Showing papers on "K-distribution published in 2004"
TL;DR: In this article, a simple generalisation of the use of the collection of order statistic distributions associated with symmetric distributions is presented, and an alternative derivation of this family of distributions is as the result of applying the inverse probability integral transformation to the beta distribution.
Abstract: Consider starting from a symmetric distributionF on ℜ and generating a family of distributions from it by employing two parameters whose role is to introduce skewness and to vary tail weight. The proposal in this paper is a simple generalisation of the use of the collection of order statistic distributions associated withF for this purpose; an alternative derivation of this family of distributions is as the result of applying the inverse probability integral transformation to the beta distribution. General properties of the proposed family of distributions are explored. It is argued that two particular special cases are especially attractive because they appear to provide the most tractable instances of families with power and exponential tails; these are the skewt distribution and the logF distribution, respectively. Limited experience with fitting the distributions to data in their four-parameter form, with location and scale parameters added, is described, and hopes for their incorporation into complex modelling situations expressed. Extensions to the multivariate case and to ℜ+ are discussed, and links are forged between the distributions underlying the skewt and logF distributions and Tadikamalla and Johnson'sLU family.
440 citations
TL;DR: An approach combining elements of both histograms and probability density distributions is proposed and all methods are applied in an Excel workbook and the procedures for using this are explained.
345 citations
TL;DR: In this article, the acceleration component probability distribution function at Rλ =690 to probabilities of less than 10−7 was presented, which is an improvement of more than an order of magnitude over past measurements and allows us to conclude that the fourth moment converges and the flatness is approximately 55.
251 citations
TL;DR: In this paper, a flexible class of skew-symmetric distributions for which the probab- ility density function has the form of a product of a symmetric density and a skewing function is proposed.
Abstract: We propose a flexible class of skew-symmetric distributions for which the probab- ility density function has the form of a product of a symmetric density and a skewing function. By constructing an enumerable dense subset of skewing functions on a compact set, we are able to consider a family of distributions, which can capture skewness, heavy tails and multimodality systematically. We present three illustrative examples for the fibreglass data, the simulated data from a mixture of two normal distributions and the Swiss bills dlata.
158 citations
TL;DR: In this paper, the suitability of the Weibull and Rayleigh functions is assessed based on a total of six parameters (of the probability density and power density distributions), calculated from 12 months of hourly time series wind speed data.
85 citations
TL;DR: In this article, a finite-number-of-scatterers representation of K-distributed reverberation is presented, which allows control of the reverberation-envelope statistics as a function of system (beamwidth and bandwidth) and environmental parameters.
Abstract: The simulation of active sonar reverberation time series has traditionally been done using either a computationally intensive point-scatterer model or a Rayleigh-distributed reverberation-envelope model with a time-varying power level. Although adequate in scenarios where reverberation arises from a multitude of scatterers, the Rayleigh model is not representative of the target-like non-Rayleigh reverberation or clutter commonly observed with modern high-resolution sonar systems operating in shallow-water environments. In this paper, techniques for simulating non-Rayleigh reverberation are developed within the context of the finite-number-of-scatterers representation of K-distributed reverberation, which allows control of the reverberation-envelope statistics as a function of system (beamwidth and bandwidth) and environmental (scatterer density and size) parameters. To avoid the high computational effort of the point-scatterer model, reverberation is simulated at the output of the matched filter and is generated using efficient approximate methods for forming K-distributed random variables. Finite impulse response filters are used to introduce the effects of multipath propagation and the shape of the reverberation power spectrum, the latter of which requires the development of a prewarping of the K distribution parameters to control the reverberation-envelope statistics. The simulation methods presented in this paper will be useful in the testing and evaluation of active sonar signal processing algorithms, as well as for simulation-based research on the effects of the sonar system and environment on the reverberation-envelope probability density function.
64 citations
TL;DR: In statistical linearization, nonlinear elements are approximated by equivalent linear elements according to recipes proposed by the pioneers of the procedure as mentioned in this paper, which require the evaluation of certain statistics which, ideally, should be evaluated using the exact probability distribution of the non-linear response.
