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Asymptotic Distributions of the Generalized Range, Midrange, Extremal Quotient, and Extremal Product, with a Comparison Study

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  • H. M. Barakat
  • E. M. Nigm
  • A. M. Elsawah

Abstract

Necessary and sufficient conditions for the weak convergence of the generalized range, midrange, extremal quotient, and extremal product are obtained. The classes of possible non degenerate limit distribution functions of these simple statistics are characterized. Comparison study between these statistics with some examples for the most important distribution functions are given.

Suggested Citation

  • H. M. Barakat & E. M. Nigm & A. M. Elsawah, 2015. "Asymptotic Distributions of the Generalized Range, Midrange, Extremal Quotient, and Extremal Product, with a Comparison Study," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 44(5), pages 900-913, March.
    • Handle: RePEc:taf:lstaxx:v:44:y:2015:i:5:p:900-913
    DOI: 10.1080/03610926.2012.750356
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