Analysis and Applications of Quantile Approach on Residual Extropy

  • Amir Hamzeh Khammar University of Sistan and Baluchestan
  • Vahideh Ahrari
  • Seyed Mahdi Amir Jahanshahi University of Sistan and Baluchestan, Statistics Department.
DOI: https://doi.org/10.19139/soic-2310-5070-1226
Keywords: Distorted distribution, Quantile function, Nonparametric estimator, Reliability measures, Residual extropy, Stochastic orders, Uncertainty measure.

Abstract

Extropy is a measure of the uncertainty of a random variable. Motivated with the wideapplicability of quantile functions in modeling and analyzing statistical data, in this paper, we studyquantile version of the extropy from residual lifetime variable, "residual quantile extropy" in short.Unlike the residual extropy function, the residual quantile extropy determines the quantile densityfunction uniquely through a simple relationship. Aging classes, stochastic orders and characterizationresults are derived, using proposed quantile measure of uncertainty. We also suggest some applicationsrelated to (n i + 1)-out-of-n systems and distorted random variables. Finally, a nonparametricestimator for residual quantile extropy is provided. In order to evaluate of proposed estimator, we usea simulation study.

Author Biography

Seyed Mahdi Amir Jahanshahi, University of Sistan and Baluchestan, Statistics Department.
Statistics Department

References

Baratpour, S. and Khammar, A.H. (2017). A quantile-based generalized dynamic cumulative measure of entropy. Communications in Statistics-Theory and Methods, 47, 3104-3117.
[2] Barlow, R.E. and Proschan, F. (1981). Statistical Theory of Reliability and Life Testing: Probability Models. Silver-Spring, To Begin With.
[3] Denneberg, D. (1990). Premium calculation: why standard deviation should be replaced by absolute deviation. Astin Bulletin, 20, 181-190.
....
Published
2023-08-03
How to Cite
Khammar, A. H., Ahrari, V., & Amir Jahanshahi, S. M. (2023). Analysis and Applications of Quantile Approach on Residual Extropy. Statistics, Optimization & Information Computing, 11(4), 876-891. https://doi.org/10.19139/soic-2310-5070-1226
Issue
Vol 11 No 4 (2023)
Section
Research Articles
Authors who publish with this journal agree to the following terms:

    1. Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
    2. Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
    3. Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).