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Full-Text Articles in Physical Sciences and Mathematics
Stochastic Comparisons Of Weighted Sums Of Arrangement Increasing Random Variables, Xiaoqing Pan, Min Yuan, Subhash C. Kochar
Stochastic Comparisons Of Weighted Sums Of Arrangement Increasing Random Variables, Xiaoqing Pan, Min Yuan, Subhash C. Kochar
Mathematics and Statistics Faculty Publications and Presentations
Assuming that the joint density of random variables X1,X2, . . . ,Xn is arrangement increasing (AI), we obtain some stochastic comparison results on weighted sums of Xi’s under some additional conditions. An application to optimal capital allocation is also given.
An Analysis Of The Practical Dpg Method, Jay Gopalakrishnan, Weifeng Qiu
An Analysis Of The Practical Dpg Method, Jay Gopalakrishnan, Weifeng Qiu
Mathematics and Statistics Faculty Publications and Presentations
We give a complete error analysis of the Discontinuous Petrov Galerkin (DPG) method, accounting for all the approximations made in its practical implementation. Specifically, we consider the DPG method that uses a trial space consisting of polynomials of degree p on each mesh element. Earlier works showed that there is a "trial-to-test" operator T, which when applied to the trial space, defines a test space that guarantees stability. In DPG formulations, this operator T is local: it can be applied element-by-element. However, an infinite dimensional problem on each mesh element needed to be solved to apply T. In practical computations, …
Some Unified Results On Comparing Linear Combinations Of Independent Gamma Random Variables, Subhash C. Kochar, Maochao Xu
Some Unified Results On Comparing Linear Combinations Of Independent Gamma Random Variables, Subhash C. Kochar, Maochao Xu
Mathematics and Statistics Faculty Publications and Presentations
In this paper, a new sufficient condition for comparing linear combinations of independent gamma random variables according to star ordering is given. This unifies some of the newly proved results on this problem. Equivalent characterizations between various stochastic orders are established by utilizing the new condition. The main results in this paper generalize and unify several results in the literature including those of Amiri, Khaledi, and Samaniego [2], Zhao [18], and Kochar and Xu [9].
Stochastic Comparisons Of Order Statistics And Spacings: A Review, Subhash C. Kochar
Stochastic Comparisons Of Order Statistics And Spacings: A Review, Subhash C. Kochar
Mathematics and Statistics Faculty Publications and Presentations
We review some of the recent developments in the area of stochastic comparisons of order statistics and sample spacings. We consider the cases when the parent observations are identically as well as nonidentically distributed. But most of the time we will be assuming that the observations are independent. The case of independent exponentials with unequal scale parameters as well as the proportional hazard rate model is discussed in detail.
A Projection-Based Error Analysis Of Hdg Methods, Jay Gopalakrishnan, Bernardo Cockburn, Francisco-Javier Sayas
A Projection-Based Error Analysis Of Hdg Methods, Jay Gopalakrishnan, Bernardo Cockburn, Francisco-Javier Sayas
Mathematics and Statistics Faculty Publications and Presentations
We introduce a new technique for the error analysis of hybridizable discontinuous Galerkin (HDG) methods. The technique relies on the use of a new projection whose design is inspired by the form of the numerical traces of the methods. This renders the analysis of the projections of the discretization errors simple and concise. By showing that these projections of the errors are bounded in terms of the distance between the solution and its projection, our studies of influence of the stabilization parameter are reduced to local analyses of approximation by the projection. We illustrate the technique on a specific HDG …
Stochastic Comparisons Of Parallel Systems When Component Have Proportional Hazard Rates, Subhash C. Kochar, Maochao Xu
Stochastic Comparisons Of Parallel Systems When Component Have Proportional Hazard Rates, Subhash C. Kochar, Maochao Xu
Mathematics and Statistics Faculty Publications and Presentations
Let Χ1, … Χn be independent random variables with Χᵢ having survival function Fλᵢ, i=1, … , n, and let Y₁, … , Yn be a random sample with common population survival distribution Fλ, where λ = Σᵢ=₁nλᵢl n. Let Χn:n and Yn:n denote the lifetimes of the parallel systems consisting of these components, respectively. It is shown that Xn:n is greater than Yn:n in terms of likelihood ratio order. It is also proved that the sample range Χn:n - Χ₁:n is larger than Yn n:n - Y₁:n according to reverse hazard rate ordering. These two results …
Correction To "Dependence, Dispersiveness, And Multivariate Hazard Rate Ordering", Baha-Eldin Khaledi, Subhash C. Kochar
Correction To "Dependence, Dispersiveness, And Multivariate Hazard Rate Ordering", Baha-Eldin Khaledi, Subhash C. Kochar
Mathematics and Statistics Faculty Publications and Presentations
In the article published last year, three inequalities should be in the opposite direction.
Stochastic Properties Of Spacings In A Single-Outlier Exponential Model, Baha-Eldin Khaledi, Subhash C. Kochar
Stochastic Properties Of Spacings In A Single-Outlier Exponential Model, Baha-Eldin Khaledi, Subhash C. Kochar
Mathematics and Statistics Faculty Publications and Presentations
Let X1,..., Xn be independent exponential random variables with possibly different scale parameters. Kochar and Korwar [J. Multivar. Anal. 57 (1996)] conjectured that, in this case, the successive normalized spacings are increasing according to hazard rate ordering. In this article, we prove this conjecture in the case of a single-outlier exponential model when all except one of the parameters are identical. We also prove that the spacings are more dispersed and larger in the sense of hazard rate ordering when the vector of scale parameters is more dispersed in the sense of majorization.
Dependence Among Spacings, Baha-Eldin Khaledi, Subhash C. Kochar
Dependence Among Spacings, Baha-Eldin Khaledi, Subhash C. Kochar
Mathematics and Statistics Faculty Publications and Presentations
In this paper, we study the dependence properties of spacings. It is proved that if X1,..., Xn are exchangeable random variables which are TP2 in pairs and their joint density is log-convex in each argument, then the spacings are MTP2 dependent. Next, we consider the case of independent but nonhomogeneous exponential random variables. It is shown that in this case, in general, the spacings are not MTP2 dependent. However, in the case of a single outlier when all except one parameters are equal, the spacings are shown to be MTP2 dependent and, hence, …
Estimation Of A Monotone Mean Residual Life, Subhash C. Kochar, Hari Mukerjee, Francisco J. Samaniego
Estimation Of A Monotone Mean Residual Life, Subhash C. Kochar, Hari Mukerjee, Francisco J. Samaniego
Mathematics and Statistics Faculty Publications and Presentations
In survival analysis and in the analysis of life tables an important biometric function of interest is the life expectancy at age x,M(x), defined by M(x)=E[X?x|X>x], where X is a lifetime. M is called the mean residual life function. In many applications it is reasonable to assume that M is decreasing (DMRL) or increasing (IMRL); we write decreasing (increasing) for nonincreasing (non-decreasing). There is some literature on empirical estimators of M and their properties. Although tests for a monotone M are discussed in the literature, we are not aware of any estimators of M under these order restrictions. In …