Unbiased Maximum-Likelihood Estimation of a Weibull Percentile when the Shape Parameter is Known

The maximum-likelihood (ML) estimator for a percentile of a Weibull distribution with a known shape parameter is considered. Multiplicative correction factors are listed for rendering the ML estimator mean or median unbiased in the cases where the samples are type II censored with or without replacement. The correction factors depend upon the number of failures and the shape parameter but are independent of the sample size and the percentile being estimated.     

Simultaneous Estimation of Location and Scale Parameters of the Weibull Distribution

This paper deals with the simultaneous estimation of the location parameter ? and the scale parameter ? of the Weibull distribution when both are unknown and the shape parameter ? is known. The best linear unbiased estimate (BLUE) (?, ?) based on a subset of k optimum ordered observations selected from the whole sample is compared with 1) Ogawa's asymptotically best linear estimate (ABLE) (?*, ?*) based on k ordered observations whose ranks are approximated by an asymptotic optimum selection, and 2) the BLUE based on the ranks in 1). Tables facilitating the computation of (?, ?) based on k = 3, 4 optimum ordered observations are provided.     

Bayes Interval Estimation for the Shape Parameter of the Power Distribution

The power distribution is considered as failure model and uses a square-error loss function. Bayes credibility interval estimators for the shape parameter have been obtained assuming 1) the following priors for the shape parameter: Jeffrey's invariant prior, gamma, and inverted gamma; 2) the following priors for reliability: beta and log gamma function. It is straightforward to obtain estimators for reliability when the estimators for the shape parameter are known.     

Life Tests with Periodic Change in the Scale Parameter of a Weibull Distribution

Two life testing procedures, namely, the progressively censored samples and Bartholomew's experiment are discussed under the assumption that the life of an item follows a specialized Weibull distribution. The scale parameter is different under two different conditions of usage of the item at regular intervals of time, the shape parameter remains unchanged throughout the experiment. The maximum likelihood estimates of the two scale parameters have been derived along with their variances. A numerical example illustrates the type of data and relevant calculations for the experiment involving progressively censored samples.     

Comparisons of Point Estimation Methods in the 2-parameter Weibull Distribution

The following 3 estimation methods in a Weibull distribution are well-known; Maximum Likelihood Estimation (MLE), Coefficient of Variation (CV), and Weibull Probability Paper (WPP). By simulation we conclude that the WPP method is best.     

Linear Estimation of the Scale Parameter of the First Asymptotic Distribution of Extreme Values

A Lagrange multiplier technique is used to obtain linear, minimum-variance, unbiased estimators for the scale parameters of the first asymptotic distributions of smallest and largest values with known mode. Coefficients for multiplying ordered observations are computed for complete and censored samples of size n = 1(1) 15. Each sample of size n is censored from above and all m-order-statistic estimators are obtained where m ? n. Then the smallest subset of # order statistics from the set of m available order statistics is found which yields a 99% efficiency relative to the m-order-statistic estimator. The Cramér-Rao lower bound for the variances of the estimators for complete samples is derived and tabled for n = 1(1) 15. For censored samples the asymptotic variances of the maximum-likelihood m-order-statistic estimators are presented for comparative purposes.     

Bayesian Analysis of the Weibull Process With Unknown Scale and Shape Parameters

Previously, the Weibull process with an unknown scale parameter was examined as a model for Bayesian decision making. The analysis is extended by treating both the shape and scale parameters as unknown. It is not possible to find a family of continuous joint prior distributions on the two parameters that is closed under sampling, so a family of prior distributions is used that places continuous distributions on the scale parameter and discrete distributions on the shape parameter. Prior and posterior analyses are examined and seen to be no more difficult than for the case in which only the scale parameter is treated as unknown, but preposterior analysis and determination of optimal sampling plans are considerably more complicated in this case. To illustrate the use of the present model, an example is presented in which it is necessary to make probability statements about the mean life and reliability of a long-life component both before and after life testing.     

Tables to Facilitate Calculation of an Asymptotically Optimal t Test for Equality of Location Parameters of a Certain Extreme-Value Distribution

A t test, proposed by Ogawa and based on the use of a few sample quantiles selected from large samples, is considered for testing the hypothesis H0: ?1 = ?2 against the hypothesis H1: ?1 ? ?2 concerning the location parameters ?1 and ?2 of two extreme-value distributions with common unknown scale parameter ?. Tables that simplify the calculation of the test statistic and an example illustrating their use are provided.     

Bayesian Analysis of the Weibull Process with Unknown Scale Parameter and Its Application to Acceptance Sampling

The Weibull process with unknown scale parameter is taken as a model for Bayesian decision making. The family of natural conjugate prior distributions for the scale parameter is exhibited and used in prior and posterior analysis. Preposterior analysis and several sampling schemes are then discussed. Preposterior analysis is given for an acceptance sampling problem with utility linear in the unknown mean of the Weibull process, in which the sampling scheme yields the first r failures in a life test of n items. An example is included.     

