Skip to main content
SpringerLink
Log in

The Odd Log-Logistic Generalized Gompertz Distribution: Properties, Applications and Different Methods of Estimation

  • Published:
Communications in Mathematics and Statistics Aims and scope Submit manuscript

Abstract

We introduce a four-parameter lifetime distribution called the odd log-logistic generalized Gompertz model to generalize the exponential, generalized exponential and generalized Gompertz distributions, among others. We obtain explicit expressions for the moments, moment-generating function, asymptotic distribution, quantile function, mean deviations and distribution of order statistics. The method of maximum likelihood estimation of parameters is compared by six different methods of estimations with simulation study. The applicability of the new model is illustrated by means of a real data set.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

References

  1. Aarset, A.S.: How to identify a bathtub hazard rate. IEEE Trans. Reliab. 36, 106–108 (1987)

    Article  Google Scholar 

  2. Anderson, T.W., Darling, D.A.: Asymptotic theory of certain “goodness of fit” criteria based on stochastic processes. Ann. Math. Stat. 23, 193–212 (1952)

    Article  MathSciNet  Google Scholar 

  3. Bemmaor, A.C., Glady, N.: Modeling purchasing behavior with sudden “death”: a flexible customer lifetime model. Manag. Sci. 58, 1012–1021 (2012)

    Article  Google Scholar 

  4. Benkhelifa, L.: The beta generalized Gompertz distribution. Appl. Math. Model. 52, 341–357 (2017)

    Article  MathSciNet  Google Scholar 

  5. Benkhelifa, L.: The Marshall-Olkin extended generalized Gompertz distribution. J. Data Sci. 15, 227–254 (2017)

    MATH  Google Scholar 

  6. Cheng, R.C.H., Amin, N.A.K.: Maximum product-of-spacings estimation with applications to the lognormal distribution. Technical Report, Department of Mathematics, University of Wales (1979)

  7. Cheng, R.C.H., Amin, N.A.K.: Estimating parameters in continuous univariate distributions with a shifted origin. J. R. Stat. Soc. Ser. B (Methodological) 45, 394–403 (1983)

    MathSciNet  MATH  Google Scholar 

  8. Choi, K., Bulgren, W.G.: An estimation procedure for mixtures of distributions. J. R. Stat. Soc. Ser. B (Methodological) 30, 444–460 (1968)

    MathSciNet  MATH  Google Scholar 

  9. da Silva, R.C., Sanchez, J.J.D., Lima, F.P., Cordeiro, G.M.: The Kumaraswamy Gompertz distribution. J. Data Sci. 13, 241–260 (2015)

    Google Scholar 

  10. Dey, S., Mazucheli, J., Nadarajah, S.: Kumaraswamy distribution: different methods of estimation. Comput. Appl. Math. 37, 2094–2111 (2018)

    Article  MathSciNet  Google Scholar 

  11. Economos, A.C.: Rate of aging, rate of dying and the mechanism of mortality. Arch. Gerontol. Geriatr. 1, 46–51 (1982)

    Google Scholar 

  12. El-Gohary, A., Al-Otaibi, A.N.: The generalized Gompertz distribution. Appl. Math. Model. 37, 13–24 (2013)

    Article  MathSciNet  Google Scholar 

  13. Gradshteyn, I.S., Ryzhik, I.M.: Table of Integrals, Series and Products. Academic Press, New York (2000)

    MATH  Google Scholar 

  14. Gompertz, B.: On the nature of the function expressive of the law of human mortality and on the new mode of determining the value of life contingencies. Philos. Trans. R. Stat. Soc. 115, 513–580 (1825)

    Article  Google Scholar 

  15. Gleaton, J.U., Lynch, J.D.: Properties of generalized log-logistic families of lifetime distributions. J. Probab. Stat. Sci. 4, 51–64 (2006)

    MathSciNet  Google Scholar 

  16. Jafari, A.A., Tahmasebi, S., Alizadeh, M.: The beta-Gompertz distribution. Rev. Colomb. Estad. 37, 141–158 (2014)

    Article  MathSciNet  Google Scholar 

  17. Merovci, F., Puka, L.: Transmuted Pareto distribution. ProbStat Forum 7, 1–11 (2014)

    MathSciNet  MATH  Google Scholar 

  18. Milgram, M.: The generalized integro-exponential function. Math. Comput. 44, 443–458 (1985)

    Article  MathSciNet  Google Scholar 

  19. Roozegar, R., Tahmsebi, S., Jafari, A.A.: The McDonald Gompertz distribution: properties and applications. Commun. Stat. Simul. Comput. 46, 3341–3355 (2017)

    Article  MathSciNet  Google Scholar 

  20. Ohishi, K., Okamura, H., Dohi, T.: Gompertz software reliability model: estimation algorithm and empirical validation. J. Syst. Softw. 82, 535–543 (2009)

    Article  Google Scholar 

  21. Swain, J.J., Venkatraman, S., Wilson, J.R.: Least-squares estimation of distribution functions in Johnson’s translation system. J. Stat. Comput. Simul. 29, 271–297 (1988)

    Article  Google Scholar 

  22. Willemse, W., Koppelaar, H.: Knowledge elicitation of Gompertz’ law of mortality. Scand. Actuar. J. 2, 168–179 (2000)

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

The authors would like to thank two anonymous reviewers and the associate editor for their helpful comments that have considerably improved this manuscript.

Author information

Authors and Affiliations

  1. Department of Statistics, Persian Gulf University, Bushehr, Iran

    Morad Alizadeh

  2. Department of Mathematics and Informatics, Larbi Ben M’Hidi University, Oum El Bouaghi, Algeria

    Lazhar Benkhelifa

  3. Department of Statistics, Faculty of Mathematical Sciences and Statistics, Malayer University, Malayer, Iran

    Mahdi Rasekhi

  4. Kermanshah Province Electricity Distribution Company, Kermanshah, Iran

    Bistoon Hosseini

Authors
  1. Morad Alizadeh
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Lazhar Benkhelifa
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Mahdi Rasekhi
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Bistoon Hosseini
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Lazhar Benkhelifa.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Alizadeh, M., Benkhelifa, L., Rasekhi, M. et al. The Odd Log-Logistic Generalized Gompertz Distribution: Properties, Applications and Different Methods of Estimation. Commun. Math. Stat. 8, 295–317 (2020). https://doi.org/10.1007/s40304-018-00175-y

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40304-018-00175-y

Keywords

Mathematics Subject Classification

Search

Navigation