Asymptotic results for lower exponential spacings

Abstract

In this paper, we investigate distributional and asymptotic properties of lower exponential spacings. We find conditions under which the sequence of logarithmic lower spacings converges in probability and with probability one.

KEYWORDS and Phrases:

• Order statistics
• ordered spacings
• exponential distribution
• limit laws
• Borel-Cantelli lemmas

Acknowledgment

The authors are deeply indebted to the anonymous referees for their valuable comments and remarks. This has contributed to a greatly improved presentation of the results of this paper.