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Some properties of the bivariate lognormal distribution for reliability applications

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  • Pushpa L. Gupta
  • Ramesh C. Gupta

Abstract

In this paper, we study the bivariate lognormal distribution from a reliability point of view. The conditional distribution of X given Y > y is found to be log‐skew normal. The monotonicity of the hazard rates of the univariate as well as the conditional distributions is discussed. Clayton's association measure is obtained in terms of the hazard gradient, and its value in the case of our model is derived. The probability distributions, in the case of series and parallel systems, are derived, and the monotonicity of their failure rates is discussed. Three real applications of the bivariate lognormal distribution are provided, two from financial economics and one from reliability. Copyright © 2012 John Wiley & Sons, Ltd.

Suggested Citation

  • Pushpa L. Gupta & Ramesh C. Gupta, 2012. "Some properties of the bivariate lognormal distribution for reliability applications," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 28(6), pages 598-606, November.
    • Handle: RePEc:wly:apsmbi:v:28:y:2012:i:6:p:598-606
    DOI: 10.1002/asmb.935
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    Cited by:

    1. A. James & N. Chandra & Nicy Sebastian, 2023. "Stress-strength reliability estimation for bivariate copula function with rayleigh marginals," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 14(1), pages 196-215, March.
    2. J. Navarro & M. Esna-Ashari & M. Asadi & J. Sarabia, 2015. "Bivariate distributions with conditionals satisfying the proportional generalized odds rate model," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 78(6), pages 691-709, August.

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