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Journal articles on the topic 'Stochastic orders'

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Published: 4 June 2021
Last updated: 11 March 2023

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1

Gollier, Christian. "Variance stochastic orders." Journal of Mathematical Economics 80 (January 2019): 1–8. http://dx.doi.org/10.1016/j.jmateco.2018.10.003.

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2

Horan, Sean. "Stochastic semi-orders." Journal of Economic Theory 192 (March 2021): 105171. http://dx.doi.org/10.1016/j.jet.2020.105171.

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3

Shaked, Moshe, Miguel A. Sordo, and Alfonso Suárez-Llorens. "Global Dependence Stochastic Orders." Methodology and Computing in Applied Probability 14, no. 3 (September 24, 2011): 617–48. http://dx.doi.org/10.1007/s11009-011-9253-8.

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4

López-Díaz, María Concepción, Miguel López-Díaz, and Sergio Martínez-Fernández. "On stochastic orders defined by other stochastic orders and transformations of probabilities." Mathematical Inequalities & Applications, no. 4 (2022): 925–39. http://dx.doi.org/10.7153/mia-2022-25-59.

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5

López-Díaz, María Concepción, Miguel López-Díaz, and Sergio Martínez-Fernández. "Directional Stochastic Orders with an Application to Financial Mathematics." Mathematics 9, no. 4 (February 14, 2021): 380. http://dx.doi.org/10.3390/math9040380.

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Relevant integral stochastic orders share a common mathematical model, they are defined by generators which are made up of increasing functions on appropriate directions. Motivated by the aim to provide a unified study of those orders, we introduce a new class of integral stochastic orders whose generators are composed of functions that are increasing on the directions of a finite number of vectors. These orders will be called directional stochastic orders. Such stochastic orders are studied in depth. In that analysis, the conical combinations of vectors in those finite subsets play a relevant role. It is proved that directional stochastic orders are generated by non-stochastic pre-orders and the class of their preserving mappings. Geometrical characterizations of directional stochastic orders are developed. Those characterizations depend on the existence of non-trivial subspaces contained in the set of conical combinations. An application of directional stochastic orders to the field of financial mathematics is developed, namely, to the comparison of investments with random cash flows.
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6

FERNÁNDEZ, F. R., J. PUERTO, and M. J. ZAFRA. "CORES OF STOCHASTIC COOPERATIVE GAMES WITH STOCHASTIC ORDERS." International Game Theory Review 04, no. 03 (September 2002): 265–80. http://dx.doi.org/10.1142/s0219198902000690.

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In this paper we analyze cooperative games where the worth of a coalition is uncertain and the players only know their probability distribution. The novelty of our analysis is that the comparison among the uncertain values is done by stochastic orders among random variables. Thus, the classical concepts in cooperative game theory have to be revisited and redefined. This form of comparison leads to two-different notions of core. Conditions are given under which these cores are nonempty. The results are applied on three families of stochastic games.
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7

Bartoszewicz, Jarosław. "Dispersive functions and stochastic orders." Applicationes Mathematicae 24, no. 4 (1997): 429–44. http://dx.doi.org/10.4064/am-24-4-429-444.

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8

Colangelo, Antonio, Marco Scarsini, and Moshe Shaked. "Some positive dependence stochastic orders." Journal of Multivariate Analysis 97, no. 1 (January 2006): 46–78. http://dx.doi.org/10.1016/j.jmva.2004.11.006.

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9

Rajan, D., and D. Vijayabalan. "Some characterizations of stochastic orders." Malaya Journal of Matematik 06, no. 03 (July 1, 2018): 614–18. http://dx.doi.org/10.26637/mjm0603/0023.

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10

Bulinskaya, E. V. "Stochastic orders and inventory problems." International Journal of Production Economics 88, no. 2 (March 2004): 125–35. http://dx.doi.org/10.1016/j.ijpe.2003.11.002.

