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Showing papers on "K-distribution published in 1997"


Journal ArticleDOI
01 Feb 1997
TL;DR: In this article, two suboptimum procedures for coherent detection of a radar target signal, in the presence of a mixture of K-distributed and Gaussian distributed clutter, are presented.
Abstract: The author introduces two suboptimum procedures for the coherent detection of a radar target signal, in the presence of a mixture of K-distributed and Gaussian distributed clutter. As a comparison, the optimum Neyman-Pearson and the whitening matched filter strategies to detect coherent pulse trains against the above mentioned disturbance are also presented. The optimum detection scheme is heavy to implement: it involves a numerical integration with respect to the texture variable of the K distribution. It strongly depends on the parameters of the clutter distribution, thus no predetermined threshold can be assigned to achieve a given probability of false alarm if such parameters are unknown. The preferred sub-optimum approach is based on the estimation of the texture variable, which is then used to determine the likelihood ratio. Applying the maximum likelihood estimate the resulting detection strategy is a linear quadratic functional of the observed vector and is clutter distribution free. The performance of the proposed detector is close to optimal and much better than the whitening matched filter detector; moreover, it guarantees approximately constant false alarm rate behaviour, regardless of the clutter distribution.

193 citations


Book
05 Dec 1997
TL;DR: Inverse Probability Confidence Limits and Curve Fitting as discussed by the authors, Bartlett S Function Estimating Likelihood Ratios Needed for an Experiment is used to estimate Likelihood Ratio.
Abstract: Preface. 1 Basic Probability Concepts. 2 Some Initial Definitions. 3 Some Results of Specific Distributions. 4 Discrete Distributions and Combinatorials,5.Specific Discrete Distributions. 6 The Normal (or Gaussian) Distribution and Other Continuous Distributions. 7 Generating Functions and Characteristic Functions. 8 The Monte Carlo Method: Computer Simulation of Experiments. 9 Queueing Theory and Other Probability Questions. 10 Two Dimensional and Multi-Dimensional Distributions.,11.The Central Limit Theorem. 12 Inverse Probability Confidence Limits. 13 Methods for Estimating Parameters. Least Squares and Maximum Likelihood. 14 Curve Fitting. 15 Bartlett S Function Estimating Likelihood Ratios Needed for an Experiment. 16 Interpolating Functions and Unfolding Problems. 17 Fitting Data with Correlations and Constraints. 18 Beyond Maximum Likelihood and Least Squares Robust Methods,References

116 citations


Journal ArticleDOI
TL;DR: N necessary and sufficient conditions for validity of the data processing theorem of information theory are established and the Burbea-Rao (1982) divergences and Bregman (1967) distances are established.
Abstract: The distances of discrete probability distributions are considered. Necessary and sufficient conditions for validity of the data processing theorem of information theory are established. These conditions are applied to the Burbea-Rao (1982) divergences and Bregman (1967) distances.

70 citations


Journal ArticleDOI
TL;DR: In this paper, minimum information distributions with uniform marginals and a specified rank correlation are studied and approximate approximations to the continuous distributions are discussed and explicit formulae are determined.
Abstract: Minimum information bivariate distributions with uniform marginals and a specified rank correlation are studied in this paper. These distributions play an important role in a particular way of modeling dependent random variables which has been used in the computer code UNICORN for carrying out uncertainty analyses. It is shown that these minimum information distributions have a particular form which makes simulation of conditional distributions very simple. Approximations to the continuous distributions are discussed and explicit formulae are determined. Finally a relation is discussed to DAD theorems, and a numerical algorithm is given (which has geometric rate of covergence) for determining the minimum information distributions.

58 citations


Journal ArticleDOI
TL;DR: In this article, the authors measured the probability distribution of total transmission of microwave radiation in waveguides filled with randomly positioned scatterers which would have values of the dimensionless conductance near unity.
Abstract: Measurements have been made of the probability distribution of total transmission of microwave radiation in waveguides filled with randomly positioned scatterers which would have values of the dimensionless conductance $g$ near unity. The distributions are markedly non-Gaussian and have exponential tails. The measured distributions are accurately described by diagrammatic and random matrix calculations carried out for nonabsorbing samples in the limit $g\ensuremath{\gg}1$ when $g$ is expressed in terms of the variance of the distribution, which equals the degree of long-range intensity correlation across the output face of the sample.

