مقایسه‌‌ تصادفی در خانواده توزیع‌های آمیخته‌مقیاس چوله-نرمال چندمتغیره براساس ترتیب هسیان و برخی از کاربردهای آن

نوع مقاله : مقاله پژوهشی

نویسندگان

1 گروه آمار، دانشکده علوم پایه، دانشگاه هرمزگان، بندرعباس، ایران

2 گروه ریاضی، دانشکده علوم، دانشگاه یاسوج، یاسوج، ایران

چکیده

در این مقاله، بردارهای تصادفی از توزیع آمیخته‌مقیاس چوله‌-نرمال چندمتغیره براساس ترتیب تصادفی هسیان مقایسه می‌شوند. شرایط لازم و کافی برای این نوع از ترتیب‌ها مورد مطالعه قرار گرفته و با در نظر گرفتن مخروط‌های محدب مختلف، نتیجه در چند حالت مهم از این نوع ترتیب بیان گردیده است. در ادامه ترتیب هسیان صعودی و شرایط لازم و کافی برای حالت‌های مهم مورد بررسی قرار گرفته است. همچنین ترتیب‌های خطی برپایه ترتیب‌های معمول و محدب نیز مورد بررسی قرار گرفته و نشان داده شده است که این ترتیب‌های خطی در خانواده توزیع آمیخته‌مقیاس چوله‌-نرمال از نوع ترتیب هسیان می‌باشند. ترتیب هماهنگی و سوپرمودولار به عنوان ابزارهایی مهم در ترتیب وابستگی، معادل با ترتیب مقادیر همبستگی بدست آمده و براساس این نتایج، ترتیب مخاطره یا نوسانات رشد نسبی مجموعه‌های مختلف در اقتصاد بر حسب ترتیب همبستگی آنها بیان شده است. در زمینه بیمه، ترتیب مخاطره مقدار مجموع بسته‌های مختلف براساس ترتیب متوسط همبستگی درون مجموعه‌ها بدست آمده است. همچنین در زمینه قابلیت اعتماد، ترتیب طول عمر سیستم‌های موازی و سری برحسب ترتیب میزان همبستگی مولفه‌های سیستم بیان گردیده است.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

Stochastic comparisons in the scale mixture of the multivariate skew-normal family of distributions based on Hessian ordering with some applications

نویسندگان [English]

  • Mehdi Amiri 1
  • Abbas Eftekharian 1
  • Roohollah Roozegar 2
1 Department of Statistics, Faculty of Basic Sciences, University of Hormozgan, Bandarabbas, Iran.
2 Department of Mathematics, Faculty of Science, Yasuj University, Yasuj, Iran.
چکیده [English]

In this paper, we compare the random vectors from the scale-mixture of multivariate skew-normal distributions, based on Hessian orderings. The necessary and sufficient conditions for this type of ordering are studied and by considering some convex cones, the results are expressed for some important cases. In the following, the increasing Hessian ordering and necessary and sufficient conditions for some important cases are investigated. Also, the linear orderings, based on usual and convex orderings, have been discussed and it has been shown that these linear orderings in the family of multivariate scale mixture of skew-normal distributions, are of the Hessian order type. The supermodular and concordance orderings, as the important tools of dependence ordering, are obtained as equivalent to the order of correlations and using these results, the order of risk or oscillations of different portfolios in economics is explained as the order of their correlations. In the insurance context, the order of risk of aggregate claims in different portfolios is obtained as equivalent to the order of average of correlations within the portfolios. Also, in the reliability context, the order of lifetimes of parallel and series systems can be expressed in terms of correlations of system components.

کلیدواژه‌ها [English]

  • Hessian orders
  • Convex cone
  • Correlation order
  • Stop-loss order
  • Parallel system
  • Series system
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