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Articles 1 - 11 of 11
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.
Stochastic Order Relations Among Parallel Systems From Weibull Distributions, Nuria Torrado, Subhash C. Kochar
Stochastic Order Relations Among Parallel Systems From Weibull Distributions, Nuria Torrado, Subhash C. Kochar
Mathematics and Statistics Faculty Publications and Presentations
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.
Some New Applications Of P-P Plots, Isha Dewan, Subhash C. Kochar
Some New Applications Of P-P Plots, Isha Dewan, Subhash C. Kochar
Mathematics and Statistics Faculty Publications and Presentations
The P-P plot is a powerful graphical tool to compare stochastically the magnitudes of two random variables. In this note, we introduce a new partial order, called P?P order based on P-P plots. For a pair of random variables (X 1, Y1) and (X 2, Y 2) one can see the relative precedence of Y 2 over X 2 versus that of Y 1 over X 1 using P-P order. We show that several seemingly very technical and difficult concepts like convex transform order and super-additive ordering can be easily explained with the …
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].
On Residual Lifetimes Of K-Out-Of-N Systems With Nonidentical Components, Subhash C. Kochar, Maochao Xu
On Residual Lifetimes Of K-Out-Of-N Systems With Nonidentical Components, Subhash C. Kochar, Maochao Xu
Mathematics and Statistics Faculty Publications and Presentations
In this article, mixture representations of survival functions of residual lifetimes of k-out-of-n systems are obtained when the components are independent but not necessarily identically distributed. Then we stochastically compare the residual lifetimes of k-out-of-n systems in one- and two-sample problems. In particular, the results extend some results in Li and Zhao [14], Khaledi and Shaked [13], Sadegh [17], Gurler and Bairamov [7] and Navarro, Balakrishnan, and Samaniego [16]. Applications in the proportional hazard rates model are presented as well.
Correction To "Stochastic Comparisons Of Parallel Systems When Components Have Proportional Hazard Rates", Subhash C. Kochar, Maochao Xu
Correction To "Stochastic Comparisons Of Parallel Systems When Components Have Proportional Hazard Rates", Subhash C. Kochar, Maochao Xu
Mathematics and Statistics Faculty Publications and Presentations
In the article "Stochastic comparisons of parallel systems when component have proportional hazard rates" we found a gap in the middle of the proof of Theorem 3.2. Therefore, we do not know whether Theorem 3.2 is true for the reverse hazard rate order. However, we could prove the following weaker result for the stochastic order.
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 …
Some Recent Results On Stochastic Comparisons And Dependence Among Order Statistics In The Case Of Phr Model, Subhash C. Kochar, Maochao Xu
Some Recent Results On Stochastic Comparisons And Dependence Among Order Statistics In The Case Of Phr Model, Subhash C. Kochar, Maochao Xu
Mathematics and Statistics Faculty Publications and Presentations
This paper reviews some recent results on stochastic orders and dependence among order statistics when the observations are independent and follow the proportional hazard rates model.
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, …