Best Bounds of kth Records from Bounded Samples

Abstract

We present optimal bounds for expectations of kth records and differences of kth records based on sequences of independent identically distributed random variables with a bounded support. Bounds are expressed in terms of support length units.

Keywords:

• Bounded variable
• kth record
• kth record difference
• Moriguti inequality

Mathematics Subject Classification:

• Primary 60E15
• Secondary 62G32

Acknowledgment

The author wishes to thank Professor Tomasz Rychlik of Polish Academy of Sciences for many valuable comments and helpful which significantly improved the final version of this article.