Assessing the performance of normal-based and REML-based confidence intervals for the intraclass correlation coefficient

Using normal distribution assumptions, one can obtain confidence intervals for variance components in a variety of applications. A normal-based interval, which has exact coverage probability under normality, is usually constructed from a pivot so that the endpoints of the interval depend on the data as well as the distribution of the pivotal quantity. Alternatively, one can employ a point estimation technique to form a large-sample (or approximate) confidence interval. A commonly used approach to estimate variance components is the restricted maximum likelihood (REML) method. The endpoints of a REML-based confidence interval depend on the data and the asymptotic distribution of the REML estimator. In this paper, simulation studies are conducted to evaluate the performance of the normal-based and the REML-based intervals for the intraclass correlation coefficient under non-normal distribution assumptions. Simulated coverage probabilities and expected lengths provide guidance as to which interval procedure is favored for a particular scenario. Estimating the kurtosis of the underlying distribution plays a central role in implementing the REML-based procedure. An empirical example is given to illustrate the usefulness of the REML-based confidence intervals under non-normality.     

The beta exponential distribution

The exponential distribution is perhaps the most widely applied statistical distribution for problems in reliability. In this note, we introduce a generalization—referred to as the beta exponential distribution—generated from the logit of a beta random variable. We provide a comprehensive treatment of the mathematical properties of the beta exponential distribution. We derive expressions for the moment generating function, characteristic function, the first four moments, variance, skewness, kurtosis, mean deviation about the mean, mean deviation about the median, Rényi entropy, Shannon entropy, the distribution of sums and ratios, and the asymptotic distribution of the extreme order statistics. We also discuss simulation issues, estimation by the methods of moments and maximum likelihood and provide an expression for the Fisher information matrix. We hope that this generalization will attract wider applicability in reliability.     

Local fault detection in helical gears via vibration and acoustic signals using EMD based statistical parameter analysis

Gear is a vital transmission element, finding numerous applications in small, medium and large machinery. Excessive loads, speeds and improper operating conditions may cause defects on their bearing surfaces, thereby triggering abnormal vibrations in whole machine structures. This paper describes the implementation of empirical mode decomposition (EMD) method for monitoring simulated faults using vibration and acoustic signals in a two stage helical gearbox. By using EMD method, a complicated signal can be decomposed into a number of intrinsic mode functions (IMF) based on the local characteristic time scale of the signal. Vibration and acoustic signals are decomposed to extract higher order statistical parameters. Results demonstrate the effectiveness of EMD based statistical parameters to diagnose severity of local faults on helical gear tooth. Kurtosis values from EMD and that obtained from vibration and acoustic signals are compared to demonstrate the superiority of EMD based technique.     

Statistical Analysis for Decision Making

In this article we consider a generalization of the univariate g-and-h distribution to the multivariate situation with the aim of providing a flexible family of multivariate distributions that incorporate skewness and kurtosis. The approach is to modify the underlying random variables and their quantiles, directly giving rise to a family of distributions in which the quantiles rather than the densities are the foci of attention. Using the ideas of multivariate quantiles, we show how to fit multivariate data to our multivariate g-and-h distribution. This provides a more flexible family than the skew-normal and skew-elliptical distributions when quantiles are of principal interest. Unlike those families, the distribution of quadratic forms from the multivariate g-and-h distribution depends on the underlying skewness. We illustrate our methods on Australian athletes data, as well as on some wind speed data from the northwest Pacific.     

基于MCKD和峭度的液压泵故障特征提取

液压泵早期故障信号具有非平稳性、强背景噪声、弱故障特征特点,故障特征难以有效提取。为此,提出基于自相关分析与最大相关峭度解卷积算法的齿轮泵故障特征提取方法,利用MCKD算法对采集信号去噪处理,增强信号中的原始冲击成分,提高信号的信噪比;基于峭度（或峭度绝对值,或峭度平方值）的特征信息提取方法,来度量机械信号的非高斯性程度,以表征机械设备的运行状态信息。试验结果证明：所提方法能够有效提取液压泵故障信号中的特征信息。     