Abstract: In statistical linearization non-linear elements are approximated by equivalent linear elements according to recipes proposed by the pioneers of the procedure. The recipes require the evaluation of certain statistics which, ideally, should be evaluated using the exact probability distribution of the non-linear response. Because the exact non-linear response distribution is unknown it has become traditional to use a Gaussian distribution as an approximation to the exact distribution. With the modern computing tools now available it is easy to use non-Gaussian distributions which can provide better approximations in cases where Gaussian distributions are not appropriate. Examples are displayed for power-law oscillators with stiffening and softening springs, and for the Duffing oscillator, and for a double-well oscillator. Two families of probability distributions with varying shape are studied.
38 citations
TL;DR: This paper proposes a new algorithm that converges even in inconsistent case, which can be efficiently implemented exploiting decomposability of considered distributions.
Abstract: In this paper we discuss the process of building a joint probability distribution from an input set of low-dimensional probability distributions. Since the solution of the problem for a consistent ...
23 citations
TL;DR: In this article, the authors derive new properties for the power-variance family of probability distributions, referred to as Tweedie laws, and reveal continuity of this family and obtain convenient common formulas for the cumulants.
Abstract: We derive new properties for the power-variance family of probability distributions, which are also referred to as Tweedie laws. They emerge in the theory of generalized linear models and have a wide range of applications. We present decomposition criteria for Tweedie distributions which generalize Cochran's and Raikov's theorems. These criteria are interpreted in terms of the additivity of a shape parameter. The intersection of the power-variance family with the class of distributions which have no indecomposable components is determined. We reveal continuity of this family and obtain convenient common formulas for the cumulants.
20 citations
21 Mar 2004
TL;DR: This work derives bounds on the pairwise error probability (PEP) for each fading model and applies the transfer function technique in conjunction with derived PEP bounds to obtain bit error rate performance.
Abstract: We analyze the error rate performance of coded wireless optical links operating over atmospheric channels, where the turbulence-induced fading is modeled by the negative exponential distribution, K distribution and I-K distribution. First, we derive bounds on the pairwise error probability (PEP) for each fading model and then apply the transfer function technique in conjunction with derived PEP bounds to obtain bit error rate performance. Simulation results are also included to confirm the analytical results.
20 citations
TL;DR: The pseudospectral time-domain (PSTD) method is an accurate and efficient scheme for solving the acoustic wave equation numerically as discussed by the authors, which provides a good basis for a general sonar simulation model because all of the fundamental processes on which sonar depend occur as natural consequences of solving the wave equation.
Abstract: The pseudospectral time-domain (PSTD) method is an accurate and efficient scheme for solving the acoustic wave equation numerically. It provides a good basis for a general sonar simulation model because all of the fundamental processes on which sonar depend occur as natural consequences of solving the wave equation. Propagation, interference, and spreading and absorption losses are intrinsic to this solution; reflection and scattering are governed by the distribution of materials within the simulated environment. These processes are analogous to those in the physical system being modeled. The method generates the full spatial and temporal evolution of the acoustic field for a specified model environment. This paper presents the application of a PSTD model to the simulation of a sidescan sonar system operating in deep water. Synthetic sidescan images of sand ripples are simulated using a directional fractal surface as the model sea bed. Different forms of time-varying gain are applied to the received signals to investigate its effects on the statistics of the resulting images. These images are visually realistic and have significantly non-Rayleigh histograms. Rayleigh distribution, Rayleigh mixtures with up to four modes, and K distribution fits to these histograms demonstrate that the form of the applied time-varying gain has a substantial effect both on the derived distribution parameters and on the probability that the data are drawn from that distribution. They also demonstrate that, with a greater chi-square test probability and with fewer fitting parameters, the K distribution provides the more appropriate description of the reverberation from the simulated sand-ripple sea bed generated with the model sonar system.
TL;DR: In this paper, the authors introduce the concepts of discrete semi-stability and geometric semisuperstability for distributions with support in Z+ and offer several properties, including characterizations, of such distributions.
Abstract: The purpose of this paper is to introduce and study the concepts of discrete semi-stability and geometric semi-stability for distributions with support inZ+. We offer several properties, including characterizations, of discrete semi-stable distributions. We establish that these distributions posses the property of infinite divisibility and that their probability generating functions admit canonical representations that are analogous to those of their continuous counterparts. Properties of discrete geometric semi-stable distributions are deduced from the results obtained for discrete semi-stability. Several limit theorems are established and some examples are constructed.