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11

Pellerey, Franco, and Saeed Zalzadeh. "A note on relationships between some univariate stochastic orders and the corresponding joint stochastic orders." Metrika 78, no. 4 (August 23, 2014): 399–414. http://dx.doi.org/10.1007/s00184-014-0509-5.

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12

Lando, Tommaso, and Lucio Bertoli-Barsotti. "Distorted stochastic dominance: A generalized family of stochastic orders." Journal of Mathematical Economics 90 (October 2020): 132–39. http://dx.doi.org/10.1016/j.jmateco.2020.07.005.

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13

Johnson, Tobias, and Matthew Junge. "Stochastic orders and the frog model." Annales de l'Institut Henri Poincaré, Probabilités et Statistiques 54, no. 2 (May 2018): 1013–30. http://dx.doi.org/10.1214/17-aihp830.

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14

Denuit, Michel, and Alfred Müller. "Smooth generators of integral stochastic orders." Annals of Applied Probability 12, no. 4 (November 2002): 1174–84. http://dx.doi.org/10.1214/aoap/1037125858.

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15

Montes, Ignacio, Enrique Miranda, and Susana Montes. "Imprecise stochastic orders and fuzzy rankings." Fuzzy Optimization and Decision Making 16, no. 3 (September 24, 2016): 297–327. http://dx.doi.org/10.1007/s10700-016-9251-y.

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16

Catana, Luigi-Ionut. "Stochastic orders for a multivariate Pareto distribution." Analele Universitatii "Ovidius" Constanta - Seria Matematica 29, no. 1 (March 1, 2021): 53–69. http://dx.doi.org/10.2478/auom-2021-0004.

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Abstract In this article we give some theoretical results for equivalence between different stochastic orders of some kind multivariate Pareto distribution family. Weak multivariate orders are equivalent or imply different stochastic orders between extremal statistics order of two random variables sequences. The random variables in this article are not neccesary independent.
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17

Zhu, Dan, and Chuancun Yin. "Two Sufficient Conditions for Convex Ordering on Risk Aggregation." Abstract and Applied Analysis 2018 (2018): 1–5. http://dx.doi.org/10.1155/2018/2937895.

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We define new stochastic orders in higher dimensions called weak correlation orders. It is shown that weak correlation orders imply stop-loss order of sums of multivariate dependent risks with the same marginals. Moreover, some properties and relations of stochastic orders are discussed.
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18

STOYANOV, STOYAN V., SVETLOZAR T. RACHEV, and FRANK J. FABOZZI. "METRIZATION OF STOCHASTIC DOMINANCE RULES." International Journal of Theoretical and Applied Finance 15, no. 02 (March 2012): 1250017. http://dx.doi.org/10.1142/s0219024912500173.

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We consider a new approach towards stochastic dominance rules which allows measuring the degree of domination or violation of a given stochastic order and represents a way of describing stochastic orders in general. Examples are provided for the n-th order stochastic dominance and stochastic orders based on a popular risk measure. We demonstrate how the new approach can be used for construction of portfolios dominating a given benchmark prospect.
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19

Denuit, Michel M., and Mhamed Mesfioui. "Generalized Increasing Convex and Directionally Convex Orders." Journal of Applied Probability 47, no. 1 (March 2010): 264–76. http://dx.doi.org/10.1239/jap/1269610830.

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In this paper, the componentwise increasing convex order, the upper orthant order, the upper orthant convex order, and the increasing directionally convex order for random vectors are generalized to hierarchical classes of integral stochastic order relations. The elements of the generating classes of functions possess nonnegative partial derivatives up to some given degrees. Some properties of these new stochastic order relations are studied. Particular attention is paid to the comparison of weighted sums of the respective components of ordered random vectors. By providing a unified derivation of standard multivariate stochastic orderings, the present paper shows how some well-known results derive from a common principle.
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20

Denuit, Michel M., and Mhamed Mesfioui. "Generalized Increasing Convex and Directionally Convex Orders." Journal of Applied Probability 47, no. 01 (March 2010): 264–76. http://dx.doi.org/10.1017/s0021900200006537.

