Skip to main content
Log in

Lindley Power Series Distributions

  • Published:
Sankhya A Aims and scope Submit manuscript

Abstract

Gui et al. (2017) proposed the Lindley geometric distribution, derived its properties including estimation issues and illustrated a data application. We introduce a new family of distributions containing the Lindley geometric distribution as a particular case. The new family is shown to provide significantly better fits. We also point out errors in various properties derived by Gui et al. (2017).

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

Similar content being viewed by others

References

  • Abd El-Monsef, M.M.E. (2016). A new Lindley distribution with location parameter. Commun. Stat.—Theory Methods45, 5204–5219.

    Article  MathSciNet  Google Scholar 

  • Abd El-Monsef, M.M.E., Hassanein, W.A. and Kilany, N.M. (2017). Erlang-Lindley distribution. Commun. Stat.—Theory Methods46, 9494–9506.

    Article  MathSciNet  Google Scholar 

  • Abouammoh, A.M., Alshangiti, A.M. and Ragab, I.E. (2015). A new generalized Lindley distribution. J. Stat. Comput. Simul.85, 3662–3678.

    Article  MathSciNet  Google Scholar 

  • Akaike, H. (1974). A new look at the statistical model identification. IEEE Trans. Autom. Control19, 716–723.

    Article  MathSciNet  Google Scholar 

  • Al-Babtain, A., Eid, A.M., Ahmed, A.N. and Merovci, F. (2015). The five parameter Lindley distribution. Pakistan J. Stat.31, 363–384.

    MathSciNet  Google Scholar 

  • Altun, G., Alizadeh, M., Altun, E. and Ozel, G. (2017). Odd Burr Lindley distribution with properties and applications. Hacettepe J. Math. Stat.46, 255–276.

    MathSciNet  MATH  Google Scholar 

  • Asgharzadeh, A., Bakouch, H.S., Nadarajah, S. and Sharafi, F. (2016). A new weighted Lindley distribution with application. Brazil. J. Probab. Stat.30, 1–27.

    Article  MathSciNet  Google Scholar 

  • Asgharzadeh, A., Nadarajah, S. and Sharafi, F. (2017). Generalized inverse Lindley distribution with application to Danish fire insurance data. Commun. Stat.–Theory Methods46, 5001–5021.

    Article  MathSciNet  Google Scholar 

  • Bhati, D., Malik, M.A. and Vaman, H.J. (2015). Lindley-exponential distribution: properties and applications. Metron73, 335–357.

    Article  MathSciNet  Google Scholar 

  • Corless, R.M., Gonnet, G.H., Hare, D.E.G., Jeffrey, D.J. and Knuth, D.E. (1996). On the Lambert W function. Adv. Comput. Math.5, 329–359.

    Article  MathSciNet  Google Scholar 

  • Gui, W., Guo, L. and Zhang, H (2017). The complementary Lindley-geometric distribution and its application in lifetime analysis. Sankhyā B. https://doi.org/10.1007/s13571-017-0142-1.

    Article  MathSciNet  Google Scholar 

  • Hassanein, W.A. and Elhaddad, T.A. (2016). Truncated Lindley gamma distribution. Pakistan J. Stat.32, 227–246.

    MathSciNet  Google Scholar 

  • Irshad, M.R. and Maya, R. (2017). Extended version of generalised Lindley distribution. South African Stat. J.51, 19–44.

    MathSciNet  MATH  Google Scholar 

  • Jodra, P. (2010). Computer generation of random variables with Lindley or Poisson-Lindley distribution via the Lambert W function. Math. Comput. Simul.81, 851–859.

    Article  MathSciNet  Google Scholar 

  • Kus, C. (2007). A new lifetime distribution. Comput. Stat. Data Anal.51, 4497–4509.

    Article  MathSciNet  Google Scholar 

  • Lindley, D. (1958). Fiducial distributions and Bayes’ theorem. J. R. Stat. Soc. B20, 102–107.

    MathSciNet  MATH  Google Scholar 

  • Mishra, A. and Sah, B.K. (2016). A generalized exponential-Lindley distribution. World Scientific Publishers, Hackensack, p. 229–238.

  • Nedjar, S. and Zeghdoudi, H. (2016). On gamma Lindley distribution: properties and simulations. J. Comput. Appl. Math.298, 167–174.

    Article  MathSciNet  Google Scholar 

  • Noack, A. (1950). A class of random variables with discrete distributions. Ann. Math. Stat.21, 127–132.

    Article  MathSciNet  Google Scholar 

  • Oluyede, B.O. and Yang, T. (2015). A new class of generalized Lindley distributions with applications. J. Stat. Comput. Simul.85, 2072–2100.

    Article  MathSciNet  Google Scholar 

  • Pararai, M., Warahena-Liyanage, G. and Oluyede, B.O. (2017). Exponentiated power Lindley-Poisson distribution: properties and applications. Commun. Stat.—Theory Methods46, 4726–4755.

    Article  MathSciNet  Google Scholar 

  • R Development Core Team (2017). A Language and Environment for Statistical Computing: R Foundation for Statistical Computing. Vienna, Austria.

  • Reyes, J., Venegas, O. and Gomez, H.W. (2017). Modified slash Lindley distribution. J. Probab. Stat.2017, Article ID 6303462.

    Article  MathSciNet  Google Scholar 

  • Shanker, R. and Mishra, A. (2016). A quasi Poisson-Lindley distribution. J. Indian Stat. Assoc.54, 113–125.

    MathSciNet  Google Scholar 

  • Sharma, V.K., Singh, S.K., Singh, U. and Merovci, F. (2016). The generalized inverse Lindley distribution: a new inverse statistical model for the study of upside-down bathtub data. Commun. Stat.—Theory Methods45, 5709–5729.

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgments

The authors would like to thank the Editor and the referee for careful reading and 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

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Si, Y., Nadarajah, S. Lindley Power Series Distributions. Sankhya A 82, 242–256 (2020). https://doi.org/10.1007/s13171-018-0150-x

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13171-018-0150-x

Keywords

AMS (2000) subject classification

Navigation