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A separation theorem for the weak s-convex orders
Institution:1. Institut de statistique, biostatistique et sciences actuarielles (ISBA), Université Catholique de Louvain, B-1348 Louvain-la-Neuve, Belgium;2. Private Enterprise Research Center, Texas A&M University, College Station, TX 77843, USA;3. Department of Economics, Michigan State University, East Lansing, MI 48824, USA;1. Department of Epidemiology, School of Health, Arak University of Medical Sciences, Arak, Iran;2. Department of Epidemiology and Biostatistics, School of Public Health, Tehran University of Medical Sciences, Tehran, Iran;3. Department of Statistics, Faculty of Mathematical Sciences, Tarbiat Modares University, Tehran, Iran;4. Department of Health Education & Promotion, Faculty of Health Sciences, Tabriz University of Medical Sciences, Tabriz, Iran;5. Department of Statistics, University of British Columbia, Vancouver, Canada;6. Faculty of Health Sciences, Simon Fraser University, Burnaby, Canada;1. Michigan State University, USA;2. University of Sydney, Australia;1. Hertsen Moscow Oncology Research Institute, Branch of the National Medical Research Radiological Center, Ministry of Health of the Russian Federation, 125284, Moscow, Russian Federation;2. Engelhardt Institute of Molecular Biology, Russian Academy of Sciences, 119991, Moscow, Russian Federation;3. Department of Anatomy and Experimental Morphology, University Cancer Center, University Medical Center Hamburg-Eppendorf, Martinistr. 52, Hamburg D-20246, Germany;4. SRC Bioclinicum, Ugreshskaya str 2/85, 115088 Moscow, Russian Federation;5. Moscow State University of Mechanical Engineering, Bolshaya Semenovskaya str 38, 107023 Moscow, Russian Federation;6. Molecular Epidemiology Group, German Cancer Research Center, Im Neuenheimer Feld 280, 69120 Heidelberg, Germany;1. School of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming, 650221, China;2. Yunnan Tongchuang Scientific Computing and Data Mining Center, China;3. School of Statistics, Renmin University of China, Beijing, 100872, China;1. Department of Psychology, Friedrich-Schiller-University, Am Steiger 3, D-07743 Jena, Germany;2. Faculty of Psychology, University of Koblenz-Landau, Fortstr. 7, D-76829 Landau/Pfalz, Germany;3. Department of Psychology, J.W. Goethe University, Varrentrappstr. 40-42, D-60486 Frankfurt, Germany
Abstract:The present paper extends to higher degrees the well-known separation theorem decomposing a shift in the increasing convex order into a combination of a shift in the usual stochastic order followed by another shift in the convex order. An application in decision making under risk is provided to illustrate the interest of the result.
Keywords:Integrated right and left tails  Upper and lower partial moments  Stationary excess operator  Khinchine representation  Risk increase  Risk aversion
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