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In this paper, the componentwise increasing convex order, the upper orthant order, the upper orthant convex order, and the increasing directionally convex order for random vectors are generalized to hierarchical classes of integral stochastic order relations. The elements of the generating classes of functions possess nonnegative partial derivatives up to some given degrees. Some properties of these new stochastic order relations are studied. Particular attention is paid to the comparison of weighted sums of the respective components of ordered random vectors. By providing a unified derivation of standard multivariate stochastic orderings, the present paper shows how some well-known results derive from a common principle.
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21

Navarro, Jorge, Felix Belzunce, and Jose M. Ruiz. "New Stochastic Orders Based on Double Truncation." Probability in the Engineering and Informational Sciences 11, no. 3 (July 1997): 395–402. http://dx.doi.org/10.1017/s0269964800004915.

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The purpose of this paper is to study definitions and characterizations of orders based on reliability measures related with the doubly truncated random variable X[x, y] = (X|x ≤ X ≤ y). The relationship between these orderings and various existing orderings of life distributions are discussed. Moreover, we give two new characterizations of the likelihood ratio order based on double truncation. These new orders complete a general diagram between orders defined from truncation.
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22

Nanda, Asok K. "Stochastic Orders in Terms of Laplace Transforms." Calcutta Statistical Association Bulletin 45, no. 3-4 (September 1995): 195–202. http://dx.doi.org/10.1177/0008068319950306.

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Recently s-FR and s-ST orderings have been defined in the literature. They are more general in the sense that most of the earlier known partial orderings reduce as particular cases of these orderings. Moreover, these orderings have helped in defining new and useful ageing criterion. In this paper, using Laplace transform, we characterize, by means of necessary and sufficient conditions. the property that two life distributions are ordered in the s-FR and s-ST sense. The characterization of LR, FR, MR, VR, STand HAMR orderings follow as particular cases.
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23

Nanda, Asok K., and Amarjit Kundu. "On Generalized Stochastic Orders of Dispersion-Type." Calcutta Statistical Association Bulletin 61, no. 1-4 (March 2009): 155–82. http://dx.doi.org/10.1177/0008068320090109.

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24

He, Xu, and Hongmei Xie. "Relative stochastic orders of weighted frailty models." Statistics 54, no. 5 (September 2, 2020): 989–1004. http://dx.doi.org/10.1080/02331888.2020.1828419.

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25

Ding, Ying, and Xinsheng Zhang. "Some stochastic orders of Kotz-type distributions." Statistics & Probability Letters 69, no. 4 (October 2004): 389–96. http://dx.doi.org/10.1016/j.spl.2004.06.001.

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26

Bartoszewicz, Jarosław. "Mixtures of exponential distributions and stochastic orders." Statistics & Probability Letters 57, no. 1 (March 2002): 23–31. http://dx.doi.org/10.1016/s0167-7152(02)00034-2.

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27

Vineshkumar, B., N. Unnikrishnan Nair, and P. G. Sankaran. "Stochastic orders using quantile-based reliability functions." Journal of the Korean Statistical Society 44, no. 2 (June 2015): 221–31. http://dx.doi.org/10.1016/j.jkss.2014.08.003.

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28

Li, Xiaohu, and Moshe Shaked. "A general family of univariate stochastic orders." Journal of Statistical Planning and Inference 137, no. 11 (November 2007): 3601–10. http://dx.doi.org/10.1016/j.jspi.2007.03.035.

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29

Hua, Lei, and Ka Chun Cheung. "Stochastic orders of scalar products with applications." Insurance: Mathematics and Economics 42, no. 3 (June 2008): 865–72. http://dx.doi.org/10.1016/j.insmatheco.2007.10.004.

