Startseite Mathematik A goodness-of-fit test for testing exponentiality based on normalized dynamic survival extropy
Artikel
Lizenziert
Nicht lizenziert Erfordert eine Authentifizierung

A goodness-of-fit test for testing exponentiality based on normalized dynamic survival extropy

  • Gaurav Kandpal EMAIL logo und Nitin Gupta
Veröffentlicht/Copyright: 9. Juni 2025
Veröffentlichen auch Sie bei De Gruyter Brill

Abstract

An updated version of the cumulative residual extropy (CRJ) with some dynamic features is introduced in this study as normalized dynamic survival extropy (NDSE). We observe that NDSE grabs attention in the reliability theory also, since NDSE of the relevant random variable in the age replacement model is always equal to the CRJ of that variable. This paper proposes an NDSE based non-parametric test that can be used to see if a data set follows an exponential trend. The proposed test makes itself unique due to its exact distribution of test statistics, scale invariant property, consistency, asymptotic normality, great power and simplicity in calculation. Being aware of the problem of censored observation, we explained how our test will be applied to it. We also provide an extensive power comparison with 5 different tests, each taking different alternatives, and a few real-life examples.


Gaurav Kandpal would like to acknowledge financial support from the University Grant Commission, Government of India (Student ID: 221610071232).


Acknowledgement

The authors are thankful to reviewers for carefully checking the mathematical accuracy of the manuscript.

  1. (Communicated by Gejza Wimmer)

References

[1] Abbasnejad, M.—Arghami, N. R.—Tavakoli, M.: A goodness-of-fit test for exponentiality based on Lin-Wong information, J. Iran. Stat. Soc. 11 (2012), 191–202.Suche in Google Scholar

[2] Abushal, T.: Estimation of the unknown parameters for the compound rayleigh distribution based on progressive first-failure-censored sampling, Open J. Stat. 1 (2011), 161–171.10.4236/ojs.2011.13020Suche in Google Scholar

[3] Baratpour, S.—Rad, A. H.: Testing goodness-of-fit for exponential distribution based on cumulative residual entropy, Comm. Statist. Theory Methods 41 (2012), 1387–1396.10.1080/03610926.2010.542857Suche in Google Scholar

[4] Baringhaus, L.—Henze, N.: A class of consistent tests for exponentiality based on the empirical Laplace transform, Ann. Inst. Stat. Math. 43 (1991), 551–664.10.1007/BF00053372Suche in Google Scholar

[5] Baringhaus, L.—Henze, N.: Tests of fit for exponentiality based on a characterization via the mean residual life function, Stat. Papers 41 (2000), 225–236.10.1007/BF02926105Suche in Google Scholar

[6] Baringhaus, L.—Henze, N.: A new weighted integral goodness-of-fit statistic for exponentiality, Stat. Probab. Lett. 78 (2008), 1006–1016.10.1016/j.spl.2007.09.060Suche in Google Scholar

[7] Barlow, R. E.—Proschan, F.: Mathematical Theory of Reliability, SIAM, 1996.10.1137/1.9781611971194Suche in Google Scholar

[8] Box, G. E.: Some theorems on quadratic forms applied in the study of analysis of variance problems, I. Effect of inequality of variance in the one-way classification, Ann. Math. Stat. 25 (1954), 290–302.10.1214/aoms/1177728786Suche in Google Scholar

[9] Choi, B.—Kim, K.—Song, S. H.: Goodness-of-fit test for exponentiality based on Kullback–Leibler information, Comm. Statist. Simulation Comput. 33 (2004), 525–536.10.1081/SAC-120037250Suche in Google Scholar

[10] Datta, S.—Bandyopadhyay, D.—Satten, G. A.: Inverse probability of censoring weighted U-statistics for right-censored data with an application to testing hypotheses, Scand. J. Stat. 37 (2010), 680–700.10.1111/j.1467-9469.2010.00697.xSuche in Google Scholar

[11] Deshpande, V. J.: A class of tests for exponentiality against increasing failure rate average alternatives, Biometrika 70 (1983), 514–518.10.1093/biomet/70.2.514Suche in Google Scholar

[12] Dube, S.—Pradhan, B.—Kundu, D.: Parameter estimation of the hybrid censored log-normal distribution, J. Stat. Comput. Simul. 81 (2011), 275–287.10.1080/00949650903292650Suche in Google Scholar

[13] Epps, T. W.—Pulley, L. B.: A test of exponentiality vs. monotone hazard alternatives derived from the empirical characteristic function, J. R. Stat. Soc. B 48 (1986), 206–213.10.1111/j.2517-6161.1986.tb01403.xSuche in Google Scholar

[14] Finkelstein, J. M.—Schafer, R. E.: Improved goodness-of-fit tests, Biometrika 58 (1971), 641–645.10.1093/biomet/58.3.641Suche in Google Scholar

[15] Gail, M. H.—Gastwirth, J. L.: A scale-free goodness-of-fit test for the exponential distribution based on the Gini statistic, J. R. Stat. Soc. B 40 (1978), 350–357.10.1111/j.2517-6161.1978.tb01048.xSuche in Google Scholar

[16] Gnedenko, B. V.—Belyayev, Y. U. K.—Solovyev, A. D.: Mathematical Models of Reliability Theory, Academic Press, London, 1969.Suche in Google Scholar

