Order statistic

We study properties of the mean residual life functions of finite mixtures. Specifically, we study ordering properties, monotonicity and the limiting behaviour. We show, under some mild conditions, that the limiting behaviour is similar to that of the strongest member (in the mean residual life order) of the mixture. We also consider the case of negative mixtures (i.e., mixtures with some negative coefficients) which is applied to study the behaviour of the mean residual life of order statistics and coherent systems with possibly dependent components.

Using the recently developed single molecule force-clamp technique we quantitatively measure the kinetics of conformational changes of polyprotein molecules at a constant force. In response to an applied force of 110 pN, we measure the dwell times of 1647 unfolding events of individual ubiquitin modules within each protein chain. We then establish a rigorous method for analyzing force-clamp data using order statistics. This allows us to test the success of an history independent, two-state model in describing the kinetics of the unfolding process. We find that the average unfolding trajectory is independent of the number of protein modules N in each trajectory, which varies between 3 and 12 (the engineered protein length), suggesting that the unfolding events in each chain are uncorrelated. We then derive a binomial distribution of dwell times to describe the stochastic dynamics of protein unfolding. This distribution successfully describes 81 % of the data with a single rate consta...

When sample observations are expensive or difficult to obtain, ranked set sampling is known to be an efficient method for estimating the population mean, and in particular to improve on the sample mean estimator. Using best linear unbiased estimators, this paper considers the simple linear regression model with replicated observations. Use of a form of ranked set sampling is shown to be markedly more efficient for normal data when compared with the traditional simple linear regression estimators.

In this paper, a class of probability models for ranking data, the order-statistics models, is investigated. We extend the usual normal order-statistics model into one where the underlying random variables follow a multivariate normal distribution. Bayesian approach and the Gibbs sampling technique are used for parameter estimation. In addition, methods to assess the adequacy of model fit are introduced. Robustness of the model is studied by considering a multivariate-t distribution. The proposed method is applied to analyze the presidential election data of the American Psychological Association (APA).

This paper is devoted to the analysis of the estimation of the mean of a sensitive variable. The use of a randomized response (RR) procedure gives confidence to the interviewed that his privacy is protected. We consider that a simple random sampling with replacement design is used for selecting a sample. The behavior of the RR procedure, when ranked set sampling is the design used, is developed under three different ranking criteria. The usual gain in accuracy associated with the use of ranked set sampling is exhibited only by one of the designs. The behavior of the models is illustrated using data provided by a study of samples of persons infected with AIDS.

Over the last ten years blind source separation (BSS) has become a prominent processing tool in the study of human electroencephalography (EEG). Without relying on head modeling BSS aims at estimating both the waveform and the scalp spatial pattern of the intracranial dipolar current responsible of the observed EEG. In this review we begin by placing the BSS linear instantaneous model of EEG within the framework of brain volume conduction theory. We then review the concept and current practice of BSS based on second-order statistics (SOS) and on higher-order statistics (HOS), the latter better known as independent component analysis (ICA). Using neurophysiological knowledge we consider the fitness of SOS-based and HOS-based methods for the extraction of spontaneous and induced EEG and their separation from extra-cranial artifacts. We then illustrate a general BSS scheme operating in the time-frequency domain using SOS only. The scheme readily extends to further data expansions in order to capture experimental source of variations as well. A simple and efficient implementation based on the approximate joint diagonalization of Fourier cospectral matrices is described (AJDC). We conclude discussing useful aspects of BSS analysis of EEG, including its assumptions and limitations.

A novel technique for the detection of nonstationary bioacoustic signals, such as explosive lung and bowel sounds, in clinical auscultative recordings is presented. The technique uses kurtosis (zero-lag fourth-order statistics) to form an iterative kurtosis-based detector (IKD). The IKD iteratively detects important peaks of the kurtosis, estimated within a sliding window along the signal under investigation, which indicate the presence of non-Gaussianity in the raw signal. The efficiency of the IKD has been illustrated by experimental results that demonstrate its ability to clearly detect bioacoustic signals of diagnostic interest in the presence of background signal with high amplitude.

We propose a new distribution, the so-called beta-Weibull geometric distribution, whose failure rate function can be decreasing, increasing or an upside-down bathtub. This distribution contains special sub-models the exponential geometric [K. Adamidis and S. Loukas, A lifetime distribution with decreasing failure rate, Statist. Probab. Lett. 39 (1998), pp. 35–42], beta exponential [S. Nadarajah and S. Kotz, The exponentiated type distributions, Acta Appl. Math. 92 (2006), pp. 97–111; The beta exponential distribution, Reliab. Eng. Syst. Saf. 91 (2006), pp. 689–697], Weibull geometric [W. Barreto-Souza, A.L. de Morais, and G.M. Cordeiro, The Weibull-geometric distribution, J. Stat. Comput. Simul. 81 (2011), pp. 645–657], generalized exponential geometric [R.B. Silva, W. Barreto-Souza, and G.M. Cordeiro, A new distribution with decreasing, increasing and upside-down bathtub failure rate, Comput. Statist. Data Anal. 54 (2010), pp. 935–944; G.O. Silva, E.M.M. Ortega, and G.M. Cordeiro, The beta modified Weibull distribution, Lifetime Data Anal. 16 (2010), pp. 409–430] and beta Weibull [S. Nadarajah, G.M. Cordeiro, and E.M.M. Ortega, General results for the Kumaraswamy-G distribution, J. Stat. Comput. Simul. (2011). DOI: 10.1080/00949655.2011.562504] distributions, among others. The density function can be expressed as a mixture of Weibull density functions. We derive expansions for the moments, generating function, mean deviations and Rénvy entropy. The parameters of the proposed model are estimated by maximum likelihood. The model fitting using envelops was conducted. The proposed distribution gives a good fit to the ozone level data in New York.

Within the last two decades a small group of researchers has built a useful, nontrivial theory of nonlinear signal processing around the median-related filters known as rank-order filters, order-statistic filters, weighted median filters, and stack filters. This required significant effort to overcome the bias, both in education and research, toward linear theory, which has been dominant since the days of Fourier, Laplace, and “Convolute.” We trace the development of this theory of nonlinear filtering from its beginnings in the study of noise-removal properties and structural behavior of the median filter to the recently developed theory of optimal stack filtering. The theory of stack filtering provides a point of view which unifies many different filter classes, including morphological filters, so it is discussed in detail. Of particular importance is the way this theory has brought together, in a single analytical framework, both the estimation-based and the structural-based approaches to the design of these filters. Some recent applications of median and stack filters are provided to demonstrate the effectiveness of this approach to nonlinear filtering. They include: the design of an optimal stack filter for image restoration; the use of vector median filters to attenuate impulsive noise in color images and to eliminate cross luminance and cross color in TV images; and the use of median-based filters for image sequence coding, reconstruction, and scan rate conversion in normal TV and HDTV systems.