IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v67y2004i2p173-182.html
   My bibliography  Save this article

A measure of discrimination between past lifetime distributions

Author

Listed:
  • Di Crescenzo, Antonio
  • Longobardi, Maria

Abstract

On the basis of Kullback-Leibler discrimination information and of discrimination information introduced by Ebrahimi and Kirmani (Ann. Inst. Statist. Math. 48 (1996a) 257), we propose a measure of discrepancy between past-life distributions. Some properties of this measure are studied and a characterization of the proportional reversed hazards model through such a measure is given.

Suggested Citation

  • Di Crescenzo, Antonio & Longobardi, Maria, 2004. "A measure of discrimination between past lifetime distributions," Statistics & Probability Letters, Elsevier, vol. 67(2), pages 173-182, April.
    • Handle: RePEc:eee:stapro:v:67:y:2004:i:2:p:173-182
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-7152(04)00032-X
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Crescenzo, Antonio Di, 2000. "Some results on the proportional reversed hazards model," Statistics & Probability Letters, Elsevier, vol. 50(4), pages 313-321, December.
    2. S. Kirmani & Ramesh Gupta, 2001. "On the Proportional Odds Model in Survival Analysis," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 53(2), pages 203-216, June.
    3. Nader Ebrahimi & S. Kirmani, 1996. "A measure of discrimination between two residual life-time distributions and its applications," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 48(2), pages 257-265, June.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. N. Unnikrishnan Nair & S. M. Sunoj & Rajesh G., 2023. "Relation between Relative Hazard Rates and Residual Divergence with some Applications to Reliability Analysis," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(1), pages 784-802, February.
    2. Vikas Kumar & H. Taneja, 2012. "On length biased dynamic measure of past inaccuracy," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 75(1), pages 73-84, January.
    3. Navarro, J. & Sunoj, S.M. & Linu, M.N., 2011. "Characterizations of bivariate models using dynamic Kullback-Leibler discrimination measures," Statistics & Probability Letters, Elsevier, vol. 81(11), pages 1594-1598, November.
    4. Maya, R. & Abdul-Sathar, E.I. & Rajesh, G., 2014. "Non-parametric estimation of the generalized past entropy function with censored dependent data," Statistics & Probability Letters, Elsevier, vol. 90(C), pages 129-135.
    5. K. Nair & P. Sankaran & S. Smitha, 2011. "Chernoff distance for truncated distributions," Statistical Papers, Springer, vol. 52(4), pages 893-909, November.
    6. Goel, Ritu & Taneja, H.C. & Kumar, Vikas, 2018. "Measure of entropy for past lifetime and k-record statistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 503(C), pages 623-631.
    7. Chanchal Kundu, 2015. "Generalized measures of information for truncated random variables," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 78(4), pages 415-435, May.
    8. Asadi, Majid & Ebrahimi, Nader & Soofi, Ehsan S., 2005. "Dynamic generalized information measures," Statistics & Probability Letters, Elsevier, vol. 71(1), pages 85-98, January.
    9. Sankaran, P.G. & Sunoj, S.M. & Nair, N. Unnikrishnan, 2016. "Kullback–Leibler divergence: A quantile approach," Statistics & Probability Letters, Elsevier, vol. 111(C), pages 72-79.
    10. Abbasnejad, M. & Arghami, N.R. & Morgenthaler, S. & Mohtashami Borzadaran, G.R., 2010. "On the dynamic survival entropy," Statistics & Probability Letters, Elsevier, vol. 80(23-24), pages 1962-1971, December.
    11. Parfait Munezero, 2022. "Efficient particle smoothing for Bayesian inference in dynamic survival models," Computational Statistics, Springer, vol. 37(2), pages 975-994, April.
    12. Vikas Kumar & H. Taneja & R. Srivastava, 2011. "A dynamic measure of inaccuracy between two past lifetime distributions," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 74(1), pages 1-10, July.
    13. Ramanathan Gayathri & Enchakudiyil Ibrahim Abdul Sathar, 2021. "On past geometric vitality function of order statistics," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(2), pages 263-280, February.
