In this article, a new censoring scheme is considered, namely, a middle part of a random sample is censored. A treatment for reconstructing the missing order statistics is investigated. The proposed procedure is studied in detail under exponential distribution which is widely used as a constant failure model in reliability.Different approaches are used to obtain point and interval reconstructors and then they are compared. A numerical example is presented for illustrating all the proposed inferential procedures. Eventually, we present some remarks including how the results of the paper can be used when the parameters of the exponential distribution are unknown.

The concept of generalized order statistics (GOSs) was introduced as a unified approach to a variety of models of ordered random variables. The purpose of this paper is to investigate conditions on the underlying distribution functions and the parameters on which GOSs are based, to establish Shaked-Shanthikumar multivariate dispersive ordering of GOSs from one sample and Khaledi-Kochar multivariate dispersive ordering of GOSs from two samples. Some applications are also given.

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A novel approach to surface electromyogram (sEMG) signal classification using its higher order statistics (HOS) is presented in this study. As the probability density function of the sEMG during isometric contraction in some cases is very close to the Gaussian distribution, it is frequently assumed to be Gaussian. As this assumption is not valid when the force is small, in this paper, we consider the non-Gaussian characteristics of the sEMG, and compute the second-, the third- and the fourth order statistics of the sEMG as its features. These features are used to classify four upper limb primitive motions, i.e., elbow flexion (EF), elbow extension (EE), forearm supination (FS), and forearm pronation (FP). We used the sequential forward selection (SFS) method to reduce the number of HOS features to a sufficient minimum while retaining their discriminatory information, and apply the Knearest neighbor method for classification. Our approach is robust against statistical variations in noise, and does not require additional computations compared to existing methods for providing high rates of correct classification of the sEMG, which makes it useful in devising real-time sEMG controlled prostheses.

In this paper‎, ‎order statistics and associated inferences are considered from Lindley distribution‎. ‎We derive the exact forms of means‎, ‎variances and covariances as well as the moment generating functions of order statistics‎. ‎These obtained forms allow us to compute the means‎, ‎variances‎, ‎and covariances of the order statistics for various values of the shape parameter‎. ‎These values are then used to compute the coefficients of the best linear unbiased estimators‎, ‎the best linear invariant estimators‎, ‎and the least square estimators of the location and scale parameters‎. ‎The variances and covariances of these estimators are also presented‎. ‎Using the best linear unbiased estimators and best linear invariant estimators we construct confidence intervals for the location and scale parameters through Monte Carlo simulations‎. ‎In addition‎, ‎based on the ordered data‎, ‎we investigate how to obtain the best linear unbiased predictor and the best linear invariant predictor for future order statistics‎. ‎Finally‎, ‎data analysis and Monte Carlo simulation have been performed for illustrative purposes and comparative studies‎, ‎respectively.

Nair and Rajesh (2000) introduced the geometric vitality function, which explains the failure pattern of components or systems based on the component's geometric mean of the remaining lifetime. Recently quantile-based studies have found greater interest among researchers as an alternative method of measuring the uncertainty of a random variable. The quantile-based measures possess some unique properties to the distribution function approach. The present paper introduces a quantile-based past geometric vitality function of order statistics and its properties. Finally, we provide an application for the new measure based on some distributions which are useful in lifetime data analysis.