Showing papers on "K-distribution published in 1996"

Detecting differences between delay vector distributions

Abstract: We propose a test for the null hypothesis that two sets of vectors are drawn from the same multidimensional probability distribution. The application to delay vector distributions provides a test for the null hypothesis that two time series have been generated by the same mechanism. \textcopyright{} 1996 The American Physical Society.

Statistics of the log‐compressed echo envelope

Abstract: Log compression of A lines to produce B‐scan images in clinical ultrasound imaging systems is a standard procedure to control the dynamic range of the images. The statistics of such compressed images in terms of underlying scatterer statistics have not been derived. The statistics are analyzed for partially formed speckle using a general K distribution model of envelope statistics to derive the density function for the log‐compressed envelope. This density function is used to elucidate the relation between the moments of the compressed envelope, the compression parameters, and the statistics of the scatterers. The analysis shows that the mean of the log‐compressed envelope is an increasing function of both the backscattered energy and the effective scatterer density. The variance of the log‐compressed envelope is a decreasing function of the effective scatterer density and is independent of the backscattered energy.

Point-estimate moment-based reliability analysis

Abstract: In moment-based reliability analysis, the probability of failure is calculated from a probability distribution fitted to the first few calculated moments of a limit state function. The calculation of the moments and the distributions fitting in the analysis are described. We suggest using the point estimate method to calculate the moments of the limit state function. A probability distribution from the Gram-Charlier series type A distributions or the Johnson family of distributions is selected to fit the calculated moments. The method, in general, does not require knowledge of the probability distributions of the basic random variables involved in the limit state function but their statistical moments. The method is simple to implement and can be used directly with an available deterministic computer program because it does not require iteration or derivatives of the limit state function.

On a class of perimeter-type distances of probability distributions.

Abstract: The class If , p G ( l ,oo] , of /-divergences investigated in this paper generalizes an /-divergence introduced by the author in [9] and applied there and by Reschenhofer and Bomze [11] in different areas of hypotheses testing. The main result of the present paper ensures that, for every p € (1, oo), the square root of the corresponding divergence defines a distance on the set of probability distributions. Thus it generalizes the respecting statement for p = 2 made in connection with Example 4 by Kafka, Osterreicher and Vincze in [6]. From the former literature on the subject the maximal powers of /-divergences defining a distance are known for the subsequent classes. For the class of Hellinger-divergences given in terms of p\u) = 1 + u — (u -\-u~) , s £ (0,1) , already Csiszar and Fischer [3] have shown that the maximal power is min(s, 1 — s). For the following two classes the maximal power coincides with their parameter. The class given in terms of f(a)(u) = | l — u \ , a € (0,1], was investigated by Boekee [2]. The previous class and this one have the special case s = a = \ in common. This famous case is attributed to Matusita [8]. The class given by

Detection of oceanic fronts at low grazing angles using an X band real aperture radar

Abstract: We examine the radar signatures and changes in the surface roughness associated with oceanic features in the low grazing angle (LGA) scattering regime. The X band (HH) radar signatures consist of high-amplitude sea spikes, step changes in the normalized radar cross-section (NRCS) modulations, and bright narrowbanded frontal structures. Using in situ observations coupled with airborne precision radiation thermometer (PRT-5) data, we show that the step changes in radar cross-section modulations are associated with either thermal stability-induced stress variations or current velocity variations. Superimposed on the step changes are additional modulations that result from wave breaking and hydrodynamic straining. The amplitudes of the NRCS LGA measurements are compared with the predictions of four backscattering models: the Bragg, the tilted-Bragg, the wedge, and the plume model. It is shown that while the simple Bragg model can describe the measurements to a limited degree, it generally tends to underpredict the results. Agreement is improved by including the tilt contribution from the longwave surface waves in the context of the composite scattering model. We use the wedge and plume models as the basis for explaining the cross sections associated with the high-amplitude sea spikes. The wedge model is used to describe scattering from sharply crested waves, and the plume model is used to describe the extreme cross sections that are associated with breaking waves near the fronts. In describing the probability density function characteristics we show that the backscattering statistics exhibit “K distribution” behavior for the Gulf Stream current region and near-frontal regions, while the cooler shelf waters have characteristics of an exponential distribution.

Analysis of sea clutter radar data

Abstract: We perform a detailed analysis of experimental data, collected at Osborne Gunnery Range with MacMaster University IPIX radar, to test the theoretical models developed in the literature. A comparison of the amplitude histograms with the K and lognormal distribution shows that VV data exhibit a K behaviour, while HH data are better fitted by a lognormal model and cross-polarised data by a K plus thermal noise model. The results have been confirmed by comparing the first four moments and through a modified version of the Kolmogoroff-Smirnoff test. The validity of the compound model, that identifies two components of clutter fluctuations, has been proved for the VV polarisation. The texture component, deriving from the spatially varying mean level has been isolated, since the speckle component was decorrelated by the frequency agility. These results are of great importance for design of optimum target detection schemes.

