Order Statistics of Additive Uniform Exponential Distribution

In this paper we investigated the order statistics by using Additive Uniform Exponential Distribution (AUED) proposed by Venkata Subbarao Uppu (2010).The probability density functions of rth order Statistics, lth moment of the rth order Statistic, minimum, maximum order statistics, mean of the maximum and minimum order statistics, the joint density function of two order statistics were calculated and discussed in detailed . Applications and several aspects were discussed Keywords: Additive Uniform Exponential Distribution, Moments, Minimum order statistic, Maximum order statistic, Joint density of the order Statistics, complete length of service.

Comprehensive Analysis of Edge Detection in Color Image Processing

Various approaches to edge detection for color images, including techniques extended from monochrome edge detection as well as vector space approaches, are examined. In particular, edge detection techniques based on vector order statistic operators and difference vector operators are studied in detail. Numerous edge detectors are obtained as special cases of these two classes of operators. The effect of distance measures on the performance of different color edge detectors is studied by employing distance measures other than the Euclidean norm. Variations are introduced to both the vector order statistic opera-tors and the difference vector operators to improve noise performance. They both demonstrate the ability to attenuate noise with added algorithm complexity. Among them, the difference vector operator with adaptive filtering shows the most promising results. Other vector directional filtering techniques are also introduced and utilized for color edge detection. Both quantitative and subjective tests are performed in evaluating the performance of the edge detectors, and a detailed comparison is presented.<div>Copyright 1999 Society of Photo‑Optical Instrumentation Engineers (SPIE). One print or electronic copy may be made for personal use only. Systematic reproduction and distribution, duplication of any material in this publication for a fee or for commercial purposes, and modification of the contents of the publication are prohibited.<br></div><div><br></div>

Higher Order Moments of the Order Statistics for the Rectangular, Exponential, Gamma and Weibull Distributions

In this paper we discuss the problem of Higher Order Moments for the order Statistics for the Rectangular, Exponential, Gamma and Weibull distributions by finding the order statistic distributions for the base distribution and modified distributions, the base distribution is to deduce the corresponding distribution by the polynomial modifier. These higher order moments are very much useful in most of the Data sciences and Image analysis.

Identify Informative Bands for Hyperspectral Target Detection Using the Third-Order Statistic

Constrained energy minimization (CEM) has been proposed and widely researched in the field of hyperspectral target detection. Generally, it selects one of the target spectra as the representative and then keeps its output constant while minimizing the average filter output energy of the data. However, it has been proven that as the number of bands (L) increases, CEM will gradually lower the average filter output energy when keeping the representative’s output constant. Unavoidably, due to the inherent spatial and temporal variation of the spectra, this will lead to an unreasonable phenomenon, i.e., if L is particularly large, when adding more bands, CEM will suppress more and more pixels, even including the target pixels. This means that the optimal solution of CEM may not correspond to the target detection result that we desire. To deal with this, in this paper, we introduce the third-order statistic (skewness) of the CEM model, served as an auxiliary index to determine whether a band is beneficial to target detection or not. Theoretically, we prove that the skewness index can always exclude the noisy bands with Gaussian distribution. In addition, experiments on several widely used remote sensing data indicate that the index can also efficiently identify informative bands for a better target detection performance.

A Note on the Accuracy of Normal Approximation of Random Quantities

For a sequence of independent, identically distributed random variable (iid rv's) [Formula: see text] and a sequence of integer-valued random variables [Formula: see text], define the random quantiles as [Formula: see text], where [Formula: see text] denote the largest integer less than or equal to [Formula: see text], and [Formula: see text] the [Formula: see text]th order statistic in a sample [Formula: see text] and [Formula: see text]. In this note, the limiting distribution and its exact order approximation are obtained for [Formula: see text]. The limiting distribution result we obtain extends the work of several including Wretman[Formula: see text]. The exact order of normal approximation generalizes the fixed sample size results of Reiss[Formula: see text]. AMS 2000 subject classification: 60F12; 60F05; 62G30.

Modeling and Exact Reliability for a Consecutive Linear (k1,k2,…,kn−r+1)-Out-of-r-from-n: F System and Consecutive Circular (k1,k2,…,kn)-Out-of-r-from-n: F System

The consecutive linear [Formula: see text]-out-of-[Formula: see text]-from-[Formula: see text]:F system consists of [Formula: see text] linear ordered components and the consecutive circular [Formula: see text]-out-of-[Formula: see text]-from-[Formula: see text]:F system consists of [Formula: see text] circular ordered components. In this paper, we suggest, for the first time, modeling and exact reliability for these models. The linear system fails if and only if there exists a [Formula: see text]-order statistic of [Formula: see text]-consecutive [Formula: see text] [Formula: see text] of components in the failed state, [Formula: see text], [Formula: see text]; and the circular system fails if and only if there exists a [Formula: see text]-order statistic of [Formula: see text]-consecutive [Formula: see text] [Formula: see text] of components in the failed state, [Formula: see text], [Formula: see text]. In this paper, we designed an innovative algorithm to obtain the exact reliability for an extensive class of consecutive linear and circular systems. In continuation, there are the MATLAB Programs of exact reliability for consecutive linear and circular systems. In the following, we applied comparative and numerical results and calculated the exact reliability of this strategic systems. Finally, we calculated the exact reliability for two real-world practical examples.