率估计的一种多段分频等长信号融合算法

在低信噪比、被测频率持续时间短的情况下,为提高频率估计精度并适用于多段分频等长信号,本文提出一种分频等长融合算法.因各段信号的被测频率不等,故生成频域分析参数矩阵以实现同频化效果;因同频化后各段信号之间仍然相位不连续,故设计相位差补偿因子矩阵以达到相位连续信号的效果;生成搜索频率序列并得到具有特定形式的功率谱矩阵.为验证算法的正确性,给出了详细的数学证明.仿真表明本文算法适用于任意类型的多段分频等长信号,抗噪性好,频率估计精度比现有方法有较大提高.     

HP-41C Programs for Bayesian Binomial and Exponential Interval Estimation with a Uniform Prior on the Reliability

HP-41C handheld calculator programs are presented for Bayes interval estimation of: 1) the reliability R of a component for binomial data; 2) both R and the MTBF for exponential data. In both cases, the ``ignorance' prior is employed: uniform on R over the range 0 to 1. The input data are numbers of trials and successes for the binomial case; and test time, mission time and failures for the exponential. This paper describes the models and includes the programs.     

Recursive Parameter Estimation Algorithms and Convergence for a Class of Nonlinear Systems with Colored Noise

Parameter estimation is important for controller design of linear systems and nonlinear systems. The parameters of the systems can be estimated through some identification algorithms. This paper presents a recursive generalized extended least squares algorithm and a generalized extended stochastic gradient (GESG) algorithm for identifying the parameters of a class of nonlinear systems. Furthermore, a multi-innovation GESG algorithm is derived to improve the estimation accuracy. The simulation example is provided to test the effectiveness of the proposed algorithms.     

Parameter Estimation and Image Reconstruction of Rotating Targets with Vibrating Interference in the Terahertz Band

Rotation is one of the typical micro-motions of radar targets. In many cases, rotation of the targets is always accompanied with vibrating interference, and it will significantly affect the parameter estimation and imaging, especially in the terahertz band. In this paper, we propose a parameter estimation method and an image reconstruction method based on the inverse Radon transform, the time-frequency analysis, and its inverse. The method can separate and estimate the rotating Doppler and the vibrating Doppler simultaneously and can obtain high-quality reconstructed images after vibration compensation. In addition, a 322-GHz radar system and a 25-GHz commercial radar are introduced and experiments on rotating corner reflectors are carried out in this paper. The results of the simulation and experiments verify the validity of the methods, which lay a foundation for the practical processing of the terahertz radar.     

Single-Position Passive Location and Navigation with Allowance for the Evolution of the Radio Signal Period at the Reception Point

Journal of Communications Technology and Electronics - In this paper, we develop a single-position method of passive location and navigation with allowance for the periodicity of the radiated radio...     

Parameter Estimation of a Simple Model of the Left Ventricle and of the Systemic Vascular Bed, with Particular Attention to the Physical Meaning of the Left Ventricular Parameters

The goal of this study is to estimate the values of the parameters of a simple electrical model of the cardiovascular system and to evaluate whether some physical interpretation can be given to the left ventricular parameters. In this model, the left ventricle is represented by a time varying capacitance C(t) analogous to the instantaneous left ventricular pressure/volume ratio, and the systemic vascular bed by two capacitances (Cl, C2), one inductance (L) and one resistance (r). The parameter values are computed from only two measurements: the instantaneous pressurepao(t) and the mean flow Q?ao at the root of the aorta during one beat. First, r is calculated as the ratio between P?ao and Q?ao. Thereafter, Jazwinski's nonlinear filter is used to compute L, C1, C2 from the diastolic part of pao (t), and C(t) from the systolic part of pao(t). The shape of ê(t), i.e., 1/?(t) during one beat, estimated from our experiments on dogs, varies strongly after isoproterenol injection (increase in myocardial contactility) but remains unchanged after neosynephrine and amyl nitrite administration (changes in peripheral vascular resistance). These results suggest that the estimated ê(t), like the actual pressure/volume ratio measured by Suga is related to the contractile state of the left ventricle.     

An Evaluation of the CMOS Technology Roadmap From the Point of View of Variability, Interconnects, and Power Dissipation

In this paper, using the new generation of model for assessment of CMOS technologies and roadmaps software, we discuss the CMOS logic roadmap in terms of circuit performance, power dissipation, and variability, such as loaded ring-oscillator delay, as well as through 6T-SRAM functionality. It is shown that these criteria will have to be taken into account in addition to the traditional 17%-per-year delay improvement to construct a new industrially viable roadmap.     

Iterative Parameter Estimation for a Class of Multivariable Systems Based on the Hierarchical Identification Principle and the Gradient Search

For a multivariable controlled autoregressive system with autoregressive noises, its corresponding identification model contains a parameter matrix and a parameter vector. This paper presents the hierarchical gradient-based iterative (HGI) algorithm to interactively estimate the parameter matrix and the parameter vector by using the hierarchical identification principle and the gradient search. The simulation results show that the HGI algorithm is effective.