Journal of the Iranian Statistical Society
پژوهشنامه انجمن آمار ایران
JIRSS
Basic Sciences
http://jirss.irstat.ir
1
admin
1726-4057
2538-189X
8
10.29252/jirss
14
1726-4057
13
en
jalali
1399
3
1
gregorian
2020
6
1
19
1
online
1
fulltext
en
Bounds for CDFs of Order Statistics Arising from INID Random Variables
62Gxx: Nonparametric inference
62Gxx: Nonparametric inference
Original Paper
Original Paper
In recent decades, studying order statistics arising from independent and not necessary identically distributed (INID) random variables has been a main concern for researchers. A cumulative distribution function (CDF) of these random variables (Fi:n) is a complex manipulating, long time consuming and a software-intensive tool that takes more and more times. Therefore, obtaining approximations and boundaries for Fi:n and other theoretical properties of these variables, such as moments, quantiles, characteristic function, and some related probabilities, has always been a main chal- lenge. Recently, Bayramoglu (2018) provided a new definition of ordering, by point to point ordering Fi’s (D-order) and showed that these new functions are CDFs and also, the corresponding random variables are independent. Thus, he suggested new CDFs (F[i]) that can be used as an alternative of Fi:n. Now with using, just F[1], and F[n], we have found the upper and lower bounds of Fi:n. Furthermore, specially a precisely approximation for F1:n and Fn:n (F1;n:n). Also in many cases approximations for other CDFs are derived. In addition, we compare approximated function with those oered by Bayramoglu and it is shown that our results of these proposed functions are far better than D-order functions.
Approximation, bounds, cumulative distribution function, independent and not necessary identically distributed, order statistics.
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http://jirss.irstat.ir/browse.php?a_code=A-11-155-1&slc_lang=en&sid=1
Jaber
Kazempoor
جابر
کاظم پور
kazempoor.jaber@mail.um.ac.ir
`10031947532846003362`

10031947532846003362
No
Department of Statistics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran.
دانشگاه فردوسی مشهد
Arezou
Habibirad
آرزو
حبیبی راد
ahabibi@um.ac.ir
`10031947532846003363`

10031947532846003363
Yes
Department of Statistics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran.
دانشگاه فردوسی مشهد
Kheirolah
Okhli
خیرالله
اخلی
kh.okhli@mail.um.ac.ir
`10031947532846003364`

10031947532846003364
No
Department of Statistics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran.
دانشگاه فردوسی مشهد