A New Discrete Weibull Distribution

This paper introduces another discrete Weibull distribution. A connection is shown to the famous Birthday Problem and to the lifetime of a series system of components.     

On estimating parameters in a discrete Weibull distribution

Two discrete Weibull distributions are discussed, and a simple method is presented to estimate the parameters for one of them. Simulation results are given to compare this method with the method of moments. The estimates obtained by the two methods appear to have almost similar properties. The discrete Weibull data arise in reliability problems when the observed variable is discrete. The modeling of such a random phenomenon has already been accomplished. Estimation of parameters in these models is considered. Since the usual methods of estimation are not easy to apply, a simple method is suggested to estimate the unknown parameters. The estimates obtained by this method are comparable to those obtained by the method of moments. The method can be applied in most inferential problems. Though the authors have restricted themselves to type I distribution, their method of proportions for the estimation of parameters can be easily applied to the type II distribution as well     

Approximate MLE's of the parameters of a discrete Weibull distribution with type I censored data

Approximate Maximum Likelihood Estimators of the parameters of a discrete Weibull distribution under censoring is discussed. These approximations are obtained by approximating the likelihood functions at a set of estimators which are easy to obtain. Simulations are carried cut to illustrate the performance of the suggested procedure.     

The α-μ Distribution: A Physical Fading Model for the Stacy Distribution

This paper introduces a fading model, which explores the nonlinearity of the propagation medium. It derives the corresponding fading distribution-the alpha-mu distribution-which is in fact a rewritten form of the Stacy (generalized Gamma) distribution. This distribution includes several others such as Gamma (and its discrete versions Erlang and central Chi-squared), Nakagami-m (and its discrete version Chi), exponential, Weibull, one-sided Gaussian, and Rayleigh. Based on the fading model proposed here, higher order statistics are obtained in closed-form formulas. More specifically, level-crossing rate, average fade duration, and joint statistics (joint probability density function, general joint moments, and general correlation coefficient) of correlated alpha-mu variates are obtained, and they are directly related to the physical fading parameters     

竞争失效产品步进加速寿命试验的优化设计

对weibull分布竞争失效产品的步进加速寿命试验进行优化设计,首先选取产品正常应力下中位寿命的极大似然计估渐近方差的估计值作为优化目标函数,并对优化目标函数进行统计推断.然后利用目标函数的连续性,提出基于离散数据的函数拟合方法,将试验优化设计转化为显函数的约束极值求解问题,同时将智能优化算法应用到步进加速寿命试验的优...     

基于实测数据的分时全极化雷达海杂波分布研究

首先基于IPIX分时全极化雷达的海杂波实测数据,分析了瑞利分布、韦布尔分布、对数正态分布和K分布对实测数据的拟合效果,发现对数正态分布拟合水平极化接收通道的杂波数据效果较好,K分布拟合垂直极化接收通道的杂波数据效果较好,但是仍然存在海杂波"拖尾"区域拟合不理想的情况.为此,假设海杂波中的布拉格散射体的回波服从K分布,离散海尖峰的回波服从对数正态分布,海杂波整体服从K分布和对数正态分布的叠加混合分布,提出了一种具有闭式表达式的混合分布,以改善海杂波分布"拖尾"部分的拟合效果.实测数据分析表明,本文提出的混合分布对海杂波幅度分布的拟合效果优于对数正态分布和K分布.     

