يك رده از متغيرهاي تصادفي وابسته: ويژگي ها و برخي كاربردها

A class of dependent random variables, properties and applications

ﭼﮑﯿﺪه: در اﯾﻦ ﻣﻘﺎﻟﻪ ﻧﺨﺴﺖ ﯾﮏ رده از ﻣﺘﻐﯿﺮﻫﺎي ﺗﺼﺎدﻓﯽ واﺑﺴﺘﻪ ،APND، ﮐﻪ ﺷﺎﻣﻞ رده ﻫﺎي ﺑﺰرﮔﯽ از ﻣﺘﻐﯿﺮﻫﺎي ﺗﺼﺎدﻓﯽ واﺑﺴﺘﻪ ﻣﻨﻔﯽ و ﺑﺮﺧﯽ رده ﻫﺎ از ﻣﺘﻐﯿﺮﻫﺎي ﺗﺼﺎدﻓﯽ واﺑﺴﺘﻪ ﻣﺜﺒﺖ ﻫﺴﺘﻨﺪ، ﻣﻌﺮﻓﯽ ﻣﯽ ﺷﻮﻧﺪ. ﺳﭙﺲ ارﺗﺒﺎط اﯾﻦ رده از ﻣﺘﻐﯿﺮﻫﺎ ﺑﺎ ﺑﺮﺧﯽ رده ﻫﺎي ﺷﻨﺎﺧﺘﻪ ﺷﺪه از ﻣﺘﻐﯿﺮﻫﺎي واﺑﺴﺘﻪ ﺗﺸﺮﯾﺢ و ﺗﻌﺪادي از رواﺑﻂ اﺳﺎﺳﯽ ﺷﺎﻣﻞ ﻧﺎﻣﺴﺎوي ﻫﺎي ﮔﺸﺘﺎوري و ﻣﺎﮐﺴﯿﻤﺎل ﺑﺮاي ردهAPND ﯾﺎ زﯾﺮ رده ﻫﺎي آن اﺛﺒﺎت ﻣﯽ ﺷﻮﻧﺪ. در ﭘﺎﯾﺎن رﻓﺘﺎر ﺣﺪي آراﯾﻪ اي اﺧﺘﯿﺎري از ﻣﺘﻐﯿﺮﻫﺎي ﺗﺼﺎدﻓﯽ ﻣﻮرد ﻣﻄﺎﻟﻌﻪ ﻗﺮار ﻣﯽ ﮔﯿﺮﻧﺪ.

In this paper, after calling a class of dependent random variables, APND, that contains some big classes of negatively dependent and some classes of positively dependent random variables, the relationship of this class of random variables with well known classes of dependent variables are explained and some basic relations, contain moment and maximal inequalities are proofed. At the end, the limiting behavior of an arbitrary array of random variables is studied.