Characterization of Lifetime Distribution Based on Generalized Interval Entropy

  • Vikas Kumar UIET, M. D. University
  • Nirdesh Singh
DOI: https://doi.org/10.19139/soic.v6i4.328
Keywords: Shannon entropy, Interval entropy, Generalized failure rate, Characterization

Abstract

In this paper, we introduce the concept of generalized interval entropy measure of order alpha and type beta for the doubly truncated random variable. A characterization problem for the generalized interval entropy measure has been studied. The exponential, the pareto and finite range distributions have been characterized in terms of the proposed entropy measure and generalized failure rate function. A lower bound to generalized interval entropy has also been derived. Finally some stochastic comparison based on generalized interval entropy are presented.

References

M. Asadi, N. Ebrahimi, and E. Soofi, Dynamic generalized information measures, Statistics and Probability Letters, vol. 71, no. 1, pp. 85–98, 2005.

M. Asadi, and N. Ebrahimi, Residual entropy and its characterizations in terms of hazard function and mean residual life function, Statistics and Probability Letters, vol. 49, no. 3, pp. 263–269, 2007.

T. Azlarov, and N. Volodin, Characterization problems associated with exponential distribution, Springer-Verlag, New York, 1986.

M. A. K. Baig, and J. G. Dar, Generalized residual entropy function and its applications, Europian Journal of Pure and Applied Mathematics, vol.1, no. 4 pp. 30–40, 2008.

F. Belzunce, J. Navarro, J. M. Ruiz, and Y. Aguila, Some results on residual entropy function, Metrika, vol. 59, no. 2, pp. 147–161, 2004.

A. Di Crescenzo, and M. Longobardi, Entropy-based measure of uncertainty in past lifetime distributions, Journal of Applied Probability, vol. 39, no. 2, pp. 434–440, 2002.

A. Di Crescenzo, and M. Longobardi, A measure of discrimination between past lifetime distributions, Statistics and Probability Letters, vol. 67, no. 2, pp. 173–182, 2004.

N. Ebrahimi, How to measure uncertainty about residual lifetime, Sankhya A , vol. 58, no. 1, pp. 48–57, 1996.

N. Ebrahimi, and F. Pellerey, New partial ordering of survival functions based on notation of uncertainty, Journal of Applied Probability, vol. 32, pp. 202–211, 1995.

J. Galambos, and S. Kotz, Characterization of probability distributions: a unified approach with an emphasis on exponential and related models, Lecture notes on Mathematics 675, Springer-Verlag, Berlin, 1978.

V. Kumar, H. C. Taneja, and R. Srivastava, A dynamic measure of inaccuracy between two past lifetime distribution, Metrika, vol.74, no. 1, pp. 1–10, 2011.

F. Misagh, and G.H. Yari, On weighted interval entropy, Statistics and Probability Letters, vol. 81, no. 2, pp. 188–194, 2011.

F. Misagh, and G.H. Yari, Interval entropy and informative distance, Entropy, vol. 14, pp. 480–490, 2012.

K. R. M. Nair, and G. Rajesh, Characterization of probability distributions using the residual entropy function, Journal of the Indian Statistical Association, vol. 36, pp. 157–166, 1998.

A. K. Nanda, and P. Paul, Some properties of past entropy and their applications, Metrika, vol. 64, no. 1, pp. 47–61, 2006.

J. Navarro, and J. M. Ruiz, Faliure rate function for doubly truncated random variables., IEEE Transactions on Information Theory, vol. 45, pp. 685–690, 1996

J. Navarro, and J. M. Ruiz,Characterization from relationships between failure rate functions and conditional moments communications in statistics: theory methods, vol. 33, no. 12, pp. 3159–3171, 2006.

M. Shaked, and J. G. Shanthikumar, Stochastic Orders and Their Applications, Academic Press, New York, 1994.

C. E. Shannon, A mathematical theory of communication, Bell System Technical Journal, vol. 27, 379–432, 1948.

S.M. Sunoj, P. G. Sankaran, S. S. Maya, Characterization of life distribution using conditional exceptations of doubly (Interval) truncated random variables, Communications in Statistics: Theory and Methods, vol. 38, no. 9, pp.1441–1452, 2009.

R. S. Verma, Generalization of Renyi’s entropy of order α, Journal of Mathematical Sciences, vol. 1, pp. 34–48, 1966.

S. Treanta Optimization on the distribution of population densities and the arrangement of urban activities, Statistics, Optimization and Information Computing, vol.6, pp. 208-218, 2018.

C. Kundu, On weighted measure of inaccuracy for doubly truncated random variables, Communication in Statistics: Theory and Methods, vol.46, pp. 3135–3147, 2017.

S. Kayal, and R. Moharana, Some Results on a doubly truncated generalized discrimination measure. 46, 3135-3147., Applications of mathematics, vol.5, pp. 585–605, 2016.

Published
2018-11-02
How to Cite
Kumar, V., & Singh, N. (2018). Characterization of Lifetime Distribution Based on Generalized Interval Entropy. Statistics, Optimization & Information Computing, 6(4), 547-559. https://doi.org/10.19139/soic.v6i4.328
Issue
Vol 6 No 4 (2018)
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).