Volume 19, Issue 1 (6-2020)                   JIRSS 2020, 19(1): 39-57 | Back to browse issues page

DOI: 10.29252/jirss.19.1.39


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Department of Statistics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran. , ahabibi@um.ac.ir
Abstract:   (1010 Views)
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 o ered by Bayramoglu and it is shown that our results of these proposed functions are far better than D-order functions.
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Type of Study: Original Paper | Subject: 62Gxx: Nonparametric inference
Received: 2019/03/26 | Accepted: 2020/01/23 | Published: 2020/07/4