Paper Info
Title
Asymptotic Expansions For The Distribution Function Of The Sample Median Constructed From A Sample With Random Size
Abstract
Statistical regularities of the information flows in contemporary communication, computational and other information systems are characterized be the presence of the so-called "heavy tails". The outlying observations make the traditional moment-type location estimators inaccurate. In this case the robust median-type location estimators are preferable. On the other hand, the random character of the intensity of the flow of informative events results in that the available sample size (traditionally this is the number of observations registered within a certain time interval) is random. The randomness of the sample size crucially changes the asymptotic properties of the estimators. In the paper, asymptotic expansions are obtained for the distribution function of the sample median constructed from a sample with random size. A general theorem on the asymptotic expansion is proved for this case. The cases of the Laplace, Student and Cauchy distributions are considered. Special attention is paid to the situations in which the heavy-tailed distributions (Cauchy, Laplace) are inherent in both the original sample and the asymptotic regularities of the sample median (Student, Laplace) due to the randomness of the sample size. This approach can be successfully used for big data mining and analysis of information flows in high-performance computing.
Year
Venue
Keywords
2016
PROCEEDINGS - 30TH EUROPEAN CONFERENCE ON MODELLING AND SIMULATION ECMS 2016
Sample median, sample with random size, asymptotic expansion, Student distribution, Cauchy distribution, Laplace distribution
DocType
Citations 
PageRank 
Conference
0
0.34
References 
Authors
0
3
Name
Order
Citations
PageRank
Vladimir E. Bening100.34
Victor Korolev21611.26
Alexander I. Zeifman34417.93