Showing papers on "K-distribution published in 1998"

Ocean acoustic inversion with estimation of a posteriori probability distributions

Abstract: Inversion methods are applied in ocean acoustics to infer parameters which characterize the environment. The objective of this paper is to provide such estimates, and means of evaluating the inherent uncertainty of the parameter estimates. In a Bayesian approach, the result of inversion is the a posteriori probability density for the estimated parameters, from which all information such as mean, higher moments, and marginal distributions can be extracted. These are multidimensional integrals of the a posteriori probability density, which are complicated to evaluate for many parameters. Various sampling options are examined and it is suggested that “importance sampling” based on a directed Monte Carlo method, such as genetic algorithms, is the preferred method. The formulation of likelihood functions and maximum-likelihood objective functions for multifrequency data on a vertical array is discussed. A priori information about the parameters may be used in the formulation. Shallow-water acoustic data obtained at several frequencies using a vertical array is used to illustrate the applicability of the technique.

Approximating Probability Distributions Using Small Sample Spaces

Abstract: We formulate the notion of a "good approximation" to a probability distribution over a finite abelian group ?. The quality of the approximating distribution is characterized by a parameter ɛ which is a bound on the difference between corresponding Fourier coefficients of the two distributions. It is also required that the sample space of the approximating distribution be of size polynomial in and 1/ɛ. Such approximations are useful in reducing or eliminating the use of randomness in certain randomized algorithms. We demonstrate the existence of such good approximations to arbitrary distributions. In the case of n random variables distributed uniformly and independently over the range , we provide an efficient construction of a good approximation. The approximation constructed has the property that any linear combination of the random variables (modulo d) has essentially the same behavior under the approximating distribution as it does under the uniform distribution over . Our analysis is based on Weil's character sum estimates. We apply this result to the construction of a non-binary linear code where the alphabet symbols appear almost uniformly in each non-zero code-word.

Exponential and scale mixtures and equilibrium distributions

Abstract: In this article we discuss mixed exponential distributions and, more generally, scale mixtures with specific consideration the purpose of insurance modeling. Results are derived for equilibrium distributions (defined via stop-loss transforms) of mixed distributions. Some recursive relations are identified for the stop-loss transforms and moments of mixed exponential distributions. Explicit expressions are obtained for equilibrium gamma distributions with arbitrary shape parameter.

Spin States and Probability Distribution Functions

Abstract: Formulation of the conventional quantum mechanics in which a state is described by probability instead of wave function and density matrix is presented. We consider the possibility of constructing the invertable map of spinors onto positive probability distributions. For any value of spin, the basis of the irreducible representation of a rotation group is realized by a family of probability distributions of the spin projection parametrized by points on a sphere. Quantum states of a symmetric top described by the probability distributions are discussed.

Exact results on Sinai's diffusion

Abstract: We study the continuum version of Sinai's problem of a random walker in a random force field in one dimension. A method of stochastic representation is used to represent various probability distributions in this problem (mean probability density function and first passage time distributions). This method reproduces already known rigorous results and also confirms directly some recent results derived using approximation schemes. We demonstrate clearly, in the Sinai scaling regime, that the disorder dominates the problem and that the thermal distributions tend to zero-one laws.

John E. Freund's Mathematical Statistics

Abstract: 1. Introduction. 2. Probability 3. Probability Distributions and Probability Densities. 4. Mathematical Expectation. 5. Special Probability Distributions. 6. Special Probability Densities. 7. Functions of Random Variables. 8. Sampling Distributions. 9. Decision Theory. 10. Estimation: Theory 11. Estimation: Applications 12. Hypothesis Testing: Theory 13. Hypothesis Testing: Applications. 14. Regression and Correlation. 15. Analysis of Variance. 16. Nonparametric Tests. Appendix A. Sums and Products. Appendix B. Special Probability Distributions. Appendix C. Special Probability Densities. Statistical Tables. Answers to Odd-Numbered Exercises. Index.

Approximate Confidence Intervals for Quantiles of Gamma and Generalized Gamma Distributions.

Abstract: In hydraulic design, one often needs to estimate flood quantiles for use as design values. It is important to assess the estimation error by constructing confidence intervals (CIs) for these quantiles. Fitting probability distributions to hydrologic data is used widely for estimating quantiles of hydrological variables. The two-parameter gamma (G2) is among the distributions commonly used, but the three-parameter generalized gamma (GG3) (also known as Kritsky-Menkel distribution) is an alternative when more shape flexibility is needed to fit the data. We use an approximate method to construct CIs for the quantiles of the G2 and GG3 distributions. This method is shown to be useful for hydrological applications where the data record is short.

Estimating state probability distributions from noisy and corrupted data

Abstract: The method of recursive state density estimation (RSDE) is developed for determining the probability distribution of the states of a system from measurements that contain both random noise and gross errors. The technique is based on the expectation maximization algorithm and is iterative in nature. Similar to EM, at each iteration the likelihood of the distribution estimated by the RSDE algorithm is guaranteed to increase, thus arriving at the most likely distribution of the true states, given the measurement data set and the algorithm initial conditions. Convergence of the algorithm to the correct solution, for a simple case where an analytical answer can be derived for comparison, is shown. Two chemical process examples that have more complex distributions are also shown. Once the probability distribution of the states has been determined, many monitoring and statistical process and quality control functions can be performed using the more accurate distributions of the process states, avoiding corruption of the distribution due to faulty measurements.

Describing spinors using probability distribution functions

Abstract: Irreducible representations of the rotation group are realized using a family of positive probability distributions of the spin projections for an arbitrary value of the spin. The family is parametrized by the points on the sphere. An invertible mapping of the spinors onto the probability distribution functions is constructed. Examples of probability distributions for the well-known states with the spins 1/2 and 1 are presented.

