Premium
DETERMINATION OF DOMAINS OF ATTRACTION BASED ON A SEQUENCE OF MAXIMA
Author(s) -
Wang J.Z.,
Cooke P.,
Li S.
Publication year - 1996
Publication title -
australian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 0004-9581
DOI - 10.1111/j.1467-842x.1996.tb00673.x
Subject(s) - maxima , monte carlo method , mathematics , sequence (biology) , order statistic , statistic , attraction , statistics , sample (material) , sample size determination , inference , test statistic , statistical physics , domain (mathematical analysis) , maxima and minima , function (biology) , statistical hypothesis testing , computer science , physics , mathematical analysis , artificial intelligence , linguistics , philosophy , art , performance art , biology , genetics , art history , thermodynamics , evolutionary biology
Summary Suppose that the maximum of a random sample from a distribution F ( x ) may be obtained in each of k equally spaced observation periods. This paper proposes a test to determine the domain of attraction of F ( x ), and investigates the properties when the sample size is very large and perhaps unknown and k is fixed and small. The test statistic is a function of the spacings between the order statistics based on the sequence of maxima and is suggested by reference to one studied previously when inference was based on the largest k observations of a random sample. A Monte Carlo study shows that the proposed test is more powerful than its main competitor. The test is illustrated by two examples.