Lower and upper bounds on the minimum mean-square error incomposite source signal estimation

The performance of a minimum mean-square error (MMSE) estimator for the output signal from a composite source model (CSM), which has been degraded by statistically independent additive noise, is analyzed for a wide class of discrete-time and continuous-time models. In both cases, the MMSE is decomposed into the MMSE of the estimator, which is informed of the exact states of the signal and noise, and an additional error term. This term is tightly upper and lower bounded. The bounds for the discrete-time signals are developed using distribution tilting and Shannon's lower bound on the probability of a random variable exceeding a given threshold. The analysis for the continuous-time signal is performed using Duncan's theorem. The bounds in this case are developed by applying the data processing theorem to sampled versions of the state process and its estimate, and by using Fano's inequality. The bounds in both cases are explicitly calculated for CSMs with Gaussian subsources. For causal estimation, these bounds approach zero harmonically as the duration of the observed signals approaches infinity     

Application of three-parameter lognormal distribution in EM data analysis

The three-parameter lognormal distribution has been demonstrated for applications in electromigration data analysis, especially for Cu interconnect structures with insufficient redundancy. Examples are given on estimating parameter values from experimental data using the maximum likelihood method. Detailed analyses are presented on confidence bound estimations of the parameters and their propagation to lifetime projections.     

恒加试验下LED照明灯的三参数Weibull分布的参数估计

三参数Weibull分布拟合LED照明灯寿命的优势较为明显,但要得到三参数Weibull分布参数较为精确的点估计较为困难。目前常用的参数估计方法有极大似然法、矩估计法、Bayes估计法等,由于其计算的方程复杂,导致软件编程繁琐,不易掌握,而且也不一定能得到参数估计。鉴于此,文章针对恒加试验提出一种简便地求解三参数Weibull分布参数估计的方法,该方法不涉及超越方程的求解问题,软件编程相当简单,且统计思想清晰。通过LED照明灯恒加试验下的几个案例数据说明方法的应用,并与已有的方法做了对比分析。     

Numerical calculation of the linewidth of Raman fiber lasers due to spontaneous Raman scattering

We calculate the spectral width of the Stokes output of Raman fiber lasers determined by spontaneous Raman scattering. The conventional model with zero bandwidths of the pump and Stokes lines is extended so that it describes a frequency-resolved Stokes band driven by the pump wave through both stimulated and spontaneous Raman scattering. To solve the boundary value problem for the Stokes spectra, a semi-analytic method is developed which reduces the spectrally resolved problem to an equivalent conventional model based on effective mirror reflectivities. The Stokes spectra are given in closed form in terms of the mirror reflection spectra. Spontaneous Raman scattering perceptibly broadens the RFL output spectra for pump powers around the lasing threshold.     

Applications and extensions of the chains-of-rare-events model

The chains-of-rare-events model (ChRE) is extended. The ChRE was originally introduced in order to analyze occurrences which can be produced with simple, double, triple, etc., multiplicity. In the original ChRE, each occurrence of multiplicity (i) is independently distributed according to a Poisson law with parameter λ_i ; and a simple relation for these parameters is considered. In this way, ChRE can be applied to analyze outcomes produced in occurrences with multiple events, such as failures, queuing, automobile accidents, telephone calls, and accidents in a factory. The original ChRE is extended to analyze the total number of outcomes in which a given total number of occurrences of different multiplicity occur. The model can be analyzed as a compound Poisson distribution where the compounding distribution is Poisson truncated at zero. Applications to reliability and queuing processes data are presented. The results compare favorably with those from other models     

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.     

A new model for step-stress testing

The mathematical intractability of the Weibull cumulative exposure model (CE-M) has impeded the development of statistical procedures for step-stress accelerated life tests. Our new model (KH-M) is based on a time transformation of the exponential CE-M. The time-transformation enables the reliability engineer to use known results for multiple-step, multiple-stress models that have been developed for the exponential step-stress model. KH-M has a realistically appealing proportional-hazard property. It is as flexible as the Weibull CE-M for fitting data, but its mathematical form makes it easier to obtain parameter estimates and standard deviations. Maximum likelihood estimates are given for test plans with unknown shape parameter. The mathematical similarity to the constant-stress Weibull model is shown. Chi-square goodness of fit tests are performed on simulated data to compare the fit of the models     

On the existence of universal nonlinearities for blind sourceseparation

Many density-based methods for blind signal separation employ one or more models for the unknown source distribution(s). This paper considers the issue of density model mismatch in maximum likelihood (ML)-type blind signal separation algorithms. We show that the score function nonlinearity, which was previously derived from the standpoint of statistical efficiency, is also the most robust in maintaining a separation solution for the ML algorithm class. We also consider the existence of a universally applicable nonlinearity for separating all signal types, deriving two results. First, among nonlinearities with a convergent Taylor series, a single fixed nonlinearity for universal separation using the natural gradient algorithm cannot exist. Second, among nonlinearities with a single adjustable parameter, a previously proposed threshold nonlinearity can separate all signals with symmetric amplitude distributions as long as the threshold parameter is properly chosen. The design of "difficult-to-separate" signal distributions is also discussed     

