Abstract
We introduce a new test for exponentiality against decreasing (increasing) mean residual life alternatives based on a cumulative residual Renyi’s entropy of order α. The exact and asymptotic distributions of the test statistic are given. The performance of the proposed test statistic is compared with other constructed tests in the literature using a simulation study. Finally, some numerical examples illustrating the theory are given.
References
[1] A. M. Abouammoh and A. Khalique, Some tests for mean residual life criteria based on the total time on test transform, Reliab. Eng. 19 (1987), 85–101. 10.1016/0143-8174(87)90104-1Suche in Google Scholar
[2] S. E. Abu-Youssef, A moment inequality for decreasing (increasing) mean residual life distributions with hypothesis testing application, Statist. Probab. Lett. 57 (2002), no. 2, 171–177. 10.1016/S0167-7152(02)00045-7Suche in Google Scholar
[3] I. A. Ahmad, A new test for mean residual life times, Biometrika 79 (1992), no. 2, 416–419. 10.1093/biomet/79.2.416Suche in Google Scholar
[4] I. A. Ahmad and A. R. Mugdadi, Further moments inequalities of life distributions with hypothesis testing applications: The IFRA, NBUC and DMRL classes, J. Statist. Plann. Inference 120 (2004), no. 1–2, 1–12. 10.1016/S0378-3758(02)00493-7Suche in Google Scholar
[5] E.-E. A. A. Aly, Tests for monotonicity properties of the mean residual life function, Scand. J. Statist. 17 (1990), no. 3, 189–200. Suche in Google Scholar
[6] M. Z. Anis, On testing exponentiality against DMRL alternatives, Econ. Qual. Control 25 (2010), no. 2, 281–299. 10.1515/eqc.2010.020Suche in Google Scholar
[7] D. Bandyopadhyay and A. P. Basu, A class of tests for exponentiality against decreasing mean residual life alternatives, Comm. Statist. Theory Methods 19 (1990), no. 3, 905–920. 10.1080/03610929008830238Suche in Google Scholar
[8] F. Belzunce, J. Candel and J. M. Ruiz, Testing mean residual alternatives by dispersion of residual lives, J. Statist. Plann. Inference 86 (2000), no. 1, 113–127. 10.1016/S0378-3758(99)00167-6Suche in Google Scholar
[9] F. Belzunce, J. F. Pinar and J. M. Ruiz, On testing the dilation order and HNBUE alternatives, Ann. Inst. Statist. Math. 57 (2005), no. 4, 803–815. 10.1007/BF02915440Suche in Google Scholar
[10] M. C. Bryson and M. M. Siddiqui, Some criteria for aging, J. Amer. Statist. Assoc. 64 (1969), 1472–1483. 10.1080/01621459.1969.10501072Suche in Google Scholar
[11] J. M. Fernández-Ponce, R. Infante-Macías and J. Muñoz Pérez, Characterization of lifetime distributions based on a quantile dispersion measure, Comput. Statist. Data Anal. 21 (1996), no. 5, 547–561. 10.1016/0167-9473(96)82295-XSuche in Google Scholar
[12] M. Hollander and F. Proschan, Tests for the mean residual life, Biometrika 62 (1975), no. 3, 585–593. 10.1093/biomet/62.3.585Suche in Google Scholar
[13] E. L. Kaplan and P. Meier, Nonparametric estimation from incomplete observations, J. Amer. Statist. Assoc. 53 (1958), no. 282, 457–481. 10.1007/978-1-4612-4380-9_25Suche in Google Scholar
[14] C.-D. Lai and M. Xie, Stochastic Ageing and Dependence for Reliability, Springer, New York, 2006. Suche in Google Scholar
[15] X. Li, W. Cao and X. Feng, A new test procedure for decreasing mean residual life, Comm. Statist. Theory Methods 35 (2006), no. 12, 2171–2183. 10.1080/03610920600854462Suche in Google Scholar
[16] J. H. Lim and J. S. Koh, On testing monotonicity of mean residual life from randomly censored data, ETRI J. 18 (1996), no. 3, 207–213. 10.4218/etrij.96.0196.0038Suche in Google Scholar
[17] E. Lorenzo, G. Malla and H. Mukerjee, A new test for decreasing mean residual lifetimes, Comm. Statist. Theory Methods 47 (2018), no. 12, 2805–2812. 10.1080/03610926.2014.985841Suche in Google Scholar
[18] F. Proschan, Theoretical explanation of observed decreasing failure rate, Technometrics 5 (1963), 375–383. 10.1080/00401706.1963.10490105Suche in Google Scholar
[19] S. M. Stigler, Linear functions of order statistics with smooth weight functions, Ann. Statist. 2 (1974), 676–693. 10.1214/aos/1176342756Suche in Google Scholar
[20] S. M. Sunoj and M. N. Linu, Dynamic cumulative residual Renyi’s entropy, Statistics 46 (2012), no. 1, 41–56. 10.1080/02331888.2010.494730Suche in Google Scholar
© 2022 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- On Generalized Reflected BSDEs with Rcll Obstacle
- Estimations of Means and Variances in a Markov Linear Model
- Impact of Financial Crisis on Economic Growth: A Stochastic Model
- A Study on Some Properties of Dynamic Survival Extropy and Its Relation to Economic Measures
- Test for Decreasing Mean Residual Lifetimes Based on the Cumulative Residual Renyi’s Entropy
- Multiple Dependent State Sampling Inspection Plan for Lindley Distributed Quality Characteristic
- The SPRT Sign Chart for Process Dispersion
Artikel in diesem Heft
- Frontmatter
- On Generalized Reflected BSDEs with Rcll Obstacle
- Estimations of Means and Variances in a Markov Linear Model
- Impact of Financial Crisis on Economic Growth: A Stochastic Model
- A Study on Some Properties of Dynamic Survival Extropy and Its Relation to Economic Measures
- Test for Decreasing Mean Residual Lifetimes Based on the Cumulative Residual Renyi’s Entropy
- Multiple Dependent State Sampling Inspection Plan for Lindley Distributed Quality Characteristic
- The SPRT Sign Chart for Process Dispersion