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A flexible parametric survival model which allows a bathtub-shaped hazard rate function

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  • William J. Reed

Abstract

A new parametric (three-parameter) survival distribution, the lognormal--power function distribution, with flexible behaviour is introduced. Its hazard rate function can be either unimodal, monotonically decreasing or can exhibit a bathtub shape. Special cases include the lognormal distribution and the power function distribution, with finite support. Regions of parameter space where the various forms of the hazard-rate function prevail are established analytically. The distribution lends itself readily to accelerated life regression modelling. Applications to five data sets taken from the literature are given. Also it is shown how the distribution can behave like a Weibull distribution (with negative aging) for certain parameter values.

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  • William J. Reed, 2011. "A flexible parametric survival model which allows a bathtub-shaped hazard rate function," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(8), pages 1665-1680, August.
    • Handle: RePEc:taf:japsta:v:38:y:2011:i:8:p:1665-1680
    DOI: 10.1080/02664763.2010.516388
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    1. Stephen W. Lagakos & Thomas A. Louis, 1988. "Use of Tumour Lethality to Interpret Tumorigenicity Experiments Lacking Cause‐Of‐Death Data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 37(2), pages 169-179, June.
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    1. Lemonte, Artur J., 2013. "A new exponential-type distribution with constant, decreasing, increasing, upside-down bathtub and bathtub-shaped failure rate function," Computational Statistics & Data Analysis, Elsevier, vol. 62(C), pages 149-170.
    2. David E. Giles, 2012. "A Note on Improved Estimation for the Topp-Leone Distribution," Econometrics Working Papers 1203, Department of Economics, University of Victoria.
    3. Manoj Kumar Rastogi & Yogesh Mani Tripathi & Shuo-Jye Wu, 2012. "Estimating the parameters of a bathtub-shaped distribution under progressive type-II censoring," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(11), pages 2389-2411, July.
    4. Rouby, Etienne & Authier, Matthieu & Cam, Emmanuelle & Siebert, Ursula & Plard, Floriane, 2024. "Addressing temporal trends in survivorship from cross-sectional sampling designs: A modelling framework with applications for megafauna conservation," Ecological Modelling, Elsevier, vol. 490(C).
    5. C. Satheesh Kumar & S. Dharmaja, 2014. "On some properties of Kies distribution," METRON, Springer;Sapienza Università di Roma, vol. 72(1), pages 97-122, April.
    6. Worku B. Ewnetu & Irène Gijbels & Anneleen Verhasselt, 2023. "Flexible two-piece distributions for right censored survival data," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 29(1), pages 34-65, January.

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