The exponentiated Weibull family: a graphical approach

The exponentiated Weibull family extends the two-parameter Weibull distribution. The shape of the Weibull plotting-paper plots are discussed, and a parametric characterization of the pdf and the failure rate for the exponentiated Weibull family are carried out. Such a study is very relevant to deciding if a given data set can be adequately modeled by such a distribution     

基于改进型Weibull密度分布的H.264视频率失真模型研究

通过对视频信源的统计分析,本文提出一种改进型Weibull密度分布,并据此密度分布建立一个新的率失真模型。文章通过使用Weibull概率密度函数,逼近实际DCT系数分布,并通过编码熵理论和失真分析,将模型表示成为两个关于视频编码量化步长的函数,即码率量化(R-Q)模型和失真量化(D-Q)模型,进而估计编码码率和量化失真。仿真结果表明,该密度分布比Cauchy密度分布更逼近于实际视频序列的DCT系数统计特性,并且该模型较基于Cauchy密度分布的率失真模型能够更为精确地估计实际编码码率和失真性能。      

Inverse gaussian distribution and its application to reliability

This paper discusses the problem of estimating parameters for the inverse Gaussian distribution when early failures dominate the problem. Since the Weibull distribution is a well-known competitor of the inverse Gaussian distribution, the estimate for the reliability function can be obtained by using the Weibull distribution. Simulation studies are performed to compare reliability by using both inverse Gaussian and Weibull distributions. Various implications of these results are discussed.     

A modified Weibull distribution

A new lifetime distribution capable of modeling a bathtub-shaped hazard-rate function is proposed. The proposed model is derived as a limiting case of the Beta Integrated Model and has both the Weibull distribution and Type 1 extreme value distribution as special cases. The model can be considered as another useful 3-parameter generalization of the Weibull distribution. An advantage of the model is that the model parameters can be estimated easily based on a Weibull probability paper (WPP) plot that serves as a tool for model identification. Model characterization based on the WPP plot is studied. A numerical example is provided and comparison with another Weibull extension, the exponentiated Weibull, is also discussed. The proposed model compares well with other competing models to fit data that exhibits a bathtub-shaped hazard-rate function.     

Correlated multivariate Weibull fading channels with selection diversity

The dependent multivariate Weibull distribution is modelled for correlated fading channels, where the probability density function of a Weibull fading factor is defined with two parameters (omega, beta), and the case of equal beta is considered. The joint cumulative distribution function and probability density function of the Weibull distribution are derived, and the outage probability of selection diversity is evaluated     

氧化铝陶瓷封接强度的统计分析

采用Weibull分布和正态分布,对氧化铝陶瓷封接强度进行统计分析,并通过Weibull模数和变异系数来表征了材料强度的离散性。同时通过Weibull分布,比较了标准组合抗拉强度、拉钉强度和抗折强度测试的数据。     

On the Weibull shape factor of intrinsic breakdown of dielectric films and its accurate experimental determination. Part I: theory, methodology, experimental techniques

Critically examined several important aspects concerning the experimental determination of Weibull shape factors (slopes). Statistical characteristics of breakdown distribution such as area scaling property and the extreme-value distribution are reviewed. We discuss the experimental measurement methodology of time-to-breakdown (T/sub BD/) or charge-to-charge (Q/sub BD/) distributions with the emphasis on the accuracy. The influence of sample numbers on the estimation of Weibull distribution parameters such as characteristic T/sub BD/ and Weibull slopes are investigated in the context of confidence limits. Some examples of the measurement fallacy on Weibull slopes are given. Three different experimental techniques to measure Weibull slopes are described and compared in terms of their advantages and disadvantages. Finally, we will give a comparison of these three methods. Having established these fundamental aspects of the Weibull slope measurements, we will present our extensive experimental data on thickness, voltage, temperature, and polarity dependence of Weibull slopes in part II.     

The statistical distribution of percolation current for soft breakdown in ultrathin gate oxide

Soft breakdown in ultrathin gate oxide has been studied using constant voltage stressing. The behavior of current increments resulting from a number of soft breakdown events has been characterized by statistical distribution. It is shown that the distribution of the current increment follows Weibull distribution rather than log normal distribution. The newly established Weibull slope is shown to be independent of the stressed voltage in the range investigated between 4.5 and 5.1 V. The temperature effect study shows that the Weibull slope reduces with increasing testing temperature. Furthermore, a strong dependence of the Weibull slope on the oxide thickness has been found. These observations can be explained well by geometrical configurations of the percolation path.     