57 citations


Journal ArticleDOI
TL;DR: The algorithm proposed here has an acceptance probability which is superior to e/4 and the efficiency of the algorithm is compared with the previous method and the improvement in terms of minimum acceptance probability is shown.
Abstract: We study the properties of truncated gamma distributions and we derive simulation algorithms which dominate the standard algorithms for these distributions. For the right truncated gamma distribution, an optimal accept–reject algorithm is based on the fact that its density can be expressed as an infinite mixture of beta distribution. For integer values of the parameters, the density of the left truncated distributions can be rewritten as a mixture which can be easily generated. We give an optimal accept–reject algorithm for the other values of the parameter. We compare the efficiency of our algorithm with the previous method and show the improvement in terms of minimum acceptance probability. The algorithm proposed here has an acceptance probability which is superior to e/4.

47 citations


Posted Content
TL;DR: In this paper, the theory of stable probability distributions and their domains of attraction is derived in a direct way (avoiding the usual route via infinitely divisible distributions) using Fourier transforms.
Abstract: textThe theory of stable probability distributions and their domains of attraction is derived in a direct way (avoiding the usual route via infinitely divisible distributions) using Fourier transforms. Regularly varying functions play an important role in the exposition.

27 citations


Proceedings ArticleDOI
14 Oct 1997
TL;DR: In this paper, the spatial and temporal correlation properties of sea clutter have been modeled more realistically and discussed the implications of these correlation properties for radar system performance, and significant success has been achieved in the analysis of pulse-to-pulse integration.
Abstract: The performance of maritime surveillance radar is inevitably limited by the presence of sea clutter, the unavoidable but unwanted radar returns from the sea surface. Realistic modelling of this clutter process is thus a prerequisite for any reliable assessment of systems of this type. It has been recognised for some time that a simple Rayleigh model cannot capture those features of sea clutter that degrade the performance of high resolution radar. The K distribution provides a much improved statistical clutter model and is now incorporated in many radar performance calculations. However, all but the simplest (`single hit' detection) radar signal processing schemes are affected by the spatial and temporal correlation properties of the clutter. Thus far the modelling of these correlation properties and their influence on radar performance has been quite crude, although significant success has been achieved in the analysis of pulse to pulse integration. We describe our attempts to model the spatial correlation in the sea clutter more realistically and discuss the implications of our findings for radar system performance.

22 citations


Journal ArticleDOI
TL;DR: It is shown that variogram model reproduction is obtained when Uniform or Dipole distributions are used instead of Gaussian distributions for drawing i.d. random values in LU simulation, or for modeling the local conditional probability distributions in sequential simulation.
Abstract: Parametric geostatistical simulations such as LU decomposition and sequential algorithms do not need Gaussian distributions. It is shown that variogram model reproduction is obtained when Uniform or Dipole distributions are used instead of Gaussian distributions for drawing i. i.d. random values in LU simulation, or for modeling the local conditional probability distributions in sequential simulation. Both algorithms yield simulated values with a marginal normal distribution no matter if Gaussian, Uniform, or Dipole distributions are used. The range of simulated values decreases as the entropy of the probability distribution decreases. Using Gaussian distributions provides a larger range of simulated normal score values than using Uniform or Dipole distributions. This feature has a negligible effect for reproduction of the normal scores variogram model but have a larger impact on the reproduction of the original values variogram. The Uniform or Dipole distributions also produce lesser fluctuations among the variograms of the simulated realizations.

