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On an extension of the exponential-geometric distribution

Author

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  • Adamidis, Konstantinos
  • Dimitrakopoulou, Theodora
  • Loukas, Sotirios

Abstract

Various statistical properties and reliability aspects of a two-parameter distribution with decreasing and increasing failure rate are explored; the model includes the exponential-geometric distribution [Marshall and Olkin, 1997. Biometrika 84, 641-652; Adamidis and Loukas, 1998. Statist. Probab. Lett. 39, 35-42] as a special case. Characterizations are given and the estimation of parameters is studied by the method of maximum likelihood. An EM algorithm [Dempster et al., 1977. J. R. Statist. Soc. B. 39, 1-38] is proposed for computing the estimates, and expressions for their asymptotic variances and covariances are derived. Numerical examples based on real data are included.

Suggested Citation

  • Adamidis, Konstantinos & Dimitrakopoulou, Theodora & Loukas, Sotirios, 2005. "On an extension of the exponential-geometric distribution," Statistics & Probability Letters, Elsevier, vol. 73(3), pages 259-269, July.
    • Handle: RePEc:eee:stapro:v:73:y:2005:i:3:p:259-269
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    References listed on IDEAS

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    1. Adamidis, K. & Loukas, S., 1998. "A lifetime distribution with decreasing failure rate," Statistics & Probability Letters, Elsevier, vol. 39(1), pages 35-42, July.
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    2. Shahsanaei Fatemeh & Rezaei Sadegh & Pak Abbas, 2012. "A New Two-Parameter Lifetime Distribution with Increasing Failure Rate," Stochastics and Quality Control, De Gruyter, vol. 27(1), pages 1-17, September.
    3. Saralees Nadarajah & Božidar Popović & Miroslav Ristić, 2013. "Compounding: an R package for computing continuous distributions obtained by compounding a continuous and a discrete distribution," Computational Statistics, Springer, vol. 28(3), pages 977-992, June.
    4. Jorge Navarro & Antonio Guillamón & María del Carmen Ruiz, 2009. "Generalized mixtures in reliability modelling: Applications to the construction of bathtub shaped hazard models and the study of systems," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 25(3), pages 323-337, May.
    5. Min Wang & Ibrahim Elbatal, 2015. "The modified Weibull geometric distribution," METRON, Springer;Sapienza Università di Roma, vol. 73(3), pages 303-315, December.
    6. Zawar Hussain & Muhammad Aslam & Zahid Asghar, 2019. "On Exponential Negative-Binomial-X Family of Distributions," Annals of Data Science, Springer, vol. 6(4), pages 651-672, December.
    7. Feyza Günay & Mehmet Yilmaz, 2018. "Different Parameter Estimation Methods for Exponential Geometric Distribution and Its Applications in Lifetime Data Analysis," Biostatistics and Biometrics Open Access Journal, Juniper Publishers Inc., vol. 8(2), pages 36-43, September.
    8. Unnikrishnan Nair, N. & Vineshkumar, B., 2011. "Ageing concepts: An approach based on quantile function," Statistics & Probability Letters, Elsevier, vol. 81(12), pages 2016-2025.
    9. Fatimah E. Almuhayfith & Mahfooz Alam & Hassan S. Bakouch & Sudeep R. Bapat & Olayan Albalawi, 2024. "Linear Combination of Order Statistics Moments from Log-Extended Exponential Geometric Distribution with Applications to Entropy," Mathematics, MDPI, vol. 12(11), pages 1-15, June.
    10. Bakouch, Hassan S. & Ristić, Miroslav M. & Asgharzadeh, A. & Esmaily, L. & Al-Zahrani, Bander M., 2012. "An exponentiated exponential binomial distribution with application," Statistics & Probability Letters, Elsevier, vol. 82(6), pages 1067-1081.
    11. Muhammad H Tahir & Gauss M. Cordeiro, 2016. "Compounding of distributions: a survey and new generalized classes," Journal of Statistical Distributions and Applications, Springer, vol. 3(1), pages 1-35, December.

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