Skip to main content
Springer Nature Link
Log in

The Exponentiated Type Distributions

  • Published:
Acta Applicandae Mathematica Aims and scope Submit manuscript

Abstract

Gupta et al. [Commun. Stat., Theory Methods 27, 887–904, 1998] introduced the exponentiated exponential distribution as a generalization of the standard exponential distribution. In this paper, we introduce four more exponentiated type distributions that generalize the standard gamma, standard Weibull, standard Gumbel and the standard Fréchet distributions in the same way the exponentiated exponential distribution generalizes the standard exponential distribution. A treatment of the mathematical properties is provided for each distribution.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

Explore related subjects

Discover the latest articles and news from researchers in related subjects, suggested using machine learning.

References

  1. Gradshteyn, I.S., Ryzhik, I.M.: Table of Integrals, Series, and Products, 6th edn. Academic, San Diego, California (2000)

    MATH  Google Scholar 

  2. Gupta, R.C., Gupta, P.L., Gupta, R.D.: Modeling failure time data by Lehman alternatives. Comm. Statist.,Theory Methods 27, 887–904 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  3. Gupta, R.D., Kundu, D.: Exponentiated exponential family: an alternative to gamma and Weibull distributions. Biom. J. 43, 117–130 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  4. Kotz, S., Nadarajah, S.: Extreme Value Distributions: Theory and Applications. Imperial College, London, UK (2000)

    MATH  Google Scholar 

  5. Mudholkar, G.S., Hutson, A.D.: The exponentiated Weibull family: some properties and a flood data application. Comm. Statist., Theory Methods 25, 3059–3083 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  6. Mudholkar, G.S., Srivastava, D.K., Freimer, M.: The exponentiated Weibull family. Technometrics 37, 436–445 (1995)

    Article  MATH  Google Scholar 

  7. Nassar, M.M., Eissa, F.H.: On the exponentiated Weibull distribution. Comm. Statist., Theory Methods 32, 1317–1336 (2003)

    Article  MathSciNet  Google Scholar 

  8. Nadarajah, S., Kotz, S.: On the exponentiated exponential distribution, to appear in Statistica (2003)

  9. Prudnikov, A.P., Brychkov, Y.A., Marichev, O.I.: Integrals and Series (vol. 1–3). Gordon and Breach Science, Amsterdam, Netherlands (1986)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Mathematics, University of Manchester, Oxford Road, Manchester, M13 9PL, UK

    Saralees Nadarajah

  2. Department of Statistics, University of Nebraska, Lincoln, NE, 68583, USA

    Samuel Kotz

Authors
  1. Saralees Nadarajah
    View author publications

    You can also search for this author inPubMed Google Scholar

  2. Samuel Kotz
    View author publications

    You can also search for this author inPubMed Google Scholar

Corresponding author

Correspondence to Saralees Nadarajah.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Nadarajah, S., Kotz, S. The Exponentiated Type Distributions. Acta Appl Math 92, 97–111 (2006). https://doi.org/10.1007/s10440-006-9055-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10440-006-9055-0

Key words

Mathematics Subject Classifications (2000)