IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v53y2009i4p1377-1387.html
   My bibliography  Save this article

Bayesian analysis of a generalized lognormal distribution

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-9473(08)00560-4
    Download Restriction: Full text for ScienceDirect subscribers only.
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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. 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.
    3. Chen, Gemai, 1995. "Generalized log-normal distributions with reliability application," Computational Statistics & Data Analysis, Elsevier, vol. 19(3), pages 309-319, March.
    4. Saralees Nadarajah, 2005. "A generalized normal distribution," Journal of Applied Statistics, Taylor & Francis Journals, vol. 32(7), pages 685-694.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Roger W. Barnard & Kent Pearce & A. Alexandre Trindade, 2018. "When is tail mean estimation more efficient than tail median? Answers and implications for quantitative risk management," Annals of Operations Research, Springer, vol. 262(1), pages 47-65, March.
    2. Robert Paige & A. Trindade & R. Wickramasinghe, 2014. "Extensions of saddlepoint-based bootstrap inference," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 66(5), pages 961-981, October.
    3. Bhupendra Singh & K. Sharma & Shubhi Rathi & Gajraj Singh, 2012. "A generalized log-normal distribution and its goodness of fit to censored data," Computational Statistics, Springer, vol. 27(1), pages 51-67, March.
    4. Klein, Ingo, 2012. "Quasi-arithmetische Mittelwerte und Normalverteilung," Discussion Papers 89/2010, Friedrich-Alexander University Erlangen-Nuremberg, Chair of Statistics and Econometrics.
    5. García, V.J. & Gómez-Déniz, E. & Vázquez-Polo, F.J., 2010. "A new skew generalization of the normal distribution: Properties and applications," Computational Statistics & Data Analysis, Elsevier, vol. 54(8), pages 2021-2034, August.
    6. Xin Chen & Zhangming Shan & Decai Tang & Biao Zhou & Valentina Boamah, 2023. "Interest rate risk of Chinese commercial banks based on the GARCH-EVT model," Palgrave Communications, Palgrave Macmillan, vol. 10(1), pages 1-11, December.
    7. Reiner Franke, 2015. "How Fat-Tailed is US Output Growth?," Metroeconomica, Wiley Blackwell, vol. 66(2), pages 213-242, May.
    8. Massimiliano Giacalone & Demetrio Panarello & Raffaele Mattera, 2018. "Multicollinearity in regression: an efficiency comparison between Lp-norm and least squares estimators," Quality & Quantity: International Journal of Methodology, Springer, vol. 52(4), pages 1831-1859, July.
    9. Mattera, Raffaele, 2017. "A GED-based regression to fit the actual data distribution," MPRA Paper 80501, University Library of Munich, Germany.
    10. Alexander Robitzsch, 2020. "L p Loss Functions in Invariance Alignment and Haberman Linking with Few or Many Groups," Stats, MDPI, vol. 3(3), pages 1-38, August.
    11. Jayles, Bertrand & Escobedo, Ramon & Cezera, Stéphane & Blanchet, Adrien & Kameda, Tatsuya & Sire, Clément & Théraulaz, Guy, 2020. "The impact of incorrect social information on collective wisdom in human groups," IAST Working Papers 20-106, Institute for Advanced Study in Toulouse (IAST).
    12. Li, Liuling & Mizrach, Bruce, 2010. "Tail return analysis of Bear Stearns' credit default swaps," Economic Modelling, Elsevier, vol. 27(6), pages 1529-1536, November.
    13. Wolf-Dieter Richter, 2017. "Statistical reasoning in dependent p-generalized elliptically contoured distributions and beyond," Journal of Statistical Distributions and Applications, Springer, vol. 4(1), pages 1-25, December.
    14. Mijeong Kim & Yanyuan Ma, 2019. "Semiparametric efficient estimators in heteroscedastic error models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(1), pages 1-28, February.
    15. Mehmet Niyazi Çankaya & Abdullah Yalçınkaya & Ömer Altındaǧ & Olcay Arslan, 2019. "On the robustness of an epsilon skew extension for Burr III distribution on the real line," Computational Statistics, Springer, vol. 34(3), pages 1247-1273, September.
    16. Punzo, Antonio & Bagnato, Luca, 2021. "Modeling the cryptocurrency return distribution via Laplace scale mixtures," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 563(C).
    17. Bertrand Jayles & Ramon Escobedo & Stéphane Cezera & Adrien Blanchet & Tatsuya Kameda & Clément Sire & Guy Théraulaz, 2020. "The impact of incorrect social information on collective wisdom in human groups," Post-Print hal-03019820, HAL.
    18. Karol I. Santoro & Héctor J. Gómez & Inmaculada Barranco-Chamorro & Héctor W. Gómez, 2022. "Extended Half-Power Exponential Distribution with Applications to COVID-19 Data," Mathematics, MDPI, vol. 10(6), pages 1-16, March.
    19. Liu, Xiaochun, 2019. "On tail fatness of macroeconomic dynamics," Journal of Macroeconomics, Elsevier, vol. 62(C).
    20. Li, Xinmin & Tian, Lili & Wang, Juan & Muindi, Josephia R., 2012. "Comparison of quantiles for several normal populations," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 2129-2138.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:csdana:v:53:y:2009:i:4:p:1377-1387. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.