On the Distributions of Certain Spacings

Abstract

A characterization of the uniform distribution based on distributions of spacings is presented which extends the existing result in this direction. Also, a result on the distribution of spacings for distributions close to the uniform one is discussed.

Keywords:

• Characterizations
• Spacings
• Uniform distributions

Mathematics Subject Classification:

• 62E10
• 60E05

Acknowledgment

We would like to thank Professor M. Ahsanullah for his comment regarding Theorem 1.1. We are grateful to Barry Arnold for his comments improving the presentation of this work.