Showing papers on "K-distribution published in 2003"

A new metric for probability distributions

Abstract: We introduce a metric for probability distributions, which is bounded, information-theoretically motivated, and has a natural Bayesian interpretation. The square root of the well-known /spl chi//sup 2/ distance is an asymptotic approximation to it. Moreover, it is a close relative of the capacitory discrimination and Jensen-Shannon divergence.

Generalized trapezoidal distributions

Abstract: We present a construction and basic properties of a class of continuous distributions of an arbitrary form defined on a compact (bounded) set by concatenating in a continuous manner three probability density functions with bounded support using a modified mixture technique These three distributions may represent growth, stability and decline stages of a physical or mental phenomenon

John E. Freund's Mathematical Statistics with Applications

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. Point Estimation. 11. Interval Estimation. 12. Hypothesis Testing. 13. Tests of Hypotheses Involving Means, Variances, and Proportions. 14. Regression and Correlation. 15. Design and Analysis of Experiments. 16. Nonparametric Tests.

Generalizations of Two Sided Power Distributions and Their Convolution

Abstract: A general form of a family of bounded two-sided continuous distributions is introduced. The uniform and triangular distributions are possibly the simplest and best known members of this family. We also describe families of continuous distribution on a bounded interval generated by convolutions of these two-sided distributions. Examples of various forms of convolutions of triangular distributions are presented and analyzed.

A fuzzy approach to stochastic dominance of random variables

Abstract: The discrete dice model essentially amounts to comparing discrete uniform probability distributions and generates reciprocal relations that exhibit a particular type of transitivity called dice-transitivity. In this contribution, this comparison method is extended and applied to general probability distributions and the generated reciprocal relations are shown to generalize the concept of stochastic dominance. For a variety of parametrized probability distributions, we analyse the transitivity properties of these reciprocal relations within the framework of cycle-transitivity. The relationship between normal probability distributions and the different types of stochastic transitivity is emphasized.

A fisher-MAP filter for SAR image processing

Abstract: Gamma-MAP filters can be processed on SAR images when both texture and speckle are modeled with Gamma distribution, yielding a global image distribution modeled by a K distribution Yet, this modeling is not relevant for some images, on urban areas for example, which exhibit heavy tailed trends By modeling texture with an Inverse Gamma distribution, and by using "second kind statistics", it is possible first to model this kind of SAR image by a Fisher distribution, second to estimate the parameters of such a distribution by using "log-cumulants" (second kind statistics cumulants) and third to design a MAP filter This "Fisher-MAP" filter is actually an adaptive filter easy to implement Illustrations are given on Paris ERS-1-PRI images

On truncated bivariate discrete distributions: A unified treatment

Abstract: A unified treatment of three types of zero class truncation for bivariate discrete distributions is presented. Using the probability generating function approach, various properties of the truncated distributions are examined in association with the corresponding properties of the initial complete form of the distribution. Expressions for moments and conditional distributions are also obtained. Bivariate versions of the Thomas and the Intervened Poisson distributions are introduced and used as illustrative examples.

Approximate discrete probability distribution representation using a multi-resolution binary tree

Abstract: Computing and storing probabilities is a hard problem as soon as one has to deal with complex distributions over multiples random variables. The problem of efficient representation of probability distributions is central in term of computational efficiency in the field of probabilistic reasoning. The main problem arises when dealing with joint probability distributions over a set of random variables: they are always represented using huge probability arrays. In this paper, a new method based on a binary-tree representation is introduced in order to store efficiently very large joint distributions. Our approach approximates any multidimensional joint distributions using an adaptive discretization of the space. We make the assumption that the lower is the probability mass of a particular region of feature space, the larger is the discretization step. This assumption leads to a very optimized representation in term of time and memory. The other advantages of our approach are the ability to refine dynamically the distribution every time it is needed leading to a more accurate representation of the probability distribution and to an anytime representation of the distribution.

Moments of Certain Deformed Probability Distributions

Abstract: We consider properties of two classes of discrete probability distributions, namely the so-called Deformed Modified Factorial Series Distributions (DMFSD) and Deformed Modified Power Series Distributions (DMPSD). The formulae for moments and recurrence relations for the moments of these deformed distributions are derived. The results obtained generalize or extend some Theorems given by Janardan (Janardan, K. G. (1984). Moments of certain series distributions and their applications. SIAM J. Appl. Math. 44:854–868) and Gupta (Gupta, R. C. (1974). Modified power series distributions and some of its applications. Sankhya, Ser. B 35:288–298).

On a Relation Between a Family of Distributions Attaining the Bhattacharyya Bound and That of Linear Combinations of the Distributions from an Exponential Family

Abstract: An unbiased estimation problem of a function g(θ) of a real parameter is considered. A relation between a family of distributions for which an unbiased estimator of a function g(θ) attains the general order Bhattacharyya lower bound and that of linear combinations of the distributions from an exponential family is discussed. An example on a family of distributions involving an exponential and a double exponential distributions with a scale parameter is given. An example on a normal distribution with a location parameter is also given.

A Stochastic Differential Equation for Modeling the “Classical” Probability Distributions

Abstract: Stochastic differential equations are a flexible way to model continuous probability distributions. The most popular differential equations are for non-stationary Lognormal, non-stationary Normal and stationary Ornstein-Uhlenbeck distributions. The probability densities are known for these distributions and the assumptions behind the differential equations are well understood. Unfortunately, the assumptions do not fit most situations. In economics and finance, prices and quantities are usually stationary and positive. The Lognormal and Normal distributions are nonstationary and the Normal and Ornstein-Uhlenbeck distributions allow negative prices and quantities. This study derives a stochastic differential equation that includes most of the classical probability distributions as special cases and greatly expands the number distributions that can be used in models of stochastic dynamic systems.

