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On the weak limit law of the maximal uniform k-spacing

  • Aleksandar Mijatović (a1) and Vladislav Vysotsky (a2)

Abstract

In this paper we give a simple proof of a limit theorem for the length of the largest interval straddling a fixed number of points that are independent and uniformly distributed on a unit interval. The key step in our argument is a classical theorem of Watson on the maxima of m-dependent stationary stochastic sequences.

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Corresponding author

Department of Mathematics, King's College London, Strand, London WC2R 2LS, UK. Email address: aleksandar.mijatovic@kcl.ac.uk
School of Mathematical and Statistical Sciences, Arizona State University, PO Box 871804, Tempe, AZ 85287, USA. Email address: vysotsky@asu.edu

References

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[1] Deheuvels, P. (1982).Strong limiting bounds for maximal uniform spacings.Ann. Prob. 10,10581065.
[2] Deheuvels, P. and Devroye, L. (1984).Strong laws for the maximal k-spacing when kclogn .Z. Wahrscheinlichkeitsth. 66,315334.
[3] Devroye, L. (1981).Laws of the iterated logarithm for order statistics of uniform spacings.Ann. Prob. 9,860867.
[4] Pyke, R. (1965).Spacings.J. R. Statist. Soc. B. 27,395449.
[5] Shorack, G. R. and Wellner, J. A. (1986).Empirical Processes with Applications to Statistics.John Wiley,New York.
[6] Watson, G. S. (1954).Extreme values in samples from m-dependent stationary stochastic processes.Ann. Math. Statist. 25,798800.

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On the weak limit law of the maximal uniform k-spacing

  • Aleksandar Mijatović (a1) and Vladislav Vysotsky (a2)

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