Skip to main content
SpringerLink
Log in

Efficient estimation for the generalized exponential distribution

  • Regular Article
  • Published:
Statistical Papers Aims and scope Submit manuscript

Abstract

In this paper, we consider estimation of the probability density function and the cumulative distribution function of the generalized exponential distribution. The following estimators are considered: uniformly minimum variance unbiased estimator, maximum likelihood estimator, percentile estimator, least squares estimator, weighted least squares estimator and moments estimator. Analytical expressions are derived for the bias and the mean squared error. Simulation studies and real data applications show that the maximum likelihood estimator performs better than others.

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

Similar content being viewed by others

References

  • Abouammoh AM, Alshingiti AM (2009) Reliability estimation of generalized inverted exponential distribution. J Stat Comput Simul 79:1301–1315

    Article  MATH  MathSciNet  Google Scholar 

  • Achcar JA, Cepeda-Cuervo E, Rodrigues ER (2012) Weibull and generalised exponential overdispersion models with an application to ozone air pollution. J Appl Stat 39:1953–1963

    Article  MathSciNet  Google Scholar 

  • Alizadeh M, Bagheri SF, Baloui Jamkhaneh E, Nadarajah S (2014). Evaluation and comparison of estimations in the exponentiated Weibull distribution. Braz J Probab Stat [Epub ahead of print]

  • Ateya SF (2014) Maximum likelihood estimation under a finite mixture of generalized exponential distributions based on censored data. Stat Pap 55:311–325

    Article  MATH  MathSciNet  Google Scholar 

  • Bagheri SF, Alizadeh M, Baloui Jamkhaneh E Nadarajah S (2013a). Evaluation and comparison of estimations in the generalized exponential-Poisson distribution. J Stat Comput Simul. doi:10.1080/00949655.793342

  • Bagheri SF, Alizadeh M Nadarajah S (2013b). Efficient estimation of the PDF and the CDF of the exponentiated Gumbel distribution. Commun Statistics-simul Comput [epub ahead of print]

  • Bagheri SF Alizadeh M, Nadarajah S (2014). Efficient estimation of the PDF and the CDF of the Weibull extension model. Commun Statistics-simul Comput [Epub ahead of print]

  • Gradshteyn IS, Ryzhik IM (2000) Tables of integrals, series and products, 6th edn. Academic Press, New York

    Google Scholar 

  • Gupta RD, Kundu D (2001) Generalized exponential distributions: different methods of estimations. J Stat Comput Simul 69:315–338

    Article  MATH  MathSciNet  Google Scholar 

  • Gupta RD, Kundu D (2002) Generalized exponential distributions: statistical inferences. J Stat Theory Appl 1:101–118

    MathSciNet  Google Scholar 

  • Johnson NL, Kotz S, Balakrishnan N (1994) Continuous univariate distribution, vol 1, 2nd edn. Wiley, New York

  • Kao JHK (1958) Computer methods for estimating Weibull parameters in reliability studies. Trans IRE-Reliab Qual Control 13:15–22

    Article  Google Scholar 

  • Kao JHK (1959) A graphical estimation of mixed Weibull parameters in life testing electron tubes. Technometrics 1:389–407

    Article  Google Scholar 

  • Khan HMR, Saxena A, Rana S, Ahmed NU (2014) Bayesian method for modeling male breast cancer survival data. Asian Pac J Cancer Prev 15:663–669

    Article  Google Scholar 

  • Kim C, Song S (2010) Bayesian estimation of the parameters of the generalized exponential distribution from doubly censored samples. Stat Pap 51:583–597

    Article  MATH  MathSciNet  Google Scholar 

  • Kundu D, Gupta RD (1999) Generalized exponential distribution. Aust N Z J Stat 41:173–188

    Article  MATH  MathSciNet  Google Scholar 

  • Kundu D, Gupta RD (2007) Generalized exponential distribution: existing results and some recent developments. J Stat Plan Inference 136:3130–3144

    MathSciNet  Google Scholar 

  • Lawless JF (1982) Stat Models Methods Lifetime Data. John Wiley and Sons, New York

    Google Scholar 

  • Linhart H, Zucchini W (1986) Model selection. Wiley, New York

    MATH  Google Scholar 

  • Lopez-Benitez M, Casadevall F (2013) Time-dimension models of spectrum usage for the analysis, design, and simulation of cognitive radio networks. IEEE Trans Veh Technol 62:2091–2104

    Article  Google Scholar 

  • Mann NR, Schafer RE, Singpurwalla ND (1974) Methods for statistical analysis of reliability and life data. Wiley, New York

    MATH  Google Scholar 

  • Raqab MZ (2002) Inference for generalized exponential distribution based on record statistics. J Stat Plan Inference 104:339–350

    Article  MATH  MathSciNet  Google Scholar 

  • Raqab MZ, Ahsanullah M (2001) Estimation of the location and scale parameters of the generalized exponential distribution based on order statistics. J Stat Comput Simul 69:109–124

    Article  MATH  MathSciNet  Google Scholar 

  • Raqab MZ, Madi MT (2005) Bayesian inference for the generalized exponential distribution. J Stat Comput Simul 75:841–852

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  Google Scholar 

  • Zheng G (2002) On the Fisher information matrix in type-II censored data from the exponentiated exponential family. Biometrical J 44:353–357

    Article  Google Scholar 

Download references

Acknowledgments

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

Author information

Authors and Affiliations

  1. Department of Statistics, Amirkabir Unviversity of Technology, Tehran, Iran

    M. Alizadeh & S. Rezaei

  2. Department of Mathematics, College of Basic Science, Yadegar–e-Imam Khomeini (RAH) Branch, Islamic Azad University, Tehran, Iran

    S. F. Bagheri

  3. School of Mathematics, University of Manchester, Manchester, UK

    S. Nadarajah

Authors
  1. M. Alizadeh
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. S. Rezaei
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. S. F. Bagheri
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. S. Nadarajah
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to S. Rezaei.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Alizadeh, M., Rezaei, S., Bagheri, S.F. et al. Efficient estimation for the generalized exponential distribution. Stat Papers 56, 1015–1031 (2015). https://doi.org/10.1007/s00362-014-0621-7

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00362-014-0621-7

Keywords

Search

Navigation