    14. Răzvan-Cornel Sfetcu & Sorina-Cezarina Sfetcu & Vasile Preda, 2021. "Ordering Awad–Varma Entropy and Applications to Some Stochastic Models," Mathematics, MDPI, vol. 9(3), pages 1-15, January.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Mansour Shrahili & Mohamed Kayid & Mhamed Mesfioui, 2023. "Relative Orderings of Modified Proportional Hazard Rate and Modified Proportional Reversed Hazard Rate Models," Mathematics, MDPI, vol. 11(22), pages 1-28, November.
    2. Farsam Misagh, 2016. "On Shift-Dependent Cumulative Entropy Measures," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2016, pages 1-8, June.
    3. Khan, Ruhul Ali, 2023. "Two-sample nonparametric test for proportional reversed hazards," Computational Statistics & Data Analysis, Elsevier, vol. 182(C).
    4. P. Sankaran & K. Jayakumar, 2008. "On proportional odds models," Statistical Papers, Springer, vol. 49(4), pages 779-789, October.
    5. Kundu, Debasis & Gupta, Rameshwar D., 2008. "Generalized exponential distribution: Bayesian estimations," Computational Statistics & Data Analysis, Elsevier, vol. 52(4), pages 1873-1883, January.
    6. Longxiang Fang & Narayanaswamy Balakrishnan & Wenyu Huang & Shuai Zhang, 2023. "Usual stochastic ordering of the sample maxima from dependent distribution‐free random variables," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 77(1), pages 99-112, February.
    7. Marco Capaldo & Antonio Di Crescenzo & Alessandra Meoli, 2024. "Cumulative information generating function and generalized Gini functions," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 87(7), pages 775-803, October.
    8. Weiyong Ding & Rui Fang & Peng Zhao, 2017. "Relative Aging of Coherent Systems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 64(4), pages 345-354, June.
    9. Capaldo, Marco & Di Crescenzo, Antonio & Pellerey, Franco, 2024. "Generalized Gini’s mean difference through distortions and copulas, and related minimizing problems," Statistics & Probability Letters, Elsevier, vol. 206(C).
    10. Tommaso Lando, 2022. "Testing convexity of the generalised hazard function," Statistical Papers, Springer, vol. 63(4), pages 1271-1289, August.
    11. Nanda, Asok K. & Das, Suchismita, 2012. "Stochastic orders of the Marshall–Olkin extended distribution," Statistics & Probability Letters, Elsevier, vol. 82(2), pages 295-302.
    12. Li, Xiaohu & Da, Gaofeng, 2010. "Stochastic comparisons in multivariate mixed model of proportional reversed hazard rate with applications," Journal of Multivariate Analysis, Elsevier, vol. 101(4), pages 1016-1025, April.
    13. Arindam Panja & Pradip Kundu & Biswabrata Pradhan, 2024. "Comparisons of coherent systems with active redundancy and component lifetimes following the proportional odds model," Annals of Operations Research, Springer, vol. 340(1), pages 367-387, September.
    14. Modibbo, Umar Muhammad & Arshad, Mohd. & Abdalghani, Omer & Ali, Irfan, 2021. "Optimization and estimation in system reliability allocation problem," Reliability Engineering and System Safety, Elsevier, vol. 212(C).
    15. Wang, Jiantian & Laniado, Henry, 2015. "A note on allocation policy in two-parallel–series and two-series–parallel systems with respect to likelihood ratio order," Statistics & Probability Letters, Elsevier, vol. 102(C), pages 17-21.
    16. P. Sankaran & V. Gleeja, 2008. "Proportional reversed hazard and frailty models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 68(3), pages 333-342, November.
    17. N. Unnikrishnan Nair & S. M. Sunoj & Rajesh G., 2023. "Relation between Relative Hazard Rates and Residual Divergence with some Applications to Reliability Analysis," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(1), pages 784-802, February.
    18. Laniado Rodas, Henry, 2013. "Allocation policies of redundancies in two-parallel-series and two-series-parallel systems," DES - Working Papers. Statistics and Econometrics. WS ws132622, Universidad Carlos III de Madrid. Departamento de Estadística.
    19. Abbasnejad, M. & Arghami, N.R. & Morgenthaler, S. & Mohtashami Borzadaran, G.R., 2010. "On the dynamic survival entropy," Statistics & Probability Letters, Elsevier, vol. 80(23-24), pages 1962-1971, December.
    20. Misra, Neeraj & Francis, Jisha, 2015. "Relative ageing of (n−k+1)-out-of-n systems," Statistics & Probability Letters, Elsevier, vol. 106(C), pages 272-280.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:stapro:v:67:y:2004:i:2:p:173-182. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.