A physically based compact device model for fully depleted andnearly fully depleted SOI MOSFET

A compact submicrometer Fully Depleted Silicon-On-Insulator (FDSOI) and Nearly FDSOI MOSFET device model suitable for analog as well as digital application has been proposed. It is an all region model. In developing this model care has been taken in retaining the basic functional form of physical models while improving the model accuracy and computational efficiency. In addition to the commonly included effects in the FDSOI MOSFET model, we have given careful consideration to parasitic source/drain resistance, Drain Induced Conductivity Enhancement (DICE) effect, floating body effect, self-heating and model continuity. A single parameter set is used for a large set of device dimensions except threshold voltage and parasitic source/drain resistance due to silicon film thickness variations. The accuracy of the model is validated with experimental data using NMOS FDSOI devices and found to be in good agreement     

Analysis of an on-off jamming situation as a dynamic game

The process of communication jamming can be modeled as a two-person zero-sum noncooperative dynamic game played between a communicator (a transmitter-receiver pair) and a jammer. We consider a one-way time-slotted packet radio communication link in the presence of a jammer, where the data rate is fixed and (1) in each slot, the communicator and jammer choose their respective power levels in a random fashion from a zero and a positive value; (2) both players are subject to temporal energy constraints which account for protection of the communicating and jamming transmitters from overheating. The payoff function is the time average of the mean payoff per slot. The game is solved for certain ranges of the players' transmitter parameters. Structures of steady-state solutions to the game are also investigated. The general behavior of the players' strategies and payoff increment is found to depend on a parameter related to the payoff matrix, which me call the payoff parameter, and the transmitters' parameters. When the payoff parameter is lower than a threshold, the optimal steady-state strategies are mixed and the payoff increment constant over time, whereas when it is greater than the threshold, the strategies are pure, and the payoff increment exhibits oscillatory behavior     

极不均匀合成孔径雷达杂波建模及恒虚警检测

基于合成孔径雷达(SAR)城区极不均匀杂波实际数据和Cramer-Von Mises距离,本文运用Rayleigh分布、Weibull分布、K分布和G分布对杂波进行了分布拟合检验.结果表明Rayleigh分布和Weibull分布难以拟合极不均匀场景回波,K分布只能部分拟合,而G分布的拟合程度最好.进而,针对G分布下的目标恒虚警检测问题,本文给出了不同参考单元条件下达到给定检测性能时信噪比随形状参数的变化曲线,分析了恒虚警(CFAR)性能损失随分布参数变化的原因,得到了确定恒虚警门限的有效方法.     

A Lifetime Distribution With an Upside-Down Bathtub-Shaped Hazard Function

A three-parameter lifetime distribution with increasing, decreasing, bathtub, and upside down bathtub shaped failure rates is introduced. The new model includes the Weibull distribution as a special case. A motivation is given using a competing risks interpretation when restricting its parametric space. Various statistical properties, and reliability aspects are explored; and the estimation of parameters is studied using the standard maximum likelihood procedures. Applications of the model to real data are also included     

A statistical model for interpreting computerized dynamic posturography data

Computerized dynamic posturography (CDP) is widely used for assessment of altered balance control. CDP trials are quantified using the equilibrium score (ES), which ranges from zero to 100, as a decreasing function of peak sway angle. The problem of how best to model and analyze ESs from a controlled study is considered. The ES often exhibits a skewed distribution in repeated trials, which can lead to incorrect inference when applying standard regression or analysis of variance models. Furthermore, CDP trials are terminated when a patient loses balance. In these situations, the ES is not observable, but is assigned the lowest possible score--zero. As a result, the response variable has a mixed discrete-continuous distribution, further compromising inference obtained by standard statistical methods. Here, we develop alternative methodology for analyzing ESs under a stochastic model extending the ES to a continuous latent random variable that always exists, but is unobserved in the event of a fall. Loss of balance occurs conditionally, with probability depending on the realized latent ES. After fitting the model by a form of quasi-maximum-likelihood, one may perform statistical inference to assess the effects of explanatory variables. An example is provided, using data from the NIH/NIA Baltimore Longitudinal Study on Aging.     

A model for residual life prediction based on Brownian motion with an adaptive drift

A degradation model is presented in this paper for the prediction of the residual life using an adapted Brownian motion-based approach with a drifting parameter. This model differs from other Brownian motion-based approaches in that the drifting parameter of the degradation process is adapted to the history of monitored information. This adaptation is performed by Kalman filtering. We also use a threshold distribution instead of the usual single threshold line which is sometime difficult to obtain in practice. We demonstrate the model using some examples and show that the model performs reasonably well and has a better prediction ability than the standard Brownian motion-based model. The model is then fitted to the data generated from a simulator using the expectation-maximization algorithm. We also fit a standard Brownian motion-based model to the same data to compare the difference and performance. The result shows that the adapted model performs better in terms of certain test statistics and the total mean square errors.     