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30

Lefèvre, Claude, and Stéphane Loisel. "Stationary-excess operator and convex stochastic orders." Insurance: Mathematics and Economics 47, no. 1 (August 2010): 64–75. http://dx.doi.org/10.1016/j.insmatheco.2010.03.009.

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31

Ahmadi, J., and N. R. Arghami. "SOME UNIVARIATE STOCHASTIC ORDERS ON RECORD VALUES." Communications in Statistics - Theory and Methods 30, no. 1 (February 4, 2001): 69–74. http://dx.doi.org/10.1081/sta-100001559.

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32

Sordo, Miguel A., and Héctor M. Ramos. "Characterization of stochastic orders by L-functionals." Statistical Papers 48, no. 2 (April 2007): 249–63. http://dx.doi.org/10.1007/s00362-006-0329-4.

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33

Longobardi, Maria. "Cumulative measures of information and stochastic orders." Ricerche di Matematica 63, S1 (August 20, 2014): 209–23. http://dx.doi.org/10.1007/s11587-014-0212-x.

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34

Shaked, Moshe, and Tityik Wong. "Stochastic orders based on ratios of Laplace transforms." Journal of Applied Probability 34, no. 2 (June 1997): 404–19. http://dx.doi.org/10.2307/3215380.

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The purpose of this paper is to study two notions of stochastic comparisons of non-negative random variables via ratios that are determined by their Laplace transforms. Some interpretations of the new orders are given, and various properties of them are derived. The relationships to other stochastic orders are also studied. Finally, some applications in reliability theory are described.
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35

Shaked, Moshe, and Tityik Wong. "Stochastic orders based on ratios of Laplace transforms." Journal of Applied Probability 34, no. 02 (June 1997): 404–19. http://dx.doi.org/10.1017/s0021900200101044.

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The purpose of this paper is to study two notions of stochastic comparisons of non-negative random variables via ratios that are determined by their Laplace transforms. Some interpretations of the new orders are given, and various properties of them are derived. The relationships to other stochastic orders are also studied. Finally, some applications in reliability theory are described.
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36

Belzunce, Félix, Taizhong Hu, and Baha-Eldin Khaledi. "DISPERSION-TYPE VARIABILITY ORDERS." Probability in the Engineering and Informational Sciences 17, no. 3 (June 6, 2003): 305–34. http://dx.doi.org/10.1017/s0269964803173020.

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Dispersion-type orders are introduced and studied. The new orders can be used to compare the variability of the underlying random variables, among which are the usual dispersive order and the right spread order. Connections among the new orders and other common stochastic orders are examined and investigated. Some closure properties of the new orders under the operation of order statistics, transformations, and mixtures are derived. Finally, several applications of the new orders are given.
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37

Falmagne, Jean-Claude, Yung-Fong Hsu, Fabio Leite, and Michel Regenwetter. "Stochastic applications of media theory: Random walks on weak orders or partial orders." Discrete Applied Mathematics 156, no. 8 (April 2008): 1183–96. http://dx.doi.org/10.1016/j.dam.2007.04.032.

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38

Müller, Alfred. "Stochastic Orders Generated by Integrals: a Unified Study." Advances in Applied Probability 29, no. 2 (June 1997): 414–28. http://dx.doi.org/10.2307/1428010.

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We consider stochastic orders of the following type. Let be a class of functions and let P and Q be probability measures. Then define , if ∫ ⨍ d P ≦ ∫ ⨍ d Q for all f in . Marshall (1991) posed the problem of characterizing the maximal cone of functions generating such an ordering. We solve this problem by using methods from functional analysis. Another purpose of this paper is to derive properties of such integral stochastic orders from conditions satisfied by the generating class of functions. The results are illustrated by several examples. Moreover, we show that the likelihood ratio order is closed with respect to weak convergence, though it is not generated by integrals.
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39

Müller, Alfred. "Stochastic Orders Generated by Integrals: a Unified Study." Advances in Applied Probability 29, no. 02 (June 1997): 414–28. http://dx.doi.org/10.1017/s0001867800028068.

