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Weak Limit of the Sample Extremal Quotient
Author(s) -
Barakat H.M.
Publication year - 1998
Publication title -
australian and new zealand journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 1369-1473
DOI - 10.1111/1467-842x.00009
Subject(s) - mathematics , quotient , independent and identically distributed random variables , limit (mathematics) , degenerate energy levels , infinity , class (philosophy) , distribution (mathematics) , random variable , convergence of random variables , weak convergence , combinatorics , discrete mathematics , pure mathematics , mathematical analysis , statistics , physics , computer security , quantum mechanics , artificial intelligence , computer science , asset (computer security)
Necessary and sufficient conditions are obtained for the weak convergence ( W →) of the sample extremal quotient of independent and identically distributed random variables as the number of observations tends to infinity. The paper fully characterizes the class of possible non‐degenerate limit distribution functions of the extremal quotient, under general conditions.