An analytical threshold voltage model of NMOSFETs with hot-carrier induced interface charge effect

An analytical threshold voltage model of NMOSFETs including the effect of hot-carrier-induced interface charges is presented. A step function describing the interface charge distribution along the channel is used to account for the hot carrier induced damage, and a pseudo-2D method is applied to derive the surface potential. The threshold voltage model is then developed by solving the gate-to-source voltage at the onset of surface inversion where the minimum surface potential equals the channel potential. Both the drain-induced barrier lowering (DIBL) and body effects are included in the present model as well. The present threshold voltage model is validated for both fresh and damaged devices. The results show that the threshold voltage shifts upward and approaches a maximum value with negative interface charges and shifts downward and reaches a minimum value with positive interface charges as the interface charge region length is increased from zero to the channel length. Model is successfully verified using simulation data obtained from TCAD (technology-based computer-aided design).     

Estimation of threshold stress in accelerated life-testing

The author presents a method that uses accelerated life-test data to estimate the mean life at the service stress and the threshold stress below which a failure is unlikely to occur. The relation between stress and mean-life at that stress is assumed to follow an inverse power law that includes a threshold stress. The failure times at a given stress are assumed to follow a Weibull distribution in which the shape parameter varies with the stress. This model extends the well-known Weibull inverse power law model. If only the mean life but not a specific percentile point at a service stress is sought, the maximum likelihood method is useful for parameter estimation. This is a tradeoff in the parametric approach. For adoption of an appropriate probability model, the likelihood ratio test as well as the Akaike Information Criterion are used. Type I right censored data are considered. Extensions of the method are discussed     

Parameter estimation of incomplete data in competing risks using the EM algorithm

Consider a system which is made up of multiple components connected in a series. In this case, the failure of the whole system is caused by the earliest failure of any of the components, which is commonly referred to as competing risks. In certain situations, it is observed that the determination of the cause of failure may be expensive, or may be very difficult to observe due to the lack of appropriate diagnostics. Therefore, it might be the case that the failure time is observed, but its corresponding cause of failure is not fully investigated. This is known as masking. Moreover, this competing risks problem is further complicated due to possible censoring. In practice, censoring is very common because of time and cost considerations on experiments. In this paper, we deal with parameter estimation of the incomplete lifetime data in competing risks using the EM algorithm, where incompleteness arises due to censoring and masking. Several studies have been carried out, but parameter estimation for incomplete data has mainly focused on exponential models. We provide the general likelihood method, and the parameter estimation of a variety of models including exponential, s-normal, and lognormal models. This method can be easily implemented to find the MLE of other models. Exponential and lognormal examples are illustrated with parameter estimation, and a graphical technique for checking model validity.     

A generalized three-parameter (3-P) aperture distribution forantenna applications

A versatile three-parameter (3-P) elliptical aperture distribution, which encompasses many of the existing circular aperture distributions, is presented. Characteristics of the 3-P distributions such as the edge taper, the taper efficiency, the aperture power, the closed-form far fields, the sidelobe levels, the beamwidth and beam efficiency are analyzed. Also derived is an asymptotic form of the far-field, based on which the far-angle features of the 3-P distributions such as the far-field envelope, the decay rate, and the positions of nulls are determined. Examples are presented to illustrate the improvements resulting from the enlarged parameter space for aperture models obtainable from the 3-P distributions. Issues concerning the total power associated with an aperture distribution are studied and the inadequacy of some commonly used approximation is demonstrated     

A nonstatistical approach to estimating confidence intervals aboutmodel parameters: application to respiratory mechanics

Estimates of parameters obtained by fitting models to physiologic data are of little use unless accompanied by confidence intervals. The standard methods for estimating confidence intervals are statistical, and make the assumption that the fitted model accounts for all the deterministic variation in the data while the residuals between the fitted model and the data reflect only stochastic noise. In practice, this is frequently not the case, as one often finds the residuals to be systematically distributed about zero. In this paper, we develop an approach for assessing confidence in a parameter estimate when the order of the model is clearly less than that of the system being modeled. Our approach does not require a parameter to have a single value located within a region of confidence. Instead, we let the parameter value vary over the data set in such a way as to provide a good fit to the entire data set. We apply our approach to the estimation of the resistance of the respiratory system in which a simple model is fitted to measurements of tracheal pressure and flow by recursive multiple linear regression. The values of resistance required to achieve a good fit are represented as a modified histogram in which the contribution of a particular resistance value to the histogram is weighted by the amount of information used in its determination. Our approach provides parameter frequency distribution functions that convey the degree of confidence one may have in the parameter, while not being based on erroneous statistical assumptions.