Skip to main content
SpringerLink
Log in

The Exponentiated Generalized Marshall–Olkin Family of Distribution: Its Properties and Applications

  • Published:
Annals of Data Science Aims and scope Submit manuscript

Abstract

A new generator of continuous distributions called Exponentiated Generalized Marshall–Olkin-G family with three additional parameters is proposed. This family of distribution contains several known distributions as sub models. The probability density function and cumulative distribution function are expressed as infinite mixture of the Marshall–Olkin distribution. Important properties like quantile function, order statistics, moment generating function, probability weighted moments, entropy and shapes are investigated. The maximum likelihood method to estimate model parameters is presented. A simulation result to assess the performance of the maximum likelihood estimation is briefly discussed. A distribution from this family is compared with two sub models and some recently introduced lifetime models by considering three real life data fitting applications.

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

Similar content being viewed by others

References

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

    Article  Google Scholar 

  2. Alizadeh M, Tahir MH, Cordeiro GM, Zubair M, Hamedani GG (2015) The Kumaraswamy Marshal–Olkin family of distributions. J Egypt Math Soc 23:546–557

    Article  Google Scholar 

  3. Alizadeh M, Tahir MH, Cordeiro GM, Zubair M, Hamedani GG (2015) The beta Marshall–Olkin family of distributions. J Stat Distrib and Appl 2:1–18

    Article  Google Scholar 

  4. Cordeiro GM, Ortega EMM, Daniel CC (2013) The exponentiated generalized class of distributions. J Data Sci 11:1–27

    Google Scholar 

  5. Chakraborty S, Handique L (2017) The generalized Marshall–Olkin–Kumaraswamy-G family of distributions. J Data Sci 15:391–422

    Google Scholar 

  6. Chakraborty S, Handique L (2018) Properties and data modelling application of the Kumaraswamy generalized Marshall–Olkin-G family of distributions. J Data Sci 16 (To appear in Vol. 16 July 2018 issue)

  7. Dias CR, Cordeiro GM, Alizadeh M, Marinho PRD, Coêlho HFC (2016) Exponentiated Marshall–Olkin family of distributions. J Stat Distrib Appl 3:1–21

    Article  Google Scholar 

  8. Greenwood JA, Landwehr JM, Matalas NC, Wallis JR (1979) Probability weighted moments: definition and relation to parameters of several distributions expressible in inverse form. Water Resour Res 15:1049–1054

    Article  Google Scholar 

  9. Handique L, Chakraborty S (2016) The Beta generalized Marshall–Olkin–G family of distributions with applications. arXiv:1608.05985

  10. Handique L, Chakraborty S (2017) A new beta generated Kumaraswamy Marshall–Olkin-G family of distributions with applications. Malays J Sci 36:157–174

    Article  Google Scholar 

  11. Handique L, Chakraborty S (2017) The Beta generalized Marshall–Olkin Kumaraswamy-G family of distributions with applications. Int J Agricu Stat Sci 13:721–733

    Google Scholar 

  12. Handique L, Chakraborty S, Hamedani GG (2017) The Marshall–Olkin–Kumaraswamy-G family of distributions. J Stat Theory Appl 16:427–447

    Google Scholar 

  13. Handique L, Chakraborty S, Ali MM (2017) Beta-generated Kumaraswamy-G family of distributions. Pak J Stat 33:467–490

    Google Scholar 

  14. Kenney JF, Keeping ES (1962) Mathematics of statistics, part 1, 3rd edn. Van Nostrand, Princeton

    Google Scholar 

  15. Lomax KS (1954) Business failures; another example of the analysis of failure data. J Am Stat Assoc 49:847–852

    Article  Google Scholar 

  16. Marshall A, Olkin I (1997) A new method for adding a parameter to a family of distributions with applications to the exponential and Weibull families. Biometrika 84:641–652

    Article  Google Scholar 

  17. Moors JJA (1988) A quantile alternative for kurtosis. Statistician 37:25–32

    Article  Google Scholar 

  18. Murthy DNP, Xie M, Jiang R (2004) Weibull models. Wiley, Hoboken

    Google Scholar 

  19. Nadarajah S, Cordeiro GM, Ortega EMM (2015) The Zografos–Balakrishnan-G family of distributions: mathematical properties and applications. Commun Stat Theory Methods 44:186–215

    Article  Google Scholar 

  20. Smith RL, Naylor JC (1987) A comparison of maximum likelihood and Bayesian estimators for the three-parameter Weibull distribution. Appl Stat 36:358–369

    Article  Google Scholar 

  21. Song KS (2001) Rényi information, log likelihood and an intrinsic distribution measure. J Stat Plan Inference 93:51–69

    Article  Google Scholar 

  22. Thiago AN, Cordeiro GM, Bourguignon M, Silva FS (2017) The exponentiated generalized standardized half-logistic distribution. Int J Stat Probab 6:24–42

    Google Scholar 

  23. Weibull W (1951) A statistical distribution function of wide applicability. J Appl Mech Trans ASME 18:293–297

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Statistics, Dibrugarh University, Dibrugarh, 786004, India

    Laba Handique & Subrata Chakraborty

  2. Federal University of Pernambuco, Recife, Brazil

    Thiago A. N. de Andrade

Authors
  1. Laba Handique
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Subrata Chakraborty
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Thiago A. N. de Andrade
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Subrata Chakraborty.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Handique, L., Chakraborty, S. & de Andrade, T.A.N. The Exponentiated Generalized Marshall–Olkin Family of Distribution: Its Properties and Applications. Ann. Data. Sci. 6, 391–411 (2019). https://doi.org/10.1007/s40745-018-0166-z

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40745-018-0166-z

Keywords

Mathematics Subject Classification

Search

Navigation