Skip to main content
Log in

A generalized Lindley distribution

Sankhya B Aims and scope Submit manuscript

Abstract

A new distribution is proposed for modeling lifetime data. It has better hazard rate properties than the gamma, lognormal and the Weibull distributions. A comprehensive account of the mathematical properties of the new distribution including estimation and simulation issues is presented. A real data example is discussed to illustrate its applicability.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  • Bonferroni, C.E. 1930. Elementi di statistica generale. Seeber, Firenze.

    Google Scholar 

  • Chen, C. 2006. Tests of fit for the three-parameter lognormal distribution. Computational Statistics and Data Analysis 50:1418–1440.

    Article  MathSciNet  MATH  Google Scholar 

  • Corless, R.M., Gonnet, G.H., Hare, D.E.G., Jeffrey, D.J., and D.E. Knuth. 1996. On the Lambert W function. Advances in Computational Mathematics 5:329–359.

    Article  MathSciNet  MATH  Google Scholar 

  • Ghitany, M.E., and D.K. Al-Mutairi. 2009. Estimation methods for the discrete Poisson-Lindley distribution. Journal of Statistical Computation and Simulation 79:1–9.

    Article  MathSciNet  MATH  Google Scholar 

  • Ghitany, M.E., Al-Mutairi, D.K., and S. Nadarajah. 2008a. Zero-truncated Poisson-Lindley distribution and its application. Mathematics and Computers in Simulation 79:279–287.

    Article  MathSciNet  MATH  Google Scholar 

  • Ghitany, M.E., Atieh, B., and S. Nadarajah. 2008b. Lindley distribution and its application. Mathematics and Computers in Simulation 78:493–506.

    Article  MathSciNet  MATH  Google Scholar 

  • Gross, A.J., and V.A. Clark. 1975. Survival distributions: Reliability applications in the biomedical sciences. New York: John Wiley and Sons.

    MATH  Google Scholar 

  • Gupta, R.D., and D. Kundu. 1999. Generalized exponential distributions. Australian and New Zealand Journal of Statistics 41:173–188.

    Article  MathSciNet  MATH  Google Scholar 

  • Gupta, R.D., and D. Kundu. 2007. Generalized exponential distribution: Existing results and some recent developments. Journal of Statistical Planning and Inference 137:3537–3547.

    Article  MathSciNet  MATH  Google Scholar 

  • Hoskings, J.R.M. 1990. L-moments: analysis and estimation of distribution using linear combinations of order statistics. Journal of the Royal Statistical Society B, 52:105–124.

    Google Scholar 

  • Jodrá, J. 2010. Computer generation of random variables with Lindley or Poisson–Lindley distribution via the Lambert W function. Mathematics and Computers in Simulation 81:851–859.

    Article  MathSciNet  MATH  Google Scholar 

  • Leadbetter, M.R., Lindgren, G., and H. Rootzén 1987. Extremes and related properties of random sequences and processes. New York: Springer Verlag.

    Google Scholar 

  • Lindley, D.V. 1958. Fiducial distributions and Bayes’ theorem. Journal of the Royal Statistical Society B, 20:102–107.

    MathSciNet  MATH  Google Scholar 

  • Murthy, D.N.P., Xie, M., and R. Jiang. 2004. Weibull models. New York: John Wiley and Sons.

    MATH  Google Scholar 

  • Nadarajah, S., Bakouch, H.S., and R. Tahmasbi. 2011. A generalized Lindley distribution. Technical Report, School of Mathematics, University of Manchester, UK.

  • Nadarajah, S., and A.K. Gupta. 2007. The exponentiated gamma distribution with application to drought data. Calcutta Statistical Association Bulletin 59:233–234.

    MathSciNet  Google Scholar 

  • Rao, C.R. 1973. Linear statistical inference and its applications, 2nd edn. New York: John Wiley and Sons.

    Book  MATH  Google Scholar 

  • Rao, M., Chen, Y., Vemuri, B.C., and F. Wang. 2004. Cumulative residual entropy: A new measure of information. IEEE Transactions on Information Theory 50:1220–1228.

    Article  MathSciNet  Google Scholar 

  • Rényi, A. 1961. On measures of entropy and information. In Proceedings of the 4th berkeley symposium on mathematical statistics and probability, vol. 1, 547–561. Berkeley: University of California Press.

    Google Scholar 

  • Shaked, M., and J.G. Shanthikumar. 1994. Stochastic orders and their applications. Boston: Academic Press.

    MATH  Google Scholar 

  • Shannon, C.E. 1951. Prediction and entropy of printed English. The Bell System Technical Journal 30:50–64.

    MATH  Google Scholar 

Download references

Acknowledgements

The authors would like to thank the Editor-in-Chief and the referee for careful reading and for their comments which greatly improved the paper.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Saralees Nadarajah.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Nadarajah, S., Bakouch, H.S. & Tahmasbi, R. A generalized Lindley distribution. Sankhya B 73, 331–359 (2011). https://doi.org/10.1007/s13571-011-0025-9

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13571-011-0025-9

Keywords

Navigation