On weighted measure of inaccuracy for doubly truncated random variables

ABSTRACT

Recently, authors have studied the weighted version of Kerridgeinaccuracy measure for left/right truncated distributions. In the present communication we introduce the notion of weighted interval inaccuracy measure and study it in the context of two-sided truncated random variables. In reliability theory and survival analysis, this measure may help to study the various characteristics of a system/component when it fails between two time points. We study various properties of this measure, including the effect of monotone transformations, and obtain its upper and lower bounds. It is shown that the proposed measure can uniquely determine the distribution function and characterizations of some important life distributions have been provided. This new measure is a generalization of recent weighted residual (past) inaccuracy measure.

Keywords and Phrases:

• Entropy
• weighted inaccuracy measure
• proportional (reversed) hazard model

MATHEMATICS SUBJECT CLASSIFICATION:

• Primary 94A17
• Secondary 62N05
• 62E10

Acknowledgments

The author thanks the anonymous reviewer for his/her valuable comments and suggestions on the earlier version of the paper which have led to considerable improvement in the contents.

Funding

The financial support (Ref. No. 2/48(4)/2015/NBHM(R.P.)/R&DII/14130) from the NBHM, Department of Atomic Energy, Government of India, is gratefully acknowledged.