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Bayesian analysis of a generalized lognormal distribution

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  • Martín, J.
  • Pérez, C.J.

Abstract

Many data arising in reliability engineering can be modeled by a lognormal distribution. Empirical evidences from many sources support this argument. However, sometimes the lognormal distribution does not completely satisfy the fitting expectations in real situations. This fact motivates the use of a more flexible family of distributions with both heavier and lighter tails compared to the lognormal one, which is always an advantage for robustness. A generalized form of the lognormal distribution is presented and analyzed from a Bayesian viewpoint. By using a mixture representation, inferences are performed via Gibbs sampling. Although the interest is focused on the analysis of lifetime data coming from engineering studies, the developed methodology is potentially applicable to many other contexts. A simulated and a real data set are presented to illustrate the applicability of the proposed approach.

Suggested Citation

  • Martín, J. & Pérez, C.J., 2009. "Bayesian analysis of a generalized lognormal distribution," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 1377-1387, February.
    • Handle: RePEc:eee:csdana:v:53:y:2009:i:4:p:1377-1387
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    References listed on IDEAS

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    1. Mineo, Angelo & Ruggieri, Mariantonietta, 2005. "A Software Tool for the Exponential Power Distribution: The normalp Package," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 12(i04).
    2. Chen, Gemai, 1995. "Generalized log-normal distributions with reliability application," Computational Statistics & Data Analysis, Elsevier, vol. 19(3), pages 309-319, March.
    3. Saralees Nadarajah, 2005. "A generalized normal distribution," Journal of Applied Statistics, Taylor & Francis Journals, vol. 32(7), pages 685-694.
    4. Perez, C.J. & Martin, J. & Rufo, M.J., 2006. "MCMC-based local parametric sensitivity estimations," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 823-835, November.
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    Cited by:

    1. Sinha, Pankaj & Jayaraman, Prabha, 2009. "Bayes reliability measures of Lognormal and inverse Gaussian distributions under ML-II ε-contaminated class of prior distributions," MPRA Paper 16528, University Library of Munich, Germany.
    2. Oh, ChoHwan & Lee, Jeong Ik, 2020. "Real time nuclear power plant operating state cognitive algorithm development using dynamic Bayesian network," Reliability Engineering and System Safety, Elsevier, vol. 198(C).

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