基于统计分析的电火花线切割加工稳定性研究

研制了电火花线切割加工间隙放电状态检测系统,并运用时序分析理论中的统计检验的方法对加工中由正常放电相对时间比率值构成的时间序列进行了分析,指出了电火花线切割加工稳定时的正常放电相对时间比率值构成的时间序列的统计特征。提出用量纲一波形参数——峰度值（峭度系数）来判断电火花线切割加工的稳定性,用试验的方法研究了该方法的可靠性,为采取适当的电参数控制策略,提高加工稳定性提供了重要的依据。     

一种适用于任意峰度非高斯信号的多目标盲波束形成方法

该文提出了一种新的适用于任意峰度非高斯信号的多目标盲波束形成算法。该方法在最大峰度算法(KMA)的基础上,引入信号的互相关约束定义了一种新的代价函数。通过对该代价函数的最大化,来盲估计波束形成器的权向量,从而完成对多目标的分离和定向。由于波束形成过程不需要正交化处理,避免了波束形成器锁定噪声的可能性。同时,采用一种复数编码的遗传算法来求解权向量,不但可避免陷入局部极值的可能性,而且还能有效提高运行速度。仿真实验验证了该算法的有效性和正确性。     

Modelling time-varying higher moments with maximum entropy density

Since the introduction of the Autoregressive Conditional Heteroscedasticity (ARCH) model of Engle [R. Engle, Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation, Econometrica 50 (1982) 987–1007], the literature of modelling the conditional second moment has become increasingly popular in the last two decades. Many extensions and alternate models of the original ARCH have been proposed in the literature aiming to capture the dynamics of volatility more accurately. Interestingly, the Quasi Maximum Likelihood Estimator (QMLE) with normal density is typically used to estimate the parameters in these models. As such, the higher moments of the underlying distribution are assumed to be the same as those of the normal distribution. However, various studies reveal that the higher moments, such as skewness and kurtosis of the distribution of financial returns are not likely to be the same as the normal distribution, and in some cases, they are not even constant over time. These have significant implications in risk management, especially in the calculation of Value-at-Risk (VaR) which focuses on the negative quantile of the return distribution. Failed to accurately capture the shape of the negative quantile would produce inaccurate measure of risk, and subsequently lead to misleading decision in risk management. This paper proposes a solution to model the distribution of financial returns more accurately by introducing a general framework to model the distribution of financial returns using maximum entropy density (MED). The main advantage of MED is that it provides a general framework to estimate the distribution function directly based on a given set of data, and it provides a convenient framework to model higher order moments up to any arbitrary finite order k. However this flexibility comes with a high cost in computational time as k increases, therefore this paper proposes an alternative model that would reduce computation time substantially. Moreover, the sensitivity of the parameters in the MED with respect to the dynamic changes of moments is derived analytically. This result is important as it relates the dynamic structure of the moments to the parameters in the MED. The usefulness of this approach will be demonstrated using 5 min intra-daily returns of the Euro/USD exchange rate.     

SORPTION DRYING OF SOYBEAN SEEDS WITH SILICA GEL. I. HYDRODYNAMICS OF A FLUIDIZED BED DRYER

ABSTRACT

Fluidization technology has been employed to mix soybean seeds and silica gel particles in aim of sorption drying of particulate agricultural products. The characteristic fluidization velocities, mixing mechanisms and fluidization quality have been studied in a 180 mm I.D. fluidized bed. Two sizes of silica gel particles (SG2 and SG3) were selected, with the mass fractions in the range of 0.33–0.75 to form a static bed with height from 100 to 280 mm (H/D = 0.56–1.56). The results show that the dispersion rate of soybean seeds is increased with addition of either SG2 or SG3, and that the frequency and the span of pressure fluctuations within the bed are increased. It is inferred that the gas–solids contacting is improved with addition of small particles in the bed of large particles. In addition, for practical design and operation of such a fluidized bed of binary mixtures, empirical correlations for characteristic fluidization velocities were developed with a wide application.     

基于最优熵与EEMD的滚动轴承微故障诊断方法

滚动轴承是易损件,为了更好并及时检测出在信噪比低的情况下的轴承早期微故障振动信号,提出了小波包最优熵和EEMD相结合的方法。运用小波包最优熵对采集信号实现信噪分离,突出了小波包降噪效果明显;通过EEMD将信号分解成多个分量;最后以互相关、峭度准则提取故障信号分量以避免分量选择的盲目性。结果表明:该方法对轴承初期故障具有良好的降噪效果,可以准确快速地检测出轴承故障,从而表明该方法是有效且可行的。