Login | Register

Survival Distributions with Bathtub Shaped Hazard: A New Distribution Family


Survival Distributions with Bathtub Shaped Hazard: A New Distribution Family

Chaubey, Yogendra P. and Zhang, Rui (2013) Survival Distributions with Bathtub Shaped Hazard: A New Distribution Family. Technical Report. Concordia University, Department of Mathematics & Statistics, Montreal, Quebec.

[thumbnail of 1-13.pdf]
Text (application/pdf)


In this article we introduce an extension of Chen’s (2000) family of distributions given by Lehman alternatives [see Gupta et al.(1998)] that is shown to present another alternative to the generalized Weibull and exponentiated Weibull families for modeling survival data. The extension proposed here can be seen as the extension to the Chen’s distribution as the exponentiated Weibull is to the Weibull. A structural analysis of the density function in terms of tail classification and extremes is carried out similar to that of generalized Weibull family carried
out in Mudholkar and Kollia (1994). The new model is also seen to fit well to the flood data used in fitting the exponentiated Weibull model in Mudholkar and Hutson (1996).

Divisions:Concordia University > Faculty of Arts and Science > Mathematics and Statistics
Item Type:Monograph (Technical Report)
Authors:Chaubey, Yogendra P. and Zhang, Rui
Series Name:Department of Mathematics & Statistics, Technical Report No. 1/13
Corporate Authors:Concordia University, Department of Mathematics & Statistics
Institution:Concordia University
Date:November 2013
ID Code:978281
Deposited On:24 Feb 2014 14:27
Last Modified:18 Jan 2018 17:46