[17] Harris, C. M.: A note on testing for exponentiality, Nav. Res. Logist. Q. 23 (1976), 169–175.10.1002/nav.3800230116Suche in Google Scholar

[18] Henze, N.: A new flexible class of omnibus tests for exponentiality, Comm. Statist. Theory Methods 22 (1993), 115–133.10.1080/03610929308831009Suche in Google Scholar

[19] Henze, N.—Klar, B.: Testing exponentiality against the L class of life distributions, Math. Methods Stat. 10 (2001), 232–246.Suche in Google Scholar

[20] Jahanshahi, S.—Zarei, H.—Khammar, A.: On cumulative residual extropy, Probab. Engrg. Inform. Sci. 34 (2020), 605–625.10.1017/S0269964819000196Suche in Google Scholar

[21] Jaynes, E. T.: Information theory and statistical mechanics, Phys. Rev. 106 (1957), 620–630.10.1103/PhysRev.106.620Suche in Google Scholar

[22] Kasilingam, D.—Sathiya Prabhakaran, S. P.—Rajendran, D. K.—Rajagopal, V.—Santhosh Kumar, T.—Soundararaj, A.: Exploring the growth of Covid-19 cases using exponential modelling across 42 countries and predicting signs of early containment using machine learning, Transboundary and Emerging Diseases 68(3) (2021), 1001–1018.10.1111/tbed.13764Suche in Google Scholar PubMed PubMed Central

[23] Kattumannil, S. K.—Anisha, P.: A simple non-parametric test for decreasing mean time to failure, Statist. Papers 60 (2019), 73–87.10.1007/s00362-016-0827-ySuche in Google Scholar

[24] Kayid, M.—Ahmad, I. A.—Izadkhah, S.—Abouammoh, A. M.: Further results involving the mean time to failure order, and the decreasing mean time to failure class, IEEE Transactions on Reliability 62 (2013), 670–678.10.1109/TR.2013.2270423Suche in Google Scholar

[25] Koul, H. L.—Susarla, V.: Testing for new better than used in expectation with incomplete data, J. Amer. Statist. Assoc. 75 (1980), 952–956.10.1080/01621459.1980.10477578Suche in Google Scholar

[26] Koul, H.—Susarla, V.—Van Ryzin, J.: Regression analysis with randomly right-censored data, Annals Statist. 9 (1981), 1276–1288.10.1214/aos/1176345644Suche in Google Scholar

[27] Lad, F.—Sanfilippo, G.—Agrò, G.: Extropy: Complementary dual of entropy, Statist. Sci. 30 (2015), 40–58.10.1214/14-STS430Suche in Google Scholar

[28] Lawless, J. F.: Statistical Models and Methods for Lifetime Data, John Wiley & Sons, 2011.Suche in Google Scholar

[29] Lehmann, E. L.: Consistency and unbiasedness of certain nonparametric tests, The Annals of Mathematical Statistics 22 (1951), 165–179.10.1214/aoms/1177729639Suche in Google Scholar

[30] Ossai, E. O.—Madukaife, M. S.—Oladugba, A. V.: A review of tests for exponentiality with Monte Carlo comparisons, J. Appl. Stat. 49(5) (2020), 1277–1304.10.1080/02664763.2020.1854202Suche in Google Scholar PubMed PubMed Central

[31] Proschan, F.: Theoretical explanation of observed decreasing failure rate, Technometrics 5 (1963), 375–383.10.1080/00401706.1963.10490105Suche in Google Scholar

[32] Rotnitzky, A.—Robins, J.: Inverse probability weighted estimation in survival analysis, Encyclopedia of Biostatistics 4 (2005), 2619–2625.10.1002/0470011815.b2a11040Suche in Google Scholar

[33] Sathar, E. A.—Nair, D. R.: On dynamic failure extropy, J. Indian Soc. Probab. Stat. 21 (2020), 287–313.10.1007/s41096-020-00083-xSuche in Google Scholar

[34] Sathar, E. A.—Nair, D. R.: On dynamic survival extropy, Comm. Statist. Theory Methods 50 (2021), 1295–1313.10.1080/03610926.2019.1649426Suche in Google Scholar

[35] Shannon, C. E.: A mathematical theory of communications, Bell Syst. Tech. J. 27 (1948), 379–423.10.1002/j.1538-7305.1948.tb01338.xSuche in Google Scholar

[36] Soest, J. V.: Some goodness of fit tests for exponential distributions, Stat. Neerl. 23 (1969), 41–51.10.1111/j.1467-9574.1969.tb00072.xSuche in Google Scholar

[37] Zardasht, V.—Parsi, S.—Mousazadeh, M.: On empirical cumulative residual entropy and a goodness-of-fit test for exponentiality, Statistical Papers 56 (2015), 677–688.10.1007/s00362-014-0603-9Suche in Google Scholar

[38] Zhao, H.—Tsiatis, A. A.: Estimating mean quality adjusted lifetime with censored data, Sankhya B 62 (2000), 175–188.Suche in Google Scholar

Received: 2024-10-01
Accepted: 2024-12-24
Published Online: 2025-06-09
Published in Print: 2025-06-26

© 2025 Mathematical Institute Slovak Academy of Sciences

Heruntergeladen am 16.12.2025 von https://www.degruyterbrill.com/document/doi/10.1515/ms-2025-0050/pdf?lang=de
Button zum nach oben scrollen