Some Characteristic Properties of a Certain Family of Probability Distributions

Abstract: Three characteristic properties of a certain class of probability distributions are given. They are based on recurrence relations between conditional moments, conditional variance and relationships between two moments of order statistics. These results shed new light on some special cases obtained by the Weibull, power, Pareto, beta and Burr type XII distributions.

Joint distributions of arbitrary variables made easy

Abstract: The successful application of joint time-frequency distributions to problems in time-varying spectral analysis has stimulated considerable interest in distributions of other variables for use when a strict time-frequency analysis is not appropriate. Joint distributions generalise single variable distributions that measure the energy content of some physical quantity in a signal. We propose a new framework for studying joint distributions of variables beyond time-frequency and time-scale. When applicable, our results turn the theory of joint distributions of arbitrary variables into an easy exercise of coordinate transformation. While straightforward, our method can generate many distributions previously attainable only by the general method of Cohen (see Time-Frequency Analysis. Englewood Cliffs, NJ: Prentice-Hall, 1995).

On a class of discrete distributions arising from the birth-death-with-immigration process

Abstract: This paper considers a class of distributions which may be regarded as the convolution of a negative binomial and a stopped-sum generalized hypergeometric factorial-moment random variables. Some properties are derived and it is shown that this class of distributions is a subset of distributions for the birth-and-death process with immigration (also reversible counter system). Formulations by mixing, limiting distributions and maximum likelihood equations are also discussed.

An Identity for the Product Moments of Order Statistics

Abstract: A general identity for the product moments of successive order statistics is given, which is valid in a class of probability distributions including Weibull, Pareto, exponential and Burr distributions.

The Selection of Appropriate Probability Distributions for Annual Maximum Rainfall Data

Abstract: The main procedure of frequency analysis is to select appropriate probability distributions fitted well to the observed data. In this study, 13 probability distribution functions were assumed to be underlying distributions for annual maximum rainfall data. The parameters of each probability distribution function were estimated by methods of moment, probability weighted moments, and maximum likelihood. The appropriate probability distribution for the applied rainfall data was selected by considering parameter validity. goodness of fit tests, and separation effects. As a result, GEV model was selected to be an appropriate probability distribution for annual maximum rainfall data of considered durations in Korea.

Functional relationships and asymptotic properties of distributions of interest in hydrologic frequency analysis

Abstract: The procedure of hydrologic frequency analysis involves fitting a theoretical probability distribution to a series of flows, water levels or rainfall. The data series must meet the criteria of being independent and identically distributed (iid). The theoretical distribution must be adequately chosen to reflect the nature of the phenomenon and the characteristics of the data being modeled (positive or negative skewness, range, etc.). A number of statistical distributions, with various numbers of parameters, have been proposed and used in a number of countries for the fitting of samples of hydrologic flood data (maximum annual discharge, for example). These distributions are reviewed in this paper, and the main characteristics of each distribution are briefly discussed. The functional relationships between these most commonly used distributions are highlighted. Proofs are derived for all the relationships that are established, and all necessary transformations of variables are identified. Special cases for each distribution are also discussed. This paper includes also a study and classification of the distributions according to their asymptotic properties (characteristics of the right tail of the distribution). One-, two-, three-, and four-parameter distributions are considered in this study. The final results are summarized in a diagram outlining the functional relationship between the variates of the different distributions, and a table detailing the probability density function (pdf) and the different forms and characteristics of each distribution. Another table classifying the asymptotic properties of these distributions is also presented.

Single point and spatial statistics of polarimetric SAR imagery

Abstract: A prerequisite for the design of any target detection scheme is an understanding of the clutter environment against which targets are to be detected. For polarimetric synthetic aperture radar (SAR) imagery, statistical models for homogeneous clutter based on both multi-variate Gaussian distributions and multi-variate K distributions have been extensively investigated. The first aim of this paper is to investigate the extent to which such models can be used to represent genuine polarimetric SAR clutter. To this end, the models have been tested on imagery obtained using a C-band airborne polarimetric SAR system, which is described. The validity of the Gaussian model as a description of the clutter statistics of a particular extended region is discussed. However, not all clutter regions can be represented by the simple Gaussian speckle model as is demonstrated in the case where the validity of using low order K distributions to describe woodland clutter is assessed. A point of particular interest is whether, when a low order K distribution description is most appropriate, the order parameters are significantly different between polarimetric channels. Suitable statistical tests have been used to address this question as described. The second aim is to investigate the spatial statistics of polarimetric SAR imagery using data provided by the C-band system. The measurement of correlation shapes and lengths and their use to determine whether there is significant variation in correlation properties is also discussed. (9 pages)