Compound representation of high resolution sea clutter

A proposed form of compound distribution to describe the non-Rayleigh distribution and correlation properties of high resolution radar sea clutter is shown to be a good fit to experimental data. From this model the K distribution is derived, and a possible physical mechanism is discussed.     

Covariance approximation of nonlinear regression

A nonlinear regression model on the basis of the covariance approximation of a multidimensional probability distribution is constructed. The model is represented by an expansion in the basis functions in the form of partial derivatives of the logarithm of the joint factor probability distribution. The weight coefficients of the expansion are the covariances of the resulting and explanatory variables. On particular examples, the efficiency of the Bayesian approximation of the proposed regression model in which the factor distribution is described by a finite mixture of ellipsoidally symmetric densities is demonstrated.     

A Birnbaum-Saunders accelerated life model

The 2-parameter family of probability distributions introduced by Birnbaum and Saunders characterizes the fatigue failure of materials subjected to cyclic stresses and strains. It is shown that the methods of accelerated life testing are applicable to the Birnbaum-Saunders distribution for analyzing accelerated lifetime data, and the (inverse) power law model is used due to its justification for describing accelerated fatigue failure in metals. This paper develops the (inverse) power law accelerated form of the Birnbaum-Saunders distribution, and explores the corresponding inference procedures-including parameter estimation techniques and the derivation of the s-expected Fisher information matrix. The model approach in this paper is different from an earlier work, which considered a log-linear form of a model with applications to accelerated life testing. Here, using an example data set, the fitted model is effectively used to estimate lower distribution percentiles and mean failure times for particular values of the acceleration variable. The benefits of having an operable closed form of the Fisher information matrix, which is unique to this article for this model, include interval estimation of model parameters and LCB on percentiles using relatively simple computational procedures     

Modeling the amplitude statistics of ultrasonic images

In this paper, a new statistical model for representing the amplitude statistics of ultrasonic images is presented. The model is called the Rician inverse Gaussian (RiIG) distribution, due to the fact that it is constructed as a mixture of the Rice distribution and the Inverse Gaussian distribution. The probability density function (pdf) of the RiIG model is given in closed form as a function of three parameters. Some theoretical background on this new model is discussed, and an iterative algorithm for estimating its parameters from data is given. Then, the appropriateness of the RiIG distribution as a model for the amplitude statistics of medical ultrasound images is experimentally studied. It is shown that the new distribution can fit to the various shapes of local histograms of linearly scaled ultrasound data better than existing models. A log-likelihood cross-validation comparison of the predictive performance of the RiIG, the K, and the generalized Nakagami models turns out in favor of the new model. Furthermore, a maximum a posteriori (MAP) filter is developed based on the RiIG distribution. Experimental studies show that the RiIG MAP filter has excellent filtering performance in the sense that it smooths homogeneous regions, and at the same time preserves details.     

Performance comparison between Gaussian interleaver, Rayleigh interleaver, and dithered golden interleaver

This paper is a proposal for a new form of random interleaver for a turbo code based on the probability distribution of channel statistic model of transmission, instead of a uniform probability distribution. In our work, we use the normal (Gaussian) and Rayleigh probability distribution in accordance with the channel type and compare them with classic random interleaver (uniform distribution) and with dithered golden interleaver [invention of the Communications Research Centre (CRC)]. The results show that this new form of random interleaver gives identical results compared to the simulated case of dithered golden interleaver.     

Gaussian parametric failure-rate model with application toquartz-crystal device aging

A model for predicting parametric failure rate for a time-dependent normal (Gaussian) distribution is obtained in closed form. The model can be applied to any device parameter that can be modeled by a normal distribution when the parameter time-dependence is known. The model is applied to the aging law of quartz surface-acoustic-wave (SAW) devices. The parametric failure rate of a 295.6 MHz SAW filter was obtained at 75°C based on data for 80 SAW filters. The frequency and phase parameters of the population were characterized over time using an accelerated test. The example illustrates how the mean and standard deviation can be characterized over time for the parametric distribution. Then using these results for the representative lot, the model predicts the population's parametric failure rate at use conditions. This application shows that when a characteristic parameter for a population device being investigated is normally distributed and ages in log(time), then the failure rate has a lognormal form in time, and that a sample standard deviation for time-dependent parameters is also time dependent     

Spatial node distribution of the random waypoint mobility model with applications

The random waypoint model (RWP) is one of the most widely used mobility models in performance analysis of ad hoc networks. We analyze the stationary spatial distribution of a node moving according to the RWP model in a given convex area. For this, we give an explicit expression, which is in the form of a one-dimensional integral giving the density up to a normalization constant. This result is also generalized to the case where the waypoints have a nonuniform distribution. As a special case, we study a modified RWP model, where the waypoints are on the perimeter. The analytical results are illustrated through numerical examples. Moreover, the analytical results are applied to study certain performance aspects of ad hoc networks, namely, connectivity and traffic load distribution.     

