Stochastic comparisons of series and parallel systems with heterogeneous components

In this paper, we discuss stochastic comparisons of parallel systems with independent heterogeneous exponentiated Nadarajah-Haghighi (ENH) components in terms of the usual stochastic order, dispersive order, convex transform order and the likelihood ratio order. In the presence of the Archimedean copula, we study stochastic comparison of series dependent systems in terms of the usual stochastic order.Comment: arXiv admin note: text overlap with arXiv:1704.0365

Stochastic ordering results in parallel and series systems with Gumble distributed random variables

The stochastic comparisons of parallel and series system are worthy of study. In this paper, we present some stochastic comparisons of parallel and series systems having independent components from Gumble distribution with two parameters (one location and one shape). Here, we first put a condition for the likelihood ratio ordering of the parallel systems and second we use the concept of vector majorization technique to compare the systems by the reversed hazard rate ordering, the hazard rate ordering, the dispersive ordering, and the less uncertainty ordering with respect to the location parameter.Comment: 11 page

Ordering properties of the smallest order statistic from Weibull G random variables

In this paper we compare the minimums of two heterogeneous samples each following Weibull-G distribution under three scenarios. In the Fifirst scenario, the units of the samples are assumed to be independently distributed and the comparisons are carried out through vector majorization. The minimums of the samples are compared in the second scenario when the independent units of the samples also experience random shocks. The last scenario describes the comparison when the units have a dependent structure sharing Archimedean copula

A new notion of majorization with applications to the comparison of extreme order statistics

In this paper, we use a new partial order, called the f-majorization order. The new order includes as special cases the majorization , the reciprocal majorization and the p-larger orders. We provide a comprehensive account of the mathematical properties of the f-majorization order and give applications of this order in the context of stochastic comparison for extreme order statistics of independent samples following the Frechet distribution and scale model. We discuss stochastic comparisons of series systems with independent heterogeneous exponentiated scale components in terms of the usual stochastic order and the hazard rate order. We also derive new result on the usual stochastic order for the largest order statistics of samples having exponentiated scale marginals and Archimedean copula structure

Some ordering properties of highest and lowest order statistics with exponentiated Gumble type-II distributed components

In this paper, we have studied the stochastic comparisons of the highest and lowest order statistics of exponentiated Gumble type-II distribution with three parameters. We have compared both the statistics by using three different stochastic ordering. First, we consider a system with different scale and outer shape parameters and then we study the usual stochastic ordering of the lowest and highest order statistics in the sense of multivariate chain majorization. In addition, we construct two examples to support our results. Second, by using the vector majorization technique, we study the usual stochastic ordering, the reversed failure rate ordering and the likelihood ratio ordering with respect to different outer shape parameters, next, by varying the inner shape parameter, we discuss the usual stochastic order of the lowest order statistics and we have shown that the highest order statistics are not comparable in the usual stochastic ordering by an example.Comment: 16 pages, 1 figure

Univariate and Bivariate Geometric Discrete Generalized Exponential Distributions

Marshall and Olkin (1997, Biometrika, 84, 641 - 652) introduced a very powerful method to introduce an additional parameter to a class of continuous distribution functions and hence it brings more flexibility to the model. They have demonstrated their method for the exponential and Weibull classes. In the same paper they have briefly indicated regarding its bivariate extension. The main aim of this paper is to introduce the same method, for the first time, to the class of discrete generalized exponential distributions both for the univariate and bivariate cases. We investigate several properties of the proposed univariate and bivariate classes. The univariate class has three parameters, whereas the bivariate class has five parameters. It is observed that depending on the parameter values the univariate class can be both zero inflated as well as heavy tailed. We propose to use EM algorithm to estimate the unknown parameters. Small simulation experiments have been performed to see the effectiveness of the proposed EM algorithm, and a bivariate data set has been analyzed and it is observed that the proposed models and the EM algorithm work quite well in practice.Comment: arXiv admin note: text overlap with arXiv:1701.0356

Stochastic Comparisons of Lifetimes of Two Series and Parallel Systems with Location-Scale Family Distributed Components having Archimedean Copulas

In this paper, we compare the lifetimes of two series and two parallel systems stochastically where the lifetime of each component follows location-scale (LS) family of distributions. The comparison is carried out under two scenarios: one, that the components of the systems have a dependent structure sharing Archimedean copula and two, that the components are independently distributed. It is shown that the systems with components in series or parallel sharing Archimedean copula with more dispersion in the location or scale parameters results in better performance in the sense of the usual stochastic order. It is also shown that if the components are independently distributed, it is possible to obtain more generalized results as compared to the dependent set-up. The results in this paper generalizes similar results in both independent and dependent set up for exponential and Weibull distributed components

Usual stochastic ordering results for series and parallel systems with components having Exponentiated Chen distribution

In this paper, we have discussed the usual stochastic ordering relations between two systems. Each system consists of n mutually independent components. The components follow Exponentiated (Extended) Chen distribution with three parameters $\alpha, \beta, \lambda$. Two popular systems are taken into consideration, one is the series system and another is the parallel system. The results in this paper are obtained by varying one parameter and the other parameters are kept constant. The hazard rate ordering or reversed hazard rate ordering relations that are not possible for series or parallel systems have been demonstrated with the help of counterexamples.Comment: 10 pages, 2 figure

A stochastic comparison study for the smallest and largest ordered statistic from Weibull-G and Gompertz Makeham distribution

In this paper, we have discussed the stochastic comparison of the smallest and largest ordered statistic from independent heterogeneous Weibull-G random variables and Gompertz Makeham random variables. We compare systems arising from taking different model parameters and obtain stochastic ordering results under the condition of multivariate chain majorization. Using the notion of vector majorization, we compare different systems and obtain stochastic ordering results.Comment: 16 pages, 2 figur

Optical Communication in Space: Challenges and Mitigation Techniques

In recent years, free space optical communication has gained significant importance owing to its unique features: large bandwidth, license-free spectrum, high data rate, easy and quick deployability, less power and low mass requirements. FSO communication uses the optical carrier in the near infrared band to establish either terrestrial links within the Earth's atmosphere or inter-satellite or deep space links or ground-to-satellite or satellite-to-ground links. However, despite the great potential of FSO communication, its performance is limited by the adverse effects viz., absorption, scattering, and turbulence of the atmospheric channel. This paper presents a comprehensive survey on various challenges faced by FSO communication system for ground-to-satellite or satellite-to-ground and inter-satellite links. It also provides details of various performance mitigation techniques in order to have high link availability and reliability. The first part of the paper will focus on various types of impairments that pose a serious challenge to the performance of optical communication system for ground-to-satellite or satellite-to-ground and inter-satellite links. The latter part of the paper will provide the reader with an exhaustive review of various techniques both at physical layer as well as at the other layers i.e., link, network or transport layer to combat the adverse effects of the atmosphere. It also uniquely presents a recently developed technique using orbital angular momentum for utilizing the high capacity advantage of the optical carrier in case of space-based and near-Earth optical communication links. This survey provides the reader with comprehensive details on the use of space-based optical backhaul links in order to provide high-capacity and low-cost backhaul solutions.Comment: 41 pages, 13 Figures and 8 Tables. arXiv admin note: substantial text overlap with arXiv:1506.0483