Stochastic order relations among parallel systems from Weibull distributions

In this article, we focus on stochastic orders to compare the magnitudes of two parallel systems from Weibull distributions when one set of scale parameters majorizes the other. The new results obtained here extend some of those proved by Dykstra et al. (1997) and Joo and Mi (2010) from exponential to Weibull distributions. Also, we present some results for parallel systems from multiple-outlier Weibull models.Comment: 14 pages, 3 figures. Journal of Applied Probability (2015

On stochastic comparisons of largest order statistics in the scale model

Let $X_{\lambda _{1}},X_{\lambda _{2}},\ldots ,X_{\lambda _{n}}$ be independent nonnegative random variables with $X_{\lambda _{i}}\sim F(\lambda _{i}t)$, $i=1,\ldots ,n$, where $\lambda _{i}>0$, $i=1,\ldots ,n$ and $F$ is an absolutely continuous distribution. It is shown that, under some conditions, one largest order statistic $X_{n:n}^{\lambda }$ is smaller than another one $X_{n:n}^{\theta }$ according to likelihood ratio ordering. Furthermore, we apply these results when $F$ is a generalized gamma distribution which includes Weibull, gamma and exponential random variables as special cases

Order restricted inference for comparing the cumulative incidence of a competing risk over several populations

There is a substantial literature on testing for the equality of the cumulative incidence functions associated with one specific cause in a competing risks setting across several populations against specific or all alternatives. In this paper we propose an asymptotically distribution-free test when the alternative is that the incidence functions are linearly ordered, but not equal. The motivation stems from the fact that in many examples such a linear ordering seems reasonable intuitively and is borne out generally from empirical observations. These tests are more powerful when the ordering is justified. We also provide estimators of the incidence functions under this ordering constraint, derive their asymptotic properties for statistical inference purposes, and show improvements over the unrestricted estimators when the order restriction holds.Comment: Published in at http://dx.doi.org/10.1214/193940307000000040 the IMS Collections (http://www.imstat.org/publications/imscollections.htm) by the Institute of Mathematical Statistics (http://www.imstat.org

A characterization of the multivariate excess wealth ordering

In this paper, some new properties of the upper-corrected orthant of a random vector are proved. The univariate right-spread or excess wealth function, introduced by Fernández-Ponce et al. (1996), is extended to multivariate random vectors, and some properties of this multivariate function are studied. Later, this function was used to define the excess wealth ordering by Shaked and Shanthikumar (1998) and Fernández-Ponce et al. (1998). The multivariate excess wealth function enable us to define a new stochastic comparison which is weaker than the multivariate dispersion orderings. Also, some properties relating the multivariate excess wealth order with stochastic dependence are describe

Teachers' Perceptions on Adaptation of Sunrise Coursebook at Sulaymaniyah Governorate in Kurdistan Region of Iraq

This study aimed to determine if teachers employ any adaptations during their classes, and if so, what kind of adaptations are employed and how these are employed. This study sought to determine if adaptations are employed in correct and authentic ways.For this study, a qualitative method was used. The tool used in this study was a semi-structured interview. The questions of the semi-structured interview were adapted from Nguyen (2015). The study cohort was made up of teachers who were using or had used the Sunrise course books (levels 7, 8, and 9) in their teaching in the Sulaymaniyah Governorate in the Kurdistan Region of Iraq (KRI). The findings of this study showed that all the teachers employ adaptations in the classroom but to different degrees; some of them use only 1 or 2 types of adaptations because of the limited time they have available in their classes, whereas others apply most of the types of adaptations. Finally, the results showed that there is a positive relationship between experience and adaptation, with those teachers who had more experience employing more methods of adaptations during their classes

Fluorescence spectroscopy for the characterization of humic and fulvic acids and their disinfection by-products formation potential

Natural Organic Matter (NOM) plays a major role in the formation of undesirable organic by-products following disinfection/oxidation of drinking water. It is suspected that most precursors to disinfection by-products (DBPs) are humic although non-humic substances have not been studied and are suspected of also contributing to DBPs. NOM reacts with many of the disinfectants used to treat drinking water, such as chlorine, chioramine, and ozone, to form a variety of DBPs. Many of these DBPs have adverse health effects in humans (i.e. carcinogenic or mutagenic effects). The primary DBPs of concern include the trihalomethanes (THMs), haloacetic acids (HAAs), and haloacetonitrile (HANs). The Spectral Fluorescent Signatures (SFS) technique was developed for the identification of the humic acids (HA), fihlvic acids (FA) and non-humic substances by fluorescence. The SFS is the total sum of emission spectra of a sample at different excitation wavelengths, recorded as a matrix of fluorescent intensity in coordinates of excitation and emission wavelengths, in a definite spectral window. For the characterization of NOM in raw water, and determination of DBP formation reactivities, samples were prepared using river HA and FA, soil HA and FA and peat HA and FA in varying concentrations from 0.5 to 10 ppm. UV-2 54, TOC, DBP formation potential, SF5 tests were conducted on each matrix of samples

A Review of Factors Affecting Consumer Behavior towards Online Shopping

Online shopping is a form of electronic commerce which allows consumers to directly buy goods or services from a seller over the Internet using a web browser. Online shopping provides a good example of business revolution. E-commerce has made life Simple and innovative of individual and groups. Consumer behavior on online shopping is different from physical market where he/she has access to see the products online shopping sites are fast replacing traditional or physical shops. Over, the years the trust of the customers for online shopping sites has increased considerably. The increase in the number of these sites on one hand has led to a fierce competition which means better and cheaper products for customers. However, at the same time customers have their privacy concerns when it comes to shopping online. Internet is changing the way consumers shop and buy goods and services and has rapidly evolved into a global phenomenon. The technology oriented factors like guaranteed quality, cash on delivery discounts and promotions are the major specific factors influencing customer’s attitudes toward online shopping. This research paper attempts to analyze the consumer behavior towards online shopping and the various factors influencing trend of online shopping