Summary
If K n denotes the k-th maximal spacing generated by an i.i.d. sequence of random variables uniformly distributed on (0,1), we show that for any p≧3,
according as ε≦0 or ε>0. We also obtain strong limiting bounds for the record times and inter-record times of K n.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Deheuvels, P.: The strong approximation of extremal processes. Z. Wahrscheinlichkeitstheorie verw. Gebiete 58, 1–6 (1981)
Deheuvels, P.: Strong limiting bounds for maximal uniform spacings. Ann. Probability. 10, 1058–1065 (1982)
Deheuvels, P.: Strong approximation in extreme value theory and applications. Coll. Math. Soc. Janos Bolyai, Vol. 36. Limit theorems in Probability and Statistics, P. Révész edit. Amsterdam: North Holland 1982
Devroye, L.: Laws of the iterated logarithm for order statistics of uniform spacings. Ann. Probability. 9, 860–867 (1981)
Devroye, L.: A Log Log law for maximal uniform spacings. Ann. Probability. 10, 863–868 (1982)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Deheuvels, P. Upper bounds for k-th maximal spacings. Z. Wahrscheinlichkeitstheorie verw Gebiete 62, 465–474 (1983). https://doi.org/10.1007/BF00534198
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF00534198