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FURTHER RESULTS ON QUANTILE ENTROPY IN THE PAST LIFETIME

Part of:Distribution theory - Probability

Published online by Cambridge University Press:  27 February 2018

Guoxin Qiu
Guoxin Qiu*
Affiliation:
Department of Business Administration, School of Business, Xinhua University of Anhui, Hefei, 230088, China and Department of Statistics and Finance, School of Management, University of Science and Technology of China, Hefei, 230026, China E-mail: qiugx02@ustc.edu.cn
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Abstract

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Bounds of the quantile entropy in the past lifetime of some ageing classes are explored firstly. The quantile entropy in the past lifetime of a random variable is shown to be increasing if its expected inactivity time is increasing. Some closure properties of the less quantile entropy in the past lifetime order are obtained under the model of generalized order statistics. Moreover, sufficient conditions are given for a function of a random variable and for a weighted random variable to have more quantile entropy in the past lifetime than original random variable.

Keywords

generalized order statisticsLPQE orderquantile entropy in the past lifetimereversed hazard rateweighted distribution

MSC classification

Primary:60E15: Inequalities; stochastic orderings

Information

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 33 , Issue 1 , January 2019, pp. 146 - 159
Copyright
Copyright © Cambridge University Press 2018 

References

1.Ahmad, I.A. & Kayid, M. (2005). Characterizations of the RHR and MIT orderings and the DRHR and IMIT classes of life distributions. Probability in the Engineering and Informational Sciences 19: 447–461.Google Scholar
2.Ahmad, I.A., Kayid, M., & Pellerey, F. (2005). Further results involving the MIT order and the IMIT class. Probability in the Engineering and Informational Sciences 19: 377–395.Google Scholar
3.Ahmed, A.N., Alzaid, A., Bartoszewicz, J., & Kochar, S.C. (1986). Dispersive and superadditive ordering. Advances in Applied Probability 18: 1019–1022.Google Scholar
4.Arnold, B.C., Balakrishnan, N., & Nagaraja, H.N. (1998). A first course in order statistics. New York: Wiley.Google Scholar
5.Badia, F.G. & Berrade, M.D. (2008). On the reversed hazard rate and mean inactivity time of mixtures. In Bedford, T., Quigley, J., & Walls, L. (eds.), Advances in mathematical modeling for reliability. Glasgow, Scotland: 5th International Conference on Mathematical Methods in Reliability, pp. 103–110.Google Scholar
6.Balakrishnan, N., Cramer, E., & Kamps, U. (2001). Bounds for means and variances of progressive type II censored order statistics. Statistics and Probability Letters 54: 301–315.Google Scholar
7.Barlow, R. & Proschan, F. (1981). Statistical theory of reliability and life testing, probability model. New York: Holt, Rinehart and Winnston.Google Scholar
8.Belzunce, F., Mercader, J.A., & Ruiz, J.M. (2005). Stochastic comparisons of generalized order statistics. Probability in the Engineering and Informational Sciences 19: 99–120.Google Scholar
9.Chandra, N.K. & Roy, D. (2001). Some results on reversed hazard rate. Probability in the Engineering and Informational Sciences 15: 95–102.Google Scholar
10.Cox, D.R. & Oakes, D. (1984). Analysis of survival data. New York: Chapman and Hall.Google Scholar
11.Cramer, E., Kamps, U., & Rychlik, T. (2002). On the existence of moments of generalized order statistics. Statistics and Probability Letters 59: 397–404.Google Scholar
12.Di Crescenzo, A. & Longobardi, M. (2002). Entropy-based measure of uncertainty in past lifetime distributions. Journal of Applied Probability 39: 434–440.Google Scholar
13.Di Crescenzo, A. & Longobardi, M. (2004). A measure of discrimination between past lifetime distributions. Statistics and Probability Letters 67: 173–182.Google Scholar
14.Finkelstein, M.S. (2001). A note on some aging properties of the accelerated life model. Reliability Engineering and System Safety 71: 109–112.Google Scholar
15.Gajek, L. & Okolewski, A. (2000). Sharp bounds on moments of generalized order statistics. Metrika 52: 27–43.Google Scholar
16.Gilchrist, W. (2000). Statistical modelling with quantile functions. Boca Raton, Florida: Chapman and Hall/CRC.Google Scholar
17.Gupta, R.C. & Kirmani, S.N.U.A. (1990). The role of weighted distributions in stochastic modeling. Communications in Statistics–Theory and Methods 19: 3147–3162.Google Scholar
18.Jain, K., Singh, H., & Bagai, I. (1989). Relations for reliability measures of weighted distributions. Communications in Statistics–Theory and Methods 18: 4393–4412.Google Scholar
19.Kamps, U. (1995a). A concept of generalized order statistics. Stuttgard: Teubner, B.G.Google Scholar
20.Kamps, U. (1995b). A concept of generalized order statistics. Journal of Statistical Planning and Inference 48: 1–23.Google Scholar
21.Kang, D. (2015). Further results on closure properties of LPQE order. Statistical Methodology 25: 23–35.Google Scholar
22.Kayid, M. & Ahmad, I.A. (2004). On the mean inactivity time ordering with reliability applications. Probability in the Engineering and Informational Sciences 18: 395–409.Google Scholar
23.Kundu, C., Nanda, A.K., & Hu, T. (2009). A note on reversed hazard rate of order statistics and record values. Journal of Statistical Planning and Inference 139: 1257–1265.Google Scholar
24.Kundu, C., Nanda, A.K., & Maiti, S.S. (2010). Some distributional results through past entropy. Journal of Statistical Planning and Inference 140: 1280–1291.Google Scholar
25.Li, X. & Xu, M. (2006). Some results about MIT order and IMIT class of life distributions. Probability in the Engineering and Informational Sciences 20: 481–496.Google Scholar
26.Marshall, A.W. & Olkin, I. (2007). Life distributions. Structure of non-parametric, semi-parametric, and parametric families. Springer Series in Statistics. New York: Springer.Google Scholar
27.Nair, N.U. & Sankaran, P.G. (2009). Quantile based reliability analysis. Communications in Statistics–Theory and Methods 38: 222–232.Google Scholar
28.Nanda, A.K. & Jain, K. (1999). Some weighted distributions results on univariate and bivariate cases. Journal of Statistical Planning and Inference 77: 169–180.Google Scholar
29.Nanda, A.K. & Paul, P. (2006a). Some properties of past entropy and their applications. Metrika 64: 47–61.Google Scholar
30.Nanda, A.K. & Paul, P. (2006b). Some results on generalized past entropy. Journal of Statistical Planning and Inference 136: 3659–3674.Google Scholar
31.Nanda, A.K., Singh, H., Misra, N., & Paul, P. (2003). Reliability properties of reversed residual lifetime. Communications in Statistics–Theory and Methods 32: 2031–2042.Google Scholar
32.Rojo, J. & He, G.Z. (1991). New properties and characterizations of the dispersive ordering. Statistics and Probability Letters 11: 365–372.Google Scholar
33.Ruiz, J.M. & Navarro, J. (1996). Characterizations based on conditional expectations of the double truncated distribution. Annals of the Institute of Statistical Mathematics 48: 563–572.Google Scholar
34.Shaked, M. & Shanthikumar, J.G. (2007). Stochastic orders. New York: Springer.Google Scholar
35.Shannon, C.E. (1948). A mathematical theory of communication. The Bell System Technical Journal 27: 379–423.Google Scholar
36.Sunoj, S.M., Sankaran, P.G., & Nanda, A.K. (2013). Quantile based entropy function in past lifetime. Statistics and Probability Letters 83: 366–372.Google Scholar