A measure of discrimination between two residual life-time distributions and its applications
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A measure of discrepancy between two residual-life distributions is proposed on the basis of Kullback-Leibler discrimination information. Properties of this measure are studied and the minimum discrimination principle is applied to obtain the proportional hazards model.
Key words and phrasesHazard function cumulative hazard function mean residual lifetime function NBU IFR Kullback-Leibler discrimination information MDI principle
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- Akaike, H. (1973). Information theory and an extension of the maximum likelihood principle, 2nd International Symposium on Information Theory (eds. B. N.Petrov and F.Csáki), 267–281, Akadémiai Kiádo, Budapest.Google Scholar
- Cox, D. R. (1959). The analysis of exponentially distributed life-times with two types of failure, J. Roy. Statist. Soc. Ser. B, 21, 411–421.Google Scholar
- Ebrahimi, N. and Kirmani, S. N. U. A. (1995). A characterization of the proportional hazards model through a measure of discrimination between two residual life distribution, Biometrika (to appear).Google Scholar
- Ebrahimi, N., Habibullah, M. and Soofi, E. S. (1992). Testing exponentiality based on Kullback-Leibler information, J. Roy. Statist. Soc. Ser. B, 54, 739–748.Google Scholar
- Efron, B. (1981). Censored data and the bootstrap, J. Amer. Statist. Assoc., 76, 312–319.Google Scholar
- Guiasu, S. (1990). A classification of the main probability distributions by minimizing weighted logarithmic meausure of deviation, Ann. Inst. Statist. Math., 42, 269–279.Google Scholar
- Kullback, S. (1954). Certain inequalities in information theory and the Cramér-Rao inequality, Ann. Math. Statist., 25, 745–751.Google Scholar
- Kullback, S. (1959). Information Theory and Statistics, Wiley, New York.Google Scholar
- Kullback, S. and Leibler, R. A. (1951). On information and sufficiency, Ann. Math. Statist., 22, 79–86.Google Scholar