Mean residual life of lifetime distributions

This paper characterizes the general behaviors of the MRL (mean residual lives) for both continuous and discrete lifetime distributions, with respect to their failure rates. For the continuous lifetime distribution with failure rates with only one or two change-points, the characteristic of the MRL depends only on its mean and failure rate at time zero. For failure rates with “roller coaster” behavior, the subsequent behavior of the MRL depends on its MRL and failure-rates at the change points. Using the characterization, their behaviors for the: Weibull; lognormal; Birnbaum-Saunders; inverse Gaussian; and bathtub failure rate distributions are tabulated in terms of their shape parameters. For discrete lifetime distributions, for upside-down bathtub failure rate with only one change point, the characteristic of the MRL depends only on its mean and the probability mass function at time zero     

Analysis and Optimization Study of Antenna Selection in Dual Hop Relay Networks over Weibull Fading Channels

Field experiments show that Weibull distribution can be considered as the most suitable distribution to model weak to high signal power levels in indoor and outdoor environments. Recently, Exponentiated Weibull which is a special case of Weibull fading, have been widely adopted in free-space optical communication systems to model weak and high levels of turbulence effects. Motivated from the increasing use of Weibull distribution, this paper studies the popular dual-hop amplify-and-forward relay network with joint transmit and receive antenna selection where closed form ergodic capacity, symbol error rate and outage probability expressions are derived for Weibull fading channels. With the help of high SNR analysis, diversity gain, array gain and optimum relay location are obtained. Finally, theoretical findings are validated by simulation results.     

Exponentiated Weibull family for analyzing bathtub failure-ratedata

A simple generalization of the Weibull distribution is presented. The distribution is well suited for modeling bathtub failure rate lifetime data and for testing goodness-of-fit of the Weibull and negative exponential models as subhypotheses     

激光大气传输接收功率闪烁的概率分布特征

在大气激光通信、激光测距、激光制导等应用中,由于大气湍流引起的接收光功率起伏对其工作效果及稳定性都有很大的影响。通过多相屏傅里叶数值模拟方法模拟了准直高斯光束在湍流大气中的传输,在考虑孔径平均效应的基础下,比较了弱起伏条件、中等起伏条件和强起伏条件下对数正态分布、Gamma-Gamma分布、指数威布尔分布和威布尔分布对仿真数据的拟合,分析得到弱起伏条件到强起伏条件下激光大气传输接收功率闪烁的概率分布服从指数威布尔分布,且该分布具有概率密度函数和累积分布函数结构简单、参数可以由大气参数计算得到的优点,为提高激光大气传输应用技术的性能提供了参考。     

相关韦布尔分布雷达杂波模拟的VC++实现与分析

韦布尔分布是雷达杂波中一种重要的概率分布模型,文中介绍了韦布尔分布杂波模拟的思路和ZMNL法模拟的步骤,重点阐述了模拟过程中的难点及解决方法,并对模拟结果进行了分析,证明了该方法的有效性和正确性。     

基于SIRP法的相关韦布尔分布雷达杂波仿真

推导了韦布尔分布参量满足的最大似然(ML)估计方程和其为球不变随机矢量(SIRV)的条件,给出了模拟相关韦布尔分布雷达杂波的原理和流程。在此基础上,基于球不变随机过程(SIRP)法仿真了具有高斯谱的韦布尔分布及其特例——瑞利和指数分布,弥补了零记忆非线性(ZMNL)法不能独立控制边缘概率密度函数(PDF)与相关函数的不足。最后不仅验证了模拟数据的PDF与理论分布,估计的功率谱与理论谱的吻合程度,而且分析了ML估计的分布参数与真实值之间的相对误差。结果表明,基于SIRP法仿真相关韦布尔分布雷达杂波是有效的。