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We consider stochastic orders of the following type. Let be a class of functions and let P and Q be probability measures. Then define , if ∫ ⨍ d P ≦ ∫ ⨍ d Q for all f in . Marshall (1991) posed the problem of characterizing the maximal cone of functions generating such an ordering. We solve this problem by using methods from functional analysis. Another purpose of this paper is to derive properties of such integral stochastic orders from conditions satisfied by the generating class of functions. The results are illustrated by several examples. Moreover, we show that the likelihood ratio order is closed with respect to weak convergence, though it is not generated by integrals.
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40

Balakrishnan, N., and Peng Zhao. "ORDERING PROPERTIES OF ORDER STATISTICS FROM HETEROGENEOUS POPULATIONS: A REVIEW WITH AN EMPHASIS ON SOME RECENT DEVELOPMENTS." Probability in the Engineering and Informational Sciences 27, no. 4 (August 13, 2013): 403–43. http://dx.doi.org/10.1017/s0269964813000156.

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In this paper, we review some recent results on the stochastic comparison of order statistics and related statistics from independent and heterogeneous proportional hazard rates models, gamma variables, geometric variables, and negative binomial variables. We highlight the close connections that exist between some classical stochastic orders and majorization-type orders.
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41

Abbasi, Somayeh, and Mohammad Hossein Alamatsaz. "Preservation properties of stochastic orders by transformation to Harris family." Probability and Mathematical Statistics 38, no. 2 (December 28, 2018): 441–58. http://dx.doi.org/10.19195/0208-4147.38.2.10.

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Stochastic comparisons of lifetime characteristics of reliability systems and their components are of common use in lifetime analysis. In this paper, using Harris family distributions, we compare lifetimes of two series systems with random number of components, with respect to several types of stochastic orders. Our results happen to enfold several previous findings in this connection. We shall also show that several stochastic orders and ageing characteristics, such as IHRA, DHRA, NBU, and NWU, are inherited by transformation to Harris family. Finally, some refinements are made concerning related existing results in the literature.
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42

Ebrahimi-Fard, Kurusch, Alexander Lundervold, Simon J. A. Malham, Hans Munthe-Kaas, and Anke Wiese. "Algebraic structure of stochastic expansions and efficient simulation." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 468, no. 2144 (April 11, 2012): 2361–82. http://dx.doi.org/10.1098/rspa.2012.0024.

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We investigate the algebraic structure underlying the stochastic Taylor solution expansion for stochastic differential systems. Our motivation is to construct efficient integrators. These are approximations that generate strong numerical integration schemes that are more accurate than the corresponding stochastic Taylor approximation, independent of the governing vector fields and to all orders. The sinhlog integrator introduced by Malham & Wiese (2009) is one example. Herein, we show that the natural context to study stochastic integrators and their properties is the convolution shuffle algebra of endomorphisms; establish a new whole class of efficient integrators; and then prove that, within this class, the sinhlog integrator generates the optimal efficient stochastic integrator at all orders.
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43

Catana, Luigi-Ionut. "Stochastic orders of log-epsilon-skew-normal distributions." Analele Universitatii "Ovidius" Constanta - Seria Matematica 30, no. 1 (February 1, 2022): 109–28. http://dx.doi.org/10.2478/auom-2022-0007.

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Abstract The log-epsilon-skew-normal distributions family is generalized class of log-normal distribution. Is widely used to model non-negative data in many areas of applied research. We give necessary and/or sufficient conditions for some stochastic orders of log-epsilon-skew-normal distributions. Also, we give sufficient conditions for orders of moments and Gini indexes. Finally, it is presented a real data application.
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44

Righter, Rhonda, and J. George Shanthikumar. "Extension of the bivariate characterization for stochastic orders." Advances in Applied Probability 24, no. 2 (June 1992): 506–8. http://dx.doi.org/10.2307/1427705.