Assessing the Value of the Threshold Parameter in the Weibull Distribution Using Bayes Paradigm

The Weibull distribution represents a wide variety of situations. Usually, the distribution is considered as a two-parameter family with a scale, and a shape parameter. If, however, the given data reflect additional information in the form of a minimum guarantee, a positive value away from zero, it is better to go for a three-parameter model with the additional parameter known as the threshold. The threshold parameter is often very important, but increases the complexity of the model. Arbitrarily going for the three-parameter form is not advisable unless it is really required by the data. This article attempts to make a simulation-based Bayesian study for checking if the threshold parameter can be taken to be zero or positive in situations representing the two models. We study the compatibility of the models for the given data set. We conduct the posterior simulation in each case using Gibbs sampling.      

Performance analysis of lognormally shadowed generalized Gamma fading channels

A new composite channel model is proposed for the performance analysis of shadowed fading channels. This model is represented as a mixture of generalized Gamma (GG) multipath fading and lognormal shadowing. GG distribution includes the Rayleigh, Nakagami, and Weibull as special cases; hence the presented model, which is referred to as GG‐L, is a generic model that covers many well‐known composite fading models, including the Rayleigh–lognormal (R‐L), Nakagami–lognormal (N‐L), and Weibull–lognormal (W‐L). The main drawback of the lognormal‐based composite models is that the composite probability density function (PDF) is not in closed form, thereby making the performance evaluation of communication links in these channels cumbersome. To bypass this problem, an approximation method is developed which makes it possible to derive a closed‐form, analytical expression for GG‐L composite distribution. The proposed method only needs the mean and the variance of the underlying lognormal distribution, and hence, bypasses the required complicated integration needed to calculate the PDF of the received signal envelope in GG‐L channel. Based on this method, the most statistical characteristics, such as cumulative density function (CDF) and moments of the GG‐L composite distribution, are derived and used for the performance analysis of a single receiver operating over GG‐L fading channel. Copyright © 2010 John Wiley & Sons, Ltd.     

Admissible, Minimax and Equivariant Estimators of Life Distributions from Type II Censored Samples

In life testing, the unique minimum variance unbiased estimator (MVUE) ? is often used when it exists. However it has been shown for certain distributions that an estimator of the form k? with uniformly smaller mean square error exists. Such extimators are derived here for a class of life distributions and are shown to be admissible, minimax, and (in most cases) equivariant. The underlying distribution from which the samples are drawn follows a generalized life model (GLM) which includes a model proposed by Epstein & Sobel, Weibull, exponential, and Rayleigh distributions as special cases. Results are also given for the Type II asymptotic distribution of largest values, Pareto, and limited distributions. In addition, admissible linear estimators of the form a? + b are obtained and it is shown that they are a form of locally best estimators for some portion of the parameter space. Both k? and a? + b could be used in nonrepetitive estimation problems where bias causes no difficulty.     

A generalized EM algorithm for 3-D Bayesian reconstruction from Poisson data using Gibbs priors

A generalized expectation-maximization (GEM) algorithm is developed for Bayesian reconstruction, based on locally correlated Markov random-field priors in the form of Gibbs functions and on the Poisson data model. For the M-step of the algorithm, a form of coordinate gradient ascent is derived. The algorithm reduces to the EM maximum-likelihood algorithm as the Markov random-field prior tends towards a uniform distribution. Three different Gibbs function priors are examined. Reconstructions of 3-D images obtained from the Poisson model of single-photon-emission computed tomography are presented.     

The Rician inverse Gaussian distribution: a new model for non-Rayleigh signal amplitude statistics.

In this paper, we introduce a new statistical distribution for modeling non-Rayleigh amplitude statistics, which we have called the Rician inverse Gaussian (RiIG) distribution. It is a mixture of the Rice distribution and the inverse Gaussian distribution. The probability density function (pdf) is given in closed form as a function of three parameters. This makes the pdf very flexible in the sense that it may be fitted to a variety of shapes, ranging from the Rayleigh-shaped pdf to a noncentral chi2-shaped pdf. The theoretical basis of the new model is quite thoroughly discussed, and we also give two iterative algorithms for estimating its parameters from data. Finally, we include some modeling examples, where we have tested the ability of the distribution to represent locale amplitude histograms of linear medical ultrasound data and single-look synthetic aperture radar data. We compare the goodness of fit of the RiIG model with that of the K model, and, in most cases, the new model turns out as a better statistical model for the data. We also include a series of log-likelihood tests to evaluate the predictive performance of the proposed model.     

