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   Bounds for CDFs of Order Statistics Arising from INID Random Variables  
   
نویسنده kazempoor jaber ,habibirad arezou ,okhli kheirolah
منبع journal of the iranian statistical society - 2020 - دوره : 19 - شماره : 1 - صفحه:39 -57
چکیده    In recent decades, studying order statistics arising from independent and not necessary identically distributed (inid) random variables has been a remarkable concern for researchers. the cumulative distribution function (cdf) of these random variables (fi:n) is a complex manipulating, long time consuming and a softwareintensive tool that takes considerable time. therefore, obtain approximations and bounds for fi:n and other theoretical properties of these variables, such as moments, quantiles, characteristic functions, and some related probabilities, has always been the main challenge. recently, bayramoglu (2018), bayramoglu (2018), has introduced a set of cdfs (f[i]), whose definitions are based on a point to point ordering of the original cdfs (fi), that can be used to approximate the cdf of i-th order statistics (fi:n). here, by using just f[1] and f[n], we provide new upper and lower bounds for the fi:n. furthermore, new approximations for f1:n and fn:n, as well as for other cases, are derived. comparisons with respect to approximations suggested by bayramoglu bayramoglu (2018) are also provided.
کلیدواژه Approximation ,Bounds ,Cumulative Distribution Function ,Independent and not Necessary Identically Distributed ,Order Statistics
آدرس ferdowsi university of mashhad, faculty of mathematical sciences, department of statistics, Iran, ferdowsi university of mashhad, faculty of mathematical sciences, department of statistics, Iran, ferdowsi university of mashhad, faculty of mathematical sciences, department of statistics, Iran
پست الکترونیکی kh.okhli@mail.um.ac.ir
 
     
   
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