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The bivariate characterization of stochastic ordering relations given by Shanthikumar and Yao (1991) is based on collections of bivariate functions g(x, y), where g(x, y) and g(y, x) satisfy certain properties. We give an alternate characterization based on collections of pairs of bivariate functions, g1(x, y) and g2(x, y), satisfying certain properties. This characterization allows us to extend results for single machine scheduling of jobs that are identical except for their processing times, to jobs that may have different costs associated with them.
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45

Mukherjee, S. P., and A. Chatterjee. "Stochastic dominance of higher orders and its implications." Communications in Statistics - Theory and Methods 21, no. 7 (January 1992): 1977–86. http://dx.doi.org/10.1080/03610929208830892.

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46

Jarrahiferiz, Jalil, G. R. Mohtashami Borzadaran, and A. H. Rezaei Roknabadi. "Glaser’s function and stochastic orders for mixture distributions." International Journal of Quality & Reliability Management 33, no. 8 (September 5, 2016): 1230–38. http://dx.doi.org/10.1108/ijqrm-04-2013-0072.

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Purpose The purpose of this paper is to study likelihood ratio order for mixture and its components via their Glaser’s functions for weighted distributions. So, some theoretical examples using exponential family and their mixtures are presented. Design/methodology/approach First, Glaser’s functions of mixture and its components for weighted distributions in different scenarios are computed. Then by them the likelihood ratio order is investigated between mixture and its components. Findings The authors find conditions for weight functions under which the mixture random variable is between of its components in likelihood ratio order. Originality/value Results are obtained for weight function in general. It is well known that the some special weights are order statistics, up and down records, hazard rate, reversed hazard rate, moment generating function, etc. So, the results are valid for all of them.
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47

Berrendero, José R., and Javier Cárcamo. "Tests for Stochastic Orders and Mean Order Statistics." Communications in Statistics - Theory and Methods 41, no. 8 (April 15, 2012): 1497–509. http://dx.doi.org/10.1080/03610926.2010.543303.

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48

de la Cal, Jesús, and Javier Cárcamo. "Stochastic orders and majorization of mean order statistics." Journal of Applied Probability 43, no. 3 (September 2006): 704–12. http://dx.doi.org/10.1239/jap/1158784940.

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We characterize the (continuous) majorization of integrable functions introduced by Hardy, Littlewood, and Pólya in terms of the (discrete) majorization of finite-dimensional vectors, introduced by the same authors. The most interesting version of this result is the characterization of the (increasing) convex order for integrable random variables in terms of majorization of vectors of expected order statistics. Such a result includes, as particular cases, previous results by Barlow and Proschan and by Alzaid and Proschan, and, in a sense, completes the picture of known results on order statistics. Applications to other stochastic orders are also briefly considered.
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49

Nanda, Asok K., and Suchismita Das. "Stochastic orders of the Marshall–Olkin extended distribution." Statistics & Probability Letters 82, no. 2 (February 2012): 295–302. http://dx.doi.org/10.1016/j.spl.2011.10.003.

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50

de la Cal, Jesús, and Javier Cárcamo. "Stochastic orders and majorization of mean order statistics." Journal of Applied Probability 43, no. 03 (September 2006): 704–12. http://dx.doi.org/10.1017/s0021900200002047.

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We characterize the (continuous) majorization of integrable functions introduced by Hardy, Littlewood, and Pólya in terms of the (discrete) majorization of finite-dimensional vectors, introduced by the same authors. The most interesting version of this result is the characterization of the (increasing) convex order for integrable random variables in terms of majorization of vectors of expected order statistics. Such a result includes, as particular cases, previous results by Barlow and Proschan and by Alzaid and Proschan, and, in a sense, completes the picture of known results on order statistics. Applications to other stochastic orders are also briefly considered.
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