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Parametric Distributions for Survival and Reliability Analyses, a Review and Historical Sketch

Author

Listed:
  • Nanami Taketomi

    (Biostatistics Center, Kurume University, Kurume 830-0011, Japan)

  • Kazuki Yamamoto

    (Biostatistics Center, Kurume University, Kurume 830-0011, Japan)

  • Christophe Chesneau

    (Department of Mathematics, University of Caen Normandie, 14000 Caen, France)

  • Takeshi Emura

    (Biostatistics Center, Kurume University, Kurume 830-0011, Japan)

Abstract

During its 330 years of history, parametric distributions have been useful for survival and reliability analyses. In this paper, we comprehensively review the historical backgrounds and statistical properties of a number of parametric distributions used in survival and reliability analyses. We provide encyclopedic coverage of the important parametric distributions, which is more extensive than the existing textbooks on survival and reliability analyses. We also explain how these distributions have been adopted in survival and reliability analyses with original and state-of-the-art references. We cover the exponential, Weibull, Rayleigh, lognormal, log-logistic, gamma, generalized gamma, Pareto (types I, II, and IV), Hjorth, Burr (types III and XII), Dagum, exponential power, Gompertz, Birnbaum-Saunders, exponential-logarithmic, piecewise exponential, generalized exponential, exponentiated Weibull, generalized modified Weibull, and spline distributions. We analyze a real dataset for illustration.

Suggested Citation

  • Nanami Taketomi & Kazuki Yamamoto & Christophe Chesneau & Takeshi Emura, 2022. "Parametric Distributions for Survival and Reliability Analyses, a Review and Historical Sketch," Mathematics, MDPI, vol. 10(20), pages 1-23, October.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:20:p:3907-:d:949323
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