基于三维纹理分割的高光谱图像异常检测

一幅复杂背景的高光谱图像可以看成是由不同纹理组合而成,纹理的统计特性可以近似用高斯分布来描述。采用纹理分割实现复杂背景的分解,从而突破异常大小和形状的限制。采用三维高斯马尔科夫场来描述高光谱图像背景的分布特性,利用最大似然估计得出模型参数,以此参数为特征进行纹理分割,在各纹理上计算像素的统计特性,进行异常检测。     

The use of WMC distribution for performance evaluation of APDoptical communication systems

In the analysis of the bit-error rate (BER) of an optical communication system with avalanche photodiode (APD) detectors, the Webb, McIntyre, Conradi (1974) distribution has been often used to approximate the APD receiver output statistics. This paper presents new simple and closed form BER expressions as well as an importance sampling technique for optical systems employing APD receivers when the WMC model is used. Comparison of the WMC model with the exact model is also carried out. In particular, it is shown that the WMC distribution is quite accurate and has the advantage of simplicity for both simulation and analysis     

The Eccentric Spheres Model as the Basis for a Study of the Role of Geometry and Inhomogeneities in Electrocardiography

To study the role of internal geometry and inhomogeneities in the "forward problem" of electrocardiography (ECG), a mathematical model was constructed which permitted manipulation of these variables. The model, which consists of two eccentric systems of concentric spheres, contains all the important torso compartments, namely the blood cavity, the myocardium, the pericardium, the lung region, the surface muscle layer, and the subcutaneous fat. An analytic solution is found in the form of a double series expansion in Legendre polynomials. The integrated effect of the inhomogeneities on the surface potential distribution is investigated. The model demonstrates the importance of interactions between the various torso components in determining the potential distribution at the surface.     

基于滑动窗与韧性函数的递归最小p范数滤波方法

稳定分布可以更好地描述实际应用中所遇到的具有显著脉冲特性的随机信号和噪声。与其它统计模型不同, 稳定分布没有统一闭式的概率密度函数,其二阶及二阶以上统计量均不存在。针对系统中存在独立SS噪声与高斯噪声,该文基于SSG分布模型,提出了一种混合噪声环境下基于滑动窗与韧性函数自适应广义递归最小p范数滤波算法,并对算法进行了分析。计算机模拟和分析表明,这种算法是一种在SSG分布背景噪声条件下具有良好鲁棒性的方法。     

Lifetime distribution based degradation analysis

The methods commonly used for degradation analysis deduce the lifetime distribution of a product from the distribution of the random parameters in the degradation path model for the product. This approach requires a functional form of the joint distribution of the random parameters, which poses certain practical difficulties. In this paper, we propose an alternative approach which makes inference directly on the lifetime distribution itself. In the proposed approach, degradation data are first used to derive predictive intervals of individual lifetimes. Then an imputation algorithm is invoked to obtain the estimate of the lifetime distribution. The approach has the following advantages: 1) the adequacy of the assumption on the lifetime distribution can be easily examined, 2) the estimated lifetime distribution has a closed form, and 3) the procedure can be more easily implemented. A simulation study is reported to demonstrate the efficiency of the proposed approach. The approach is applied to two real degradation data sets, and compared with Lu-Meeker's two stage method in the applications.     

Electromagnetic wave scattering from a forest or vegetation canopy:ongoing research at the University of Texas at Arlington

A scattering model for forest or vegetation, based on the theory of electromagnetic wave scattering in random media, is described. The model generalizes the assumptions imposed by earlier models, and the results compare well with measurements from several forest canopies. It is shown how the model elements are integrated to obtain the scattering characteristics of different forest canopies. The scattering characteristics may be displayed in the form of polarimetric signatures, represented by like- and cross-polarized scattering coefficients, for an elliptically polarized wave, or in the form of signal distribution curves. Results illustrating both types of scattering characteristics are given     

Cost analysis and minimization of movement-based location management schemes in wireless communication networks: a renewal process approach

The paper makes new contributions to cost analysis and minimization of movement-based location management schemes in wireless communication networks. The main contributions of the paper are three-fold. First, we consider two different call handling models, that is, the call plus location update (CPLU) model and the call without location update (CWLU) model. We point out that all existing analysis of location update cost of a movement-based location management scheme (MBLMS) do not accurately capture the essence of the two models. Second, we analyze the exact location update cost of an MBLMS under both CPLU and CWLU models using a renewal process approach which has rarely been used before. We find that the location update cost of an MBLMS under the CWLU model is much easier to analyze than that of an MBLMS under the CPLU model. Furthermore, an MBLMS operated under the CWLU model has lower location update cost than an MBLMS operated under the CPLU model. Third, we are able to derive a closed form solution to the movement threshold that minimizes the total cost of location management in an MBLMS for the CPLU model when the inter-call time has an arbitrary distribution and the cell residence time has an Erlang distribution, and for the CWLU model when both inter-call time and cell residence time have arbitrary distributions. Such closed form solutions have not been available in the existing literature.     

Multivariate Nakagami-m distribution with constant correlation model

In this paper, a multivariate Nakagami-m distribution is derived using Royen's gamma distributions of one-factorial accompanying matrices for a constant correlation model. The cumulative distribution function, the probability density function and the covariances are obtained in infinite series form. From these results, we derive outage probabilities of selection combiners in both interference- and noise-limited scenarios with a constant correlation model over Nakagami-m fading assuming arbitrary average powers at each input of the combiner.