Radar backscatter statistics from the sea surface: Implications of SIR‐C/X‐SAR observations from the NE Atlantic

Abstract: Multichannel synthetic aperture radar (SAR) observations from the spaceborne imaging radar-C/X-band SAR (SIR-C/X-SAR) experiment in the NE Atlantic (April 1994) are analyzed to test models of both the mean and the distribution of radar backscatter from the sea surface. The data cover incidence angles from about 20° to 40° and wind speeds from about 5 to 10 m s -1 . Empirical models of the mean fit the data well at C band to an accuracy of within 1-2 dB. Discrepancies at L band are a function of incidence angle, and we cannot rule out the possibility that they arise from systematic calibration errors. Single-look SIR-C/X-SAR data (spatial resolution ∼ 7-10 m) fit well to a K distribution, but multilook data (spatial resolution ∼25 m) fit better to a lognormal distribution. The observed second moments of image intensity can be explained by the modulations of resolved ocean surface waves but only if relatively large hydrodynamic modulations, which are generally consistent with those inferred from tower radar data, are assumed.

Textural-partially correlated polarimetric K-distribution

Abstract: A generalized polarimetric K-distribution is derived for characterizing multi-look fully polarimetric SAR data, on the basis that the underlying texture structures in polarization channels assume a trivariate joint gamma distribution with partial correlation and that the co-polarized and cross-polarized speckle components are de-correlated. Since the resulting K-distribution is in the form of a one-dimensional integral-difficult to be tested experimentally-a validation scheme for the model is then suggested using the theoretical joint moments corresponding to the generalized K-distribution.

Statistics of Simulated Ocean Clutter

Abstract: The statistical description of ocean clutter, which is made use of by the modern clutter suppression algorithms, is examined for sea states 0 and 4, for a grazing angle range 0.14° gr 89.5° , for all polarizations, and for upwind and crosswind returns. The data for statistical description are obtained by a radar simulation program in which the electromagnetic pulses are traced in a user defined radar environment. In this simulation environment, the returns which are backscattered from the ocean surface are recorded individually along with their polarization, amplitude, phase, arrival time and Doppler shift. Based on the likelihood ratios of commonly used Rayleigh, Lognormal, Weibull and K-distribution families, the best fitting distributions to the observed data are chosen. When the results obtained are compared with those available in the literature, a good agreement is observed. Due to the limitations of experimental studies, the data necessary for the statistical description of the amplitude and the po...

New physical-statistical models and methods for clutter and reverberation: KA-distributions

Abstract: New approaches to scattering theory, shown to be equivalent to classical formulations, are concisely noted. These yield new nongaussian pdf (probability distributions and densities) needed in signal processing for radar, sonar, and some aspects of telecommunications.

GA0 distribution model in edge-preserving parameter estimation of SAR images

Abstract: The multiplicative model has been widely used to explain the statistical properties of SAR images. In it, the model for the image Z is a 2D random field, that is regarded as the result of the product of X, the backscatter that depends on the physical characteristics of the sensed area, and Y, the speckle that depends on the number of looks used to generate the image Z. The most famous distribution for SAR images based on the multiplicative model is the K distribution (Jackeman et al). Recently Frery et al. proposed an alternative distribution, the G0A((alpha) ,(gamma) ,n) distribution which models very well extremely heterogenous areas (cities) as well as moderately heterogeneous areas (forest) and homogeneous areas (crop fields). The ground truth at each pixel can be characterized by the statistical parameters (alpha) and (gamma) , while n is constant for all of the pixels. The purpose of estimating these parameters for every pixel is twofold: first, it can be used to perform a segmentation process and, second, it can be used for gray level restoration. In this work we follow a Markov random field approach and propose an energy function derived from the statistical model adopted: G0A((alpha) ,(gamma) ,n). Edge- preservation is taken into account implicitly in the energy function.© (1998) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Note on probability distributions for generation time

Abstract: Sir—I would like this considered for publication as a comment on the 1996 paper by Ratkowsky and colleagues. I have no reason to quarrel with the experiment or its results, but I believe the authors have taken one or two false steps in drawing conclusions. Specifically, the results tell us nothing about the shape of the distribution (contrary to the claim by Ratkowsky et al. that they imply a gamma distribution with an a of 150). What the results do say is that the coefficient of variation does not depend upon temperature.

Note on probability distributions for generation time

Abstract: Sir—I would like this considered for publication as a comment on the 1996 paper by Ratkowsky and colleagues. I have no reason to quarrel with the experiment or its results, but I believe the authors have taken one or two false steps in drawing conclusions. Specifically, the results tell us nothing about the shape of the distribution (contrary to the claim by Ratkowsky et al. that they imply a gamma distribution with an a of 150). What the results do say is that the coefficient of variation does not depend upon temperature.

Textural-partially Correlated Polarimetric K-distribution

Abstract: Following the way of establishing compound statistical model for radar data, a generalized polarimetric K- distribution is derived in this paper for characterizing multi- look fully polarimetric SAR data, on the basis that the underlying texture structures in polarization channels assume a trivariate joint gamma distribution with partial correlation and that the co-polarized and cross-polarized speckle components are de-correlated Since the resulting K- distribution is in the form of an one-dimensional integral-- difficult to be tested experimentally--a validation scheme for the model is then suggested using the theoretical joint moments corresponding to the generalized K-distribution

Probability density functions in binary mixtures

Abstract: A theory of probability distributions of temperature and concentration fluctuations in turbulence of binary mixtures is presented. The Soret and Dufour effects couple concentration and temperature fluctuations modifying the scalar dissipation rates and the fluctuation-dissipation relations usual in one-component systems.