Study of inaccuracy measures of record values

TL;DR

This paper extends classical inaccuracy measures to record values, analyzing their relationship with parent distributions and illustrating their behavior across various lifetime distributions.

Contribution

It introduces new inaccuracy measures for record values and derives their expressions, enhancing understanding of information measures in record analysis.

Findings

Inaccuracy varies with record order and distribution parameters.

Derived expressions for inaccuracy measures for several lifetime distributions.

Illustrated applications to exponential, Pareto, and Weibull distributions.

Abstract

In this paper, we investigate inaccuracy measures based on record values, focusing on the relationship between the distribution of the n-th upper and lower k-record values and the parent distribution. We extend the classical Kerridge inaccuracy measure, originally developed for comparing two distributions, to record values and derive expressions for both upper and lower record values. In addition, we explore various other inaccuracybased measures, such as cumulative residual inaccuracy, cumulative past inaccuracy, and extropy inaccuracy measures, and their applications in characterizing symmetric distributions. We compute these measures through illustrative examples for several well-known lifetime distributions, including the exponential, Pareto, and Weibull distributions. Our findings provide insights into how inaccuracy varies with record order and distribution parameters, contributing to a deeper understanding of information-theoretic measures applied to records.