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The limiting behaviour of the maximal spacing generated by an i.i.d. sequence of Gaussian random variables

Published online by Cambridge University Press:  14 July 2016

Paul Deheuvels
Paul Deheuvels*
Affiliation:
Université Paris VI
*
∗ Postal address: 7 Avenue du Château, 92340 Bourg-la-Reine, France.
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Abstract

Let Mn be the maximal spacing generated in the sample's range by Χ1,· ··, Χ n, independent and identically distributed Gaussian N(0, 1) random variables. We obtain the limiting distribution of and show that

according to whether ε> 0 or ε < 0.

Keywords

ORDER STATISTICSSTRONG LAWS. LAWS OF THE ITERATED LOGARITHMALMOST SURE CONVERGENCE
Type
Research Papers
Information
Journal of Applied Probability , Volume 22 , Issue 4 , December 1985 , pp. 816 - 827
Copyright
Copyright © Applied Probability Trust 1985 

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