11 Dec 2004
TL;DR: The modeling and simulation of K-distributed sea clutter is discussed to help in understanding the clutter characteristics from a statistical viewpoint and will lead to a way of optimally fixing the threshold to improve detection performance.
Abstract: Modern radars have become increasingly more complex and less tractable for mathematical analysis. So simulation is an obvious prerequisite if the radar is set to operate in hostile scenarios. The very commonly used and well established base band equivalent model for radar clutter is a complex Gaussian process, which implies that Chi-Square for power, or equivalently Rayleigh for amplitude. However, the statistical property of the radar cross-section on the area of sea surface is generally found to be non-Rayleigh. Also that the received clutter results from a large number of independent and identically distributed (IID) elementary scatterers does not hold good. In fact, if only a limited number of such scatterers actually contribute to the received clutter echo, as is the case for high resolution and/or low grazing angles, then the measured amplitude probability density function (APDF) exhibits large deviations from the Rayleigh distribution and is better fitted by families of APDFs such as K-distribution. This paper discusses the modeling and simulation of K-distributed sea clutter to help in understanding the clutter characteristics from a statistical viewpoint. This simulation will lead to a way of optimally fixing the threshold to improve detection performance.
23 Aug 2004
TL;DR: The properties and benefits of this approach to estimating high dimensional discrete probability distributions with decomposable graphical models are discussed and it is compared to the well-studied Chow-Liu algorithm.
Abstract: We present an approach to estimating high dimensional discrete probability distributions with decomposable graphical models. Starting with the independence assumption we add edges and thus gradually increase the complexity of our model. Bounded by the minimum description length principle we are able to produce highly accurate models without overfitting. We discuss the properties and benefits of this approach in an experimental evaluation and compare it to the well-studied Chow-Liu algorithm.
TL;DR: A new function whose value is measure of the dissimilarity between several probability distributions that can be used for an arbitrary number of probability distributions is introduced.
Abstract: In this article we introduce a new function whose value is measure of the dissimilarity between several probability distributions. After a brief review of some previous measures for two probability distributions, a new function is introduced and its useful characteristics are presented. The most interesting feature of this new function is that it can be used for an arbitrary number of probability distributions.
TL;DR: It is shown that the outage probability can be significantly overestimated if the probability density function of the differential group delay is approximated by a Maxwellian distribution.
Abstract: We give an analytical expression for the probability density function of the differential group delay for a concatenation of Maxwellian fiber sections and an arbitrary number of lumped elements with constant and isotropically oriented birefringence. When the contribution of the average squared of the constant birefringence elements is a significant fraction of the total, we show that the outage probability can be significantly overestimated if the probability density function of the differential group delay is approximated by a Maxwellian distribution.
TL;DR: In this article, the double gamma distribution on the real line λc with Laplace transform (1−t2)−c and the distributions of the products of independent random variables X,Y1,…,Yp,U1, etc.
TL;DR: In this article, the authors introduce max-multiscaling distributions as solutions to a functional equation which, in a natural way, extends the one fulfilled by max-semistable distributions.
Abstract: We introduce max-multiscaling distributions as solutions to a functional equation which, in a natural way, extends the one fulfilled by max-semistable distributions. We establish that strictly max-multiscaling distributions are products of at most two max-semistable distributions. Next, we show how to obtain these solutions as limit laws of normalized maximum of suitable independent sequences of random variables when sample size has geometric growth.
Journal Article•
04 May 2004
TL;DR: This communication presents a new method for non-stationary signal interpretation, which consists of extracting and characterizing time-frequency structures based on a modelling of a time- frequencies representation probability density function as a mixture of central and noncentral chi-square distributions.
Abstract: This communication presents a new method for non-stationary signal interpretation, which consists of extracting and characterizing time-frequency structures It is based on a modelling of a time-frequency representation probability density function as a mixture of central and noncentral chi-square distributions The problem of interpretation is reduced to a problem of estimation and classification solved by a specific formulation of the EM algorithm for such mixture