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Information Generating Function of \(\boldsymbol{k}\)-Record Values and Its Applications

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Abstract

In this paper, we study the information-generating (IG) measure of \(k\)-record values and examine some of its main properties. We establish some bounds for the IG measure of \(k\)-record values. In addition, we present some results related to the characterization of an exponential distribution by maximization (minimization) of the IG measure of record values under certain conditions. We also examine the relative information generating (RIG) measure between the distribution of record values and the corresponding underlying distribution and present some results in this regard. Several examples have been provided throughout the study to illustrate the results. We also consider the problem of estimation of the IG measure for a two-parameter Weibull distribution based on the upper \(k\)-record values.

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ACKNOWLEDGEMENTS

The authors would like to thank the editor and the reviewers for their constructive comments, which helped to improve the quality of the paper.

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Authors and Affiliations

  1. Department of Statistics, University of Kerala, 695581, Kariavattom, Trivandrum, India

    Manoj Chacko & Annie Grace

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  1. Manoj Chacko
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  2. Annie Grace
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Correspondence to Manoj Chacko or Annie Grace.

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Chacko, M., Grace, A. Information Generating Function of \(\boldsymbol{k}\)-Record Values and Its Applications. Math. Meth. Stat. 32, 176–196 (2023). https://doi.org/10.3103/S106653072303002X

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  • DOI: https://doi.org/10.3103/S106653072303002X

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