On the asymptotic distributions of high‐order spacings statistics | Zendy

Guttorp P. | Zendy; Lockhart R. A. | Zendy

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On the asymptotic distributions of high‐order spacings statistics

Author(s) -

Guttorp P.,

Lockhart R. A.

Publication year - 1989

Publication title -

canadian journal of statistics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.804

H-Index - 51

eISSN - 1708-945X

pISSN - 0319-5724

DOI - 10.2307/3315481

Subject(s) - statistic , mathematics , limiting , order statistic , monte carlo method , asymptotic analysis , asymptotic distribution , statistics , goodness of fit , distribution (mathematics) , statistical physics , mathematical analysis , physics , mechanical engineering , estimator , engineering

Goodness‐of‐fit tests for the uniform distribution based on sums of smooth functions of m ‐spacings are studied. A limiting sum‐of‐weighted‐chi‐squareds approximation is shown to be accurate uniformly in m for the special cases of analogues of Greenwooďs statistic and Moran's statistic. Asymptotic critical points are provided; theory and Monte Carlo studies show they are accurate for all m provided n is moderately large.

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