SHARP BOUNDS FOR THE MEAN OF kTH RECORD VALUE

ABSTRACT

We present optimal bounds for the moments of k-record statistics expressed in terms of scale units generated by absolute central population moments of different orders. The bounds are based on the Moriguti monotone approximations combined with the Hölder inequality. We determine the distributions for which the bounds are attained. The results are also numerically compared with other classical bounds.

Keywords:

• Record statistics
• Hölder inequality
• Moriguti monotone approximation
• Sharp bound
• AMS Subject Classification: 62G30
• 62G32
• 62E10
• 62E15

ACKNOWLEDGMENTS

The first author would like to thank the University of Jordan for research work. This research work was done when the first author was on sabbatical leave at UAE University. The second author was partially supported by KBN (Polish State Committee for Scientific Research) under Grant 5 P03A 012 20.