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On an extension of the exponential-geometric distribution

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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.
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    5. Min Wang & Ibrahim Elbatal, 2015. "The modified Weibull geometric distribution," METRON, Springer;Sapienza Università di Roma, vol. 73(3), pages 303-315, December.
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    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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