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Limit theorems for the logarithm of sample spacings

Author

Listed:
  • Shao, Yongzhao
  • Hahn, Marjorie G.

Abstract

Many statistical problems can be reformulated in terms of tests of uniformity. Some strong laws of large numbers and a central limit theorem for the logarithm of transformed spacings are obtained. These theorems provide a characterization of the uniform distribution. A general information-type inequality is deduced which gives a quantitative measurement (using the Kullback-Leibler number) of the discrepancy between an arbitrary distribution and the uniform distribution.

Suggested Citation

  • Shao, Yongzhao & Hahn, Marjorie G., 1995. "Limit theorems for the logarithm of sample spacings," Statistics & Probability Letters, Elsevier, vol. 24(2), pages 121-132, August.
    • Handle: RePEc:eee:stapro:v:24:y:1995:i:2:p:121-132
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    Cited by:

    1. R. Jiménez & J. E. Yukich, 2002. "Asymptotics for Statistical Distances Based on Voronoi Tessellations," Journal of Theoretical Probability, Springer, vol. 15(2), pages 503-541, April.
    2. Marcin Kamiński & Alberto Corigliano, 2022. "Shannon Entropy in Stochastic Analysis of Some Mems," Energies, MDPI, vol. 15(15), pages 1-14, July.
    3. Yongzhao Shao & Raúl Jiménez, 1998. "Entropy for Random Partitions and Its Applications," Journal of Theoretical Probability, Springer, vol. 11(2), pages 417-433, April.

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