[1] Aarset, M. V.(1987). How to identify bathtub hazard rate, IEEE Trans. Reliability R-36, 106-108.
[2] Barlow, Richard E. and Campo, R. (1975). Total time on test processes and applications to failure data analysis. In Reliability and fault tree analysis (Eds.: R.E. Barlow, J. B. Fussell and N. D. Singpurwalla), SIAM, Philadelphia, 451–481.
[3] Bergman, B. and Klefsjo, B. (1984). The total time on test concept and its use in reliability theory., Operations Research 32, 596-606.
[4] Bergman, B. and Klefsjo, B. (1985). Burn-in models and TTT transforms. Qual. and Reliab. Int. 1, 125-130.
[5] Bourguignon, M., Silva, R.B. and Cordeiro, G.M. (2014). The Weibull-G Family of Probability Distributions. J. Data Sc. 12, 53–68.
[6] Burnham, K.P. and Anderson, D.R. (2002). Model Selection and Multimodel Inference: A Practical Information-Theoretic Approach (2nd ed.), Springer-Verlag, Berlin.
[7] Chen, Z. (2000). A new two-parameter lifetime distribution with bathtub shape or increasing failure rate function. Stat. & Prob. Lett. 49, 155-161.
[8] Davison, A.C. and Hinkley, D.V. (1997). Bootstrap Methods and Their Application, Cambridge University Press, London.
[9] Efron, B. and Tibshirani, R. (1985). Bootstrap Methods for Standard Errors, Confidence Intervals, and Other Measures fo Statistical Accuracy, Statistical Science
1, 54-77.
[10] Friemer, M., Mudholkar, G.S., Kollia, G. and Lin, C.T. (1988). A study of the generalized Tukey lambda family, Commun. Statist.-Theory Meth. 17(10), 3547-3567.
[11] Friemer, M., Mudholkar, G.S., Kollia, G. and Lin, C.T. (1989). Extremes, extreme spacings and outliers in the Tukey andWeibull families, Commun. Statist.-Theory Meth. 18(11), 4261-4274.
[12] Gupta, R.D. and Kundu, D. (1999). Generalized exponential distributions. Austr. NZ. Jour. Stat. 41, 17–188.
[13] Gupta, R.C., Gupta, P.L. and Gupta, R.D. (1998). Modeling failure time data by Lehman alternatives. Comm. Statist. Theory – Methods 27, 887-904.
[14] Gurvich, M.R., DiBenedetto, A.T. and Ranade, S.V. (1997). A new statistical distribution for characterizing the random strength of brittle materials. Journal of
Materials Science 32, 2559–2564.
[15] Johnson, N.L., Kotz, S. and Balakrishnan, N. (1994). Continuous Univariate Distributions, Vol. 1 (2nd Ed.), Wiley, New York.
[16] Marshall, A.W. and Olkin, I. (1997). A new method for adding a parameter to a family of distributions with applications to exponential and Weibull families. Biometrika 84, 641–652.
[17] Mudholkar, G.S. and Hutson, A.D. (1996). The exponentiated weibull family: some properties and a flood data application, Commun. Statist.-Theory Meth. 25, 3059-3083.
[18] Mudholkar, G.S., Kollia, G.D. (1994). Generalized Weibull family: a structural analysis. Comm. Statist. Theory – Methods 23, 1149–1171.
[19] Mudholkar, G.S., Kollia, G.D., Lin, C.T. and Patel, K.R. (1991). A graphical procedure for comparing goodness-of-fit tests. J. Roy. Statist. Soc. Ser. B 53, 221–
[20] Mudholkar, G.S. and Srivastava, D.K. (1993). Exponentiated Weibull family for analyzing bathtub failure-rate data, IEEE Trans. Reliab. 42, 209-302.
[21] Mudholkar, G.S., Srivastava, D.K. and Kollia, G.D. (1996). A generalization of the Weibull distribution with application to the analysis of survival data. J. Amer.
Statist. Assoc. 91, 1575-1583.
[22] Murthy, D.N.P., Xie, M. and Jiang, R. (2003). Weibull Models, Hoboken, NJ, USA.
[23] Nadarajah, S. (2009). Bathtub-shaped failure rate functions. Qual. Quant. 43, 855–863.
[24] Nadarajah, S., Cordeiro, G.M. and Ortega, E.M.M. (2013). The exponentiated Weibull distribution: A survey. Stat. Papers 54, 839-877.
[25] Nadarajah, S. and Kotz, S. (2006). The exponentiated type distributions. Acta Appl. Math. 92, 97–111.
[26] Pappas, V., Adamaidis, K. and Loukas, S. (2012). A family of lifetime distributions. Int. J. Qual., Stat. Rel. 2012, Article ID: 760-687.
[27] Parzen, E. (1979). Nonparametric statistical data modelling. Journal of the American Statistical Association 74, 105–131.
[28] Rajarshi, S. and Rajarshi, M.B. (1988). Bathtub distributions: A review. Comm. Stat. – Theor. Methods 17, 2597–2621.
[29] Schuster, E.F. (1984). Classification of probability laws by tail behavior. Jour. Amer. Statist. Assoc. 79, 936-939.
[30] Smith, R.M. and Bain, L.J.(1975). An exponential power life-testing distribution. Comm. Statist. 4, 469-481.
[31] Tang, Y., Xie, M. and Goh, T.N. (2003). Statistical Analysis of a Weibull Extension Model. Comm. Statist. Theory – Methods 32, 913–928.
[32] Weibull, W. (1951). A statistical distribution function of wide applicability. J. Appl. Mech.-Trans. ASME 18, 293–297.
[33] Xie, M., Tang, Y. and Goh, T.N. (2002). A modified Weibull extension with bathtub failure rate function. Reliab. Eng. System Saf. 76,279–285.
[34] Zografos, K. and Balakrishnan, N. (2009). On families of beta- and generalized gamma-generated distributions and associated inference. Statistical Methodology 6, 344-362.
All items in Spectrum are protected by copyright, with all rights reserved. The use of items is governed by Spectrum's terms of access.

Repository Staff Only: item control page

Downloads per month over past year

Research related to the current document (at the CORE website)
- Research related to the current document (at the CORE website)
Back to top Back to top