are geometrically infinitely divisible and form a generalization of the geometrically stable distributions. Two characterizations of these distributions are given.