On Approximating Multidimensional Probability Distributions by Compositional Models.

Abstract: Because of computational problems, multidimensional probability distributions must be approximated by distributions which can be defined by a reasonable number of parameters. As a rule, distributions with a special dependence structure (i.e., complying with a system of conditional independence relations) are considered; graphical Markov models and especially Bayesian networks are often used. This paper proposes application of compositional models for this puropose. In addition to a theoretical background, a heuristic algorithm solving one part of a model learning process is presented. Its basic idea, construction of an approximation exploiting informational content of given low-dimensional distributions in a maximal possible way, was proposed by Albert Perez as early as in 1977.

On Discrete Multivariate Distributions Symmetric in Frequencies.

Abstract: In this paper we describe a new class of discrete multivariate distributions which verify that their probability mass function is invariant when their univariate variables are permuted. These distributions may be generated by a multivariate extension of the Gauss function 2F1 with matrix argument. A methodology that permits the fit of these distributions to real data is developed. A fit of a distribution for bivariate real data is shown and is compared with fits obtained by means of other usual bivariate distributions generated by extensions of the Gauss function.

CIRCULAR POLYA DISTRIBUTIONS OF ORDER k

Abstract: Two circular Polya distributions of order k are derived by means of generalized urn models and by compounding, respectively, the type I and type II circular binomial distributions of order k of Makri and Philippou (1994) with the beta distribution. It is noted that the above two distributions include, as special cases, new circular hypergeometric, negative hypergeometric, and discrete uniform distributions of the same order and type. The means of the new distributions are obtained and two asymptotic results are established relating them to the above-mentioned circular binomial distributions of order k.

Parametric Methods for Comparing Two Survival Distributions

Abstract: For each case in the sample, we define three variables, Time, Status and Treat. Let Time denote the survival time (exact or censored), Status be a dummy variable with Status=0 if Time is censored and 1 otherwise and Treat be a variable with Treat = MP if the patient received 6-MP and P if the patient receive Placebo. Assume that the data have been saved in “C:\Example.dat” as a text file, which contains three columns (Time, in the first column, Status in the second column, and Treat in the third column), separated by space(s).

Estimation of the distribution type and parameters based on multimodal histograms

Abstract: In many applications involving measuring a physical phenomenon, the output data contains a mixture of different type of distributions. The data set consists often of unimodal distributions, which overlap, i.e. the ranges of the corresponding random variables have a significant intersection. After observing a multimodal histogram that has several partially overlapping distributions the aim is to separate them by inferring the correct types of the probability density functions (PDFs) and their parameters. The method is based on the non-linear least squares estimation, where several types of PDFs are fitted to the region mostly affected by a single distribution. The possible candidate PDFs are those of the Pearson system, Weibull, Fisher, chi-squared and Rayleigh distributions. This method can be extended to multidimensional cases in certain situations. The methods developed earlier for this task are based for example on the QQ-plot technique and on order statistic filter banks. The found distribution types and their parameters can be applied to different tasks in image processing and system analysis. This algorithm can be used e.g. to the estimation of PDFs of certain phenomena and to global thresholding of images. The method is applied to real two-dimensional data sets having values coming from several distributions.

Statistics of Reflected Speckle Intensities Arising from Localized States Inside the GAP of Disordered Photonic Crystals

Abstract: The field distributions of reflected speckles arising from localized states inside the gap of disordered photonic crystals in two dimensions were studied through numerical simulations using the multiple-scattering method. By separating the field into the coherent and diffuse parts, we have studied the statistics of field and phase distributions for both diffuse and total fields as well as their speckle contrasts as a function of the amount of disorder. For the non-Bragg angles, it is found that the intensity distribution crosses over from non-Rayleigh to Rayleigh statistics when disorder is increased. This is similar to the crossover from ballistic to diffusive wave propagation for the transmitted waves and can be described by the random-phasor-sum model (RPS). For the Bragg angle, only non-Rayleigh statistics were found. Both the RPS and K distribution have limited range of validity in this case.

Estimation of K-distribution parameters with application to target detection.

Abstract: Probabilistic models have been used extensively in the past to underpin classification algorithms in statistical pattern recognition. The most widely used model is the Gaussian distribution. However, signals of impulsive nature usually deviate from Gaussian and it is necessary to work with more realistic models. K-distribution is one of the long-tailed density which is known in the signal processing community for fitting the radar sea clutter accurately. The work presented in this thesis reflects the efforts made to model the background features, extracted from the sea images, by using a K-distribution. A novel approach for estimating the parameter of K-distribution is presented. The method utilises the empirical characteristic function, and is proven to perform better than any existing estimation technique. A classifier is then developed from the empirical characteristic function. This technique is applied to a problem of automatic target recognition with promising results.

Joint Fuzzy Probability Distributions

Abstract: This Chapter generalizes Chapters 4 and 8 to multivariable fuzzy probability distributions. Since the discrete case and the continuous case are similar, just interchange summation and integrals symbols, we only present the continuous case in Section 10.2. Applications are in the next Chapter. The continuous case is based on [1]. For simplicity we will consider only the joint fuzzy probability distributions for two fuzzy random variables.

On the bilateral truncated exponential distributions

Abstract: There is a special class of probability distributions, namely the exponential family of probability distributions, for which complete sufficient statistics with fixed dimension always exist. This class includes some, but not all, of the commonly used distributions. The objective of this paper is to give some definitions and some properties for some probability distributions which belong to such class. Also, we shall investigate some measures of the information of the unknown parameters which appear in such exponential family.