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A new class of distribution functions for lifetime data

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  • Domma, Filippo
  • Condino, Francesca

Abstract

This paper deals with the issue of building a parametric model from the empirical and/or qualitative information about the hazard rate. We propose a new class of models for survival data analysis. This class is characterized by a distribution function which includes, in its expression, a function that defines the sign of the first derivative of a monotonic transformation of the hazard rate. We show that certain parametric models used in survival analysis belong to the proposed class. Finally, by using the proposed method, we build two new distributions which allow us to achieve a highly flexible hazard rate. The first one is based on an m-degree polynomial and allows us to get BT, IFR and UBT-BT hazard rates, while the second, based on trigonometric functions, enables us to obtain monotonically increasing or decreasing hazard rates or hazard rates with a non-monotonic behavior. The usefulness of the new method is illustrated through two applications to real data.

Suggested Citation

  • Domma, Filippo & Condino, Francesca, 2014. "A new class of distribution functions for lifetime data," Reliability Engineering and System Safety, Elsevier, vol. 129(C), pages 36-45.
    • Handle: RePEc:eee:reensy:v:129:y:2014:i:c:p:36-45
    DOI: 10.1016/j.ress.2014.04.026
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    1. Mark Bagnoli & Ted Bergstrom, 2006. "Log-concave probability and its applications," Studies in Economic Theory, in: Charalambos D. Aliprantis & Rosa L. Matzkin & Daniel L. McFadden & James C. Moore & Nicholas C. Yann (ed.), Rationality and Equilibrium, pages 217-241, Springer.
    2. T. Addison, John & Portugal, Pedro, 1998. "Some specification issues in unemployment duration analysis," Labour Economics, Elsevier, vol. 5(1), pages 53-66, March.
    3. Obereder, Andreas & Scherzer, Otmar & Kovac, Arne, 2007. "Bivariate density estimation using BV regularisation," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 5622-5634, August.
    4. Eilers, Paul H.C. & Borgdorff, M.W., 2007. "Non-parametric log-concave mixtures," Computational Statistics & Data Analysis, Elsevier, vol. 51(11), pages 5444-5451, July.
    5. Denis Conniffe, 2007. "The Generalised Extreme Value Distribution as Utility Function," The Economic and Social Review, Economic and Social Studies, vol. 38(3), pages 275-288.
    6. Singh, S K & Maddala, G S, 1976. "A Function for Size Distribution of Incomes," Econometrica, Econometric Society, vol. 44(5), pages 963-970, September.
    7. Chen, Zhenmin, 2000. "A new two-parameter lifetime distribution with bathtub shape or increasing failure rate function," Statistics & Probability Letters, Elsevier, vol. 49(2), pages 155-161, August.
    8. Jiang, R., 2013. "A new bathtub curve model with a finite support," Reliability Engineering and System Safety, Elsevier, vol. 119(C), pages 44-51.
    9. Francisco Louzada-Neto, 1999. "Polyhazard Models for Lifetime Data," Biometrics, The International Biometric Society, vol. 55(4), pages 1281-1285, December.
    10. Joost M.E. Pennings & Philip Garcia, 2009. "The informational content of the shape of utility functions: financial strategic behavior," Managerial and Decision Economics, John Wiley & Sons, Ltd., vol. 30(2), pages 83-90.
    11. Gauss Cordeiro & Cláudio Cristino & Elizabeth Hashimoto & Edwin Ortega, 2013. "The beta generalized Rayleigh distribution with applications to lifetime data," Statistical Papers, Springer, vol. 54(1), pages 133-161, February.
    12. A. Azzalini & A.W. Bowman, 1990. "A Look at Some Data on the Old Faithful Geyser," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 39(3), pages 357-365, November.
    13. Laurent Bordes & Céline Delmas & Pierre Vandekerkhove, 2006. "Semiparametric Estimation of a Two‐component Mixture Model where One Component is known," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 33(4), pages 733-752, December.
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    Cited by:

    1. Zeng, Hongtao & Lan, Tian & Chen, Qiming, 2016. "Five and four-parameter lifetime distributions for bathtub-shaped failure rate using Perks mortality equation," Reliability Engineering and System Safety, Elsevier, vol. 152(C), pages 307-315.
    2. Shakhatreh, Mohammed K. & Lemonte, Artur J. & Moreno–Arenas, Germán, 2019. "The log-normal modified Weibull distribution and its reliability implications," Reliability Engineering and System Safety, Elsevier, vol. 188(C), pages 6-22.
    3. Yihai He & Linbo Wang & Zhenzhen He & Xun Xiao, 2016. "Modelling infant failure rate of electromechanical products with multilayered quality variations from manufacturing process," International Journal of Production Research, Taylor & Francis Journals, vol. 54(21), pages 6594-6612, November.

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