ترتیب تصادفی هسیان در توزیع های هذلولوی تعمیم یافته چندمتغیره و کاربردهای آن

نویسندگان
مهدی امیری 1
احد جمالیزاده 2
سلمان ایزدخواه 3
1 دانشگاه هرمزگان
2 دانشگاه شهید باهنر کرمان
3 دانشگاه کردستان
چکیده
در این نوشتار، بردارهای تصادفی برگرفته از خانواده توزیع­های هذلولوی تعمیم­یافته چندمتغیره (GH)را در غالب ترتیب تصادفی هسیان مقایسه می ­کنیم. خانواده توزیع­های GH شامل طیف گسترده ­ای از توزیع های متقارن و نامتقارن و با برجستگی­ های متفاوت بوده که می­ توانند در تحلیل و برازش داده ­های چوله و نیز دم­ سنگین بکار روند. ضمن معرفی و یادآوری برخی مفاهیم مقدماتی، با در نظر گرفتن چند مخروط محدب بسته و دوگان­ های آن­ها، شرایط لازم و کافی برای چند ترتیب­ تصادفی با اهمیت را بدست می­ آوریم. نشان خواهیم داد که تحت شرایطی، ترتیب­ های خطی محدب با ترتیب ­های چندمتغیره­ ای از نوع هسیان معادل هستند. بر اساس مفصل­ های تولید شده توسط خانواده GH، آشکارا خواهیم دید که ترتیب ساختار همبستگی معادل با برخی از ترتیب­ های تصادفی هسیان در این خانواده است. به ­عنوان کاربرد، نتایج در زمینه ­های بیمه و اقتصاد تفسیر گردیده­ اند.
کلیدواژه‌ها
ترتیب هسیان
مخروط محدب
ترتیب محدب خطی
توزیع هذلولوی تعمیم یافته

عنوان مقاله English

Hessian Stochastic Ordering in the Family of multivariate Generalized Hyperbolic Distributions and its Applications

نویسندگان English

Mehdi Amiri 1
Ahad Jamalizadeh 2
Salman Izadkhah 3
1 University of hormozgan
2 Shahid Bahonar University of Kerman
3 University of Kurdistan
چکیده English

In this paper, random vectors following the multivariate generalized hyperbolic (GH) distribution are compared using the hessian stochastic order. This family includes the classes of symmetric and asymmetric distributions by which different behaviors of kurtosis in skewed and heavy tail data can be captured. By considering some closed convex cones and their duals, we derive some necessary and sufficient conditions for some important applied stochastic orderings. The linear convex orderings are shown to be equivalent with a certain kind of hessian orderings. Based on copulas generated by the GH distributions, it is revealed that the ordering of the GH distributions in terms of their dependence structures corresponds to some hessian stochastic orderings being satisfied. The results are shown to be relevant to some insurance and economic applications.

کلیدواژه‌ها English

Hessian ordering
Convex cone
Linear convex ordering
Generalized hyperbolic distribution
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