17 citations


Journal ArticleDOI
TL;DR: In this article, the authors consider parameter estimation for a family of discrete distributions characterized by probability generating functions (pgf's), and derive asymptotic theory for these estimators and consider some examples.
Abstract: We consider parameter estimation for a family of discrete distributions characterized by probability generating functions (pgf's). Kemp and Kemp (1988) suggest estimators based on the empirical probability generating function (epgf) the methods involve solving estimating equations obtained by equating functionals of the epgf and pgf on a fixed, finite set of values. We derive asymptotic theory for these estimators and consider some examples. Graphical techniques based on the theory are shown to be useful for exploratory analysis

15 citations



Proceedings ArticleDOI
03 Aug 1997
TL;DR: In this article, a first order mean field model for scattering from a woodland canopy is developed in the distorted Born approximation, applied to simulated mixed woodland, and the resulting simulated SAR images are barely distinguishable from real C-band SAR images of woodland, showing intensity speckle distributions that are well modelled by the K distribution at low to moderate resolutions.
Abstract: A first order, mean field model for scattering from a woodland canopy is developed in the distorted Born approximation. The model is applied to simulated mixed woodland. Full account is taken of shading, shadowing and the SAR imaging process. The resulting simulated SAR images are barely distinguishable from real C-band SAR images of woodland, and show intensity speckle distributions that are well modelled by the K distribution at low to moderate resolutions. Speckle distribution shape is revealed to depend upon resolution, incidence angle, canopy topography and instrument function and the physical origins of these dependencies are identified within the context of the model.

Journal ArticleDOI
TL;DR: In this paper, the class of modified power series distributions is widened by removing the restriction that the functions f(z) and g(z), as two probability generating functions defined on nonnegative integers, be probability generation functions.
Abstract: Starting with the second Lagrange expansion, with f(z) and g(z) as two probability generating functions defined on non-negative integers, Janardan and Rao( 1983) introduced a new class of discrete distributions called the Lagrange Distributions (LD2) of the second kind. In this note, this class of LD2 distributions is widened by removing the restriction that the functions f(z) and g(z) be probability generation functions. It is also shown that the class of modified power series distributions is a subclass of LD2.

Proceedings ArticleDOI
03 Aug 1997
TL;DR: A new class of G-distributions has been proposed to characterize the statistical properties of multi-look processed SAR data over the wide range of homogeneous, heterogeneous and extremely heterogeneous backscattering of terrain classes.
Abstract: A new class of G-distributions has been proposed to characterize the statistical properties of multi-look processed SAR data over the wide range of homogeneous, heterogeneous and extremely heterogeneous backscattering of terrain classes. The probability density function was derived as a product of a gamma distributed complex speckle variable and the generalized inverse Gaussian distribution for terrain backscatter. The latter is the outcome of a compound Poisson process which describes statistically the underlying physical scattering process. A particular case of the G-distribution is the K-distribution. Another limiting case is the called here G/sup 0/-distribution, which is able to model extremely heterogeneous clutter, such as that of urban areas, that cannot be properly modeled with K-distribution. As the G-distribution is scaleable it can be standardized by normalizing the SAR data with the mean intensity. The other two parameters, which are responsible for shape and spread of the distribution, are estimated by the method of moments where the negative moments are generated by inverse transformation of the normalized SAR data.

Journal ArticleDOI
TL;DR: In this paper, the spatial statistics of a C-band airborne polarimetric SAR system operated by the Defence Research Agency (DRA) of the U.K. were investigated using Gaussian and K distribution models.
Abstract: A prerequisite for the design of any target detection scheme is an understanding of the surrounding clutter environment. This paper aims firstly to investigate the extent to which Gaussian and K distribution models can be used to represent genuine polarimetric SAR clutter and secondly to investigate the spatial statistics of such clutter. To this end data analysis has been performed on imagery obtained using a C -band airborne polarimetric SAR system operated by the Defence Research Agency (DRA) of the U.K. In particular, the behaviour of the single point and spatial statistics between polarimetric channels has been investigated. Both an uncorrelated Gaussian model and a correlated K distribution model have been found to be required to fit the different clutter types encountered. However no inter-channel variation in single point or spatial statistics has been detected.

