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Log‐concave and concave distributions in reliability

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  • Debasis Sengupta
  • Asok K. Nanda

Abstract

Nonparametric classes of life distributions are usually based on the pattern of aging in some sense. The common parametric families of life distributions also feature monotone aging. In this paper we consider the class of log‐concave distributions and the subclass of concave distributions. The work is motivated by the fact that most of the common parametric models of life distributions (including Weibull, Gamma, log‐normal, Pareto, and Gompertz distributions) are log‐concave, while the remaining life of maintained and old units tend to have a concave distribution. The classes of concave and log‐concave distributions do not feature monotone aging. Nevertheless, these two classes are shown to have several interesting and useful properties. We examine the closure of these classes under a number of reliability operations, and provide sharp reliability bounds for nonmaintained and maintained units having life distribution belonging to these classes. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 419–433, 1999

Suggested Citation

  • Debasis Sengupta & Asok K. Nanda, 1999. "Log‐concave and concave distributions in reliability," Naval Research Logistics (NRL), John Wiley & Sons, vol. 46(4), pages 419-433, June.
    • Handle: RePEc:wly:navres:v:46:y:1999:i:4:p:419-433
    DOI: 10.1002/(SICI)1520-6750(199906)46:43.0.CO;2-B
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    Cited by:

    1. John D. Rice & Brent A. Johnson & Robert L. Strawderman, 2022. "Screening for chronic diseases: optimizing lead time through balancing prescribed frequency and individual adherence," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 28(4), pages 605-636, October.
    2. Ghobad Barmalzan & Narayanaswamy Balakrishnan & Hadi Saboori, 2019. "Characterizations of Proportional Hazard and Reversed Hazard Rate Models Based on Symmetric and Asymmetric Kullback-Leibler Divergences," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 81(1), pages 26-38, June.

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