Shannon Information In k-records

Abstract

In this article, we present results on the Shannon information (SI) contained in upper(lower) k-record values and associated k-record times. We then establish an interesting relationship between the SI content of a random sample of fixed size, and the SI in the data consisting of sequential maxima. We also consider the information contained in the k-record data from an inverse sampling plan (ISP).

Keywords:

• Record values
• Record times
• k-record values
• k-record times
• Shannon information
• Fisher information
• Euler’s constant
• Digamma function
• Zeta function

Mathematics Subject Classification:

• Primary 62G30
• Secondary 94A17