Proceedings ArticleDOI
J. How1, H. Leung
21 Jul 1997
TL;DR: It is found that the K-distribution fits better the sea-clutter amplitude statistics than the alpha-stable distribution, which is a failure of the stable model based on the analytical stable noise modeling.
Abstract: The alpha-stable distribution is a theoretical model for impulsive noise that currently enjoys wide success. In this paper, we test its applicability to high resolution radars that are capable of resolving fine structure of the sea surface. The received sea clutter signal by such systems is not well modeled by a Gaussian process, and we expected that stable distributions may provide better description of noise statistics than the conventional non-Gaussian models such as the K-distribution. However, in the important for radar low probability of false alarm region, we found that the K-distribution fits better the sea-clutter amplitude statistics than the alpha-stable distribution. In the application considered, we explain this failure of the stable model based on the analytical stable noise modeling.

Journal ArticleDOI
TL;DR: In this article, a new family of discrete probability distributions is introduced, whose probability function includes explieitly the Striling-Carlitz polynomial of the first or the second kind.
Abstract: In this paper. introduced is a family of discrete probability distributions. whose probability function includes explieitly the Striling-Carlitz polynomial of the first or the second kind. The new family extends the stirling family of distributions. Sibuya (1988) includes the conditional distributions of the orginal ones and enlarges the application area.

Proceedings ArticleDOI
14 Oct 1997
TL;DR: Sea clutter amplitude is often modeled as a compound random variable Z=AX, where A is a positive valued random variable and X has a Rayleigh distribution.
Abstract: Sea clutter amplitude is often modeled as a compound random variable Z=AX, where A is a positive valued random variable and X has a Rayleigh distribution. The K and discrete Rayleigh mixture distributions arise from this model using a gamma or discrete distribution, respectively, for A. In certain applications, successive values of A may be correlated. If this correlation is modeled as a finite Markov process, Z is described by a hidden Markov model (HMM). Amplitude only and phase coherent detection statistics are derived from the HMM models using locally optimal and likelihood ratio techniques, respectively. The performance of these algorithms are compared with CFAR and Doppler processors using radar data.

Proceedings ArticleDOI
14 Oct 1997
TL;DR: In this article, a large high-resolution SAR scene is analyzed containing a variety of textures from ploughed fields, to orchards and towns, and a method of automatically selecting homogeneous image patches from the whole scene is developed to allow a large number of independent measurements to be made of the image properties.
Abstract: Synthetic aperture radar (SAR) systems produce imagery that looks like a map of the region of interest. To detect small objects in SAR scenes a description of the surrounding area is usually required. This surrounding area of clutter, usually natural in origin, typically shows high pixel to pixel intensity fluctuations. Statistical noise models based on the K distribution have described well these clutter textural properties at low resolutions. This paper analyses whether statistical noise models, like the K distribution, provide a good description of natural clutter textures over a range of imaging resolutions. To obtain the most statistically significant result, a large high resolution SAR scene is analysed containing a variety of textures from ploughed fields, to orchards and towns. Statistical noise models require the region under analysis to be homogeneous, i.e. spatially invariant in its statistical properties. A method of automatically selecting homogeneous image patches from the whole scene is developed to allow a large number of independent measurements to be made of the image properties. For the purposes of testing, it is assumed that statistical noise models are appropriate and the degree to which the models fit the data is examined. Deviation from fitting is assessed as a function of distributional form and image resolution using the Kolmogorov Smirnov distribution test. Distribution parameters are found by maximising the likelihood of the data matching the distributions.


Journal ArticleDOI
TL;DR: In this paper, a coarse-grained phase distribution is introduced that approximate to the Susskind-Glogower cosine and sine phase distributions to any desired degree of accuracy.
Abstract: Coarse-grained phase distributions are introduced that approximate to the Susskind-Glogower cosine and sine phase distributions to any desired degree of accuracy. The integral relations between the phase distributions and the phase-parametrized field-strength distributions observable in balanced homodyning are derived and the integral kernels are analyzed. It is shown that the phase distributions can be directly sampled from the field-strength distributions which offers the possibility of measuring the Susskind-Glogower cosine and sine phase distributions with sufficiently high precision. Numerical simulations are performed to demonstrate the applicability of the method.

Journal ArticleDOI
TL;DR: In this article, the authors give characterizations of normal and gamma distributions via conditional structure, and show that the normal distribution is more stable than the gamma distribution, while the gamma distributions are less stable.
Abstract: This paper gives characterizations of normal and gamma distributions .via conditional structure.