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A New Extension of Extended Exponential Distribution with Applications

Author

Listed:
  • Ateq Alghamedi

    (King Abdulaziz University)

  • Sanku Dey

    (St. Anthony’s College)

  • Devendra Kumar

    (Central University of Haryana)

  • Saeed A. Dobbah

    (King Abdulaziz University)

Abstract

We introduce a new lifetime distribution, called the alpha-power transformed extended exponential distribution which generalizes the extended exponential distribution proposed by Nadarajah and Haghighi (Statistics 45:543–558, 2011) to provide greater flexibility in modeling data from a practical point of view. The new model includes the exponential; extended exponential, and $$\alpha $$α power transformed exponential (Mahdavi and Kundu in Commun Stat Theory Methods, 2017) distributions as a special case. This distribution exhibits five hazard rate shapes such as constant, increasing, decreasing, bathtub and upside-down bathtub. Various properties of the proposed distribution, including explicit expressions for the quantiles, moments, conditional moments, stochastic ordering, Bonferroni and Lorenz curve, stress–strength reliability and order statistics are derived. The maximum likelihood estimators of the three unknown parameters of alpha-power transformed extended exponential distribution and the associated confidence intervals are obtained. A simulation study is carried out to examine the performances of the maximum likelihood estimates in terms of their bias and mean squared error using simulated samples. Finally, the potentiality of the distribution is analyzed by means of two real data sets. For the two real data sets, this distribution is found to be superior in its ability to sufficiently model the data as compared to the Weibull distribution, Generalized exponential distribution, Marshall–Olkin extended exponentiated exponential distribution and exponentiated Nadarajah–Haghighi distributions.

Suggested Citation

  • Ateq Alghamedi & Sanku Dey & Devendra Kumar & Saeed A. Dobbah, 2020. "A New Extension of Extended Exponential Distribution with Applications," Annals of Data Science, Springer, vol. 7(1), pages 139-162, March.
    • Handle: RePEc:spr:aodasc:v:7:y:2020:i:1:d:10.1007_s40745-020-00240-w
    DOI: 10.1007/s40745-020-00240-w
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    References listed on IDEAS

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    1. Min-Tsai Lai, 2013. "Optimum number of minimal repairs for a system under increasing failure rate shock model with cumulative repair-cost limit," International Journal of Reliability and Safety, Inderscience Enterprises Ltd, vol. 7(2), pages 95-107.
    2. Sanku Dey & Indranil Ghosh & Devendra Kumar, 2019. "Alpha-Power Transformed Lindley Distribution: Properties and Associated Inference with Application to Earthquake Data," Annals of Data Science, Springer, vol. 6(4), pages 623-650, December.
    3. Sanku Dey & Vikas Kumar Sharma & Mhamed Mesfioui, 2017. "A New Extension of Weibull Distribution with Application to Lifetime Data," Annals of Data Science, Springer, vol. 4(1), pages 31-61, March.
    4. Lemonte, Artur J., 2013. "A new exponential-type distribution with constant, decreasing, increasing, upside-down bathtub and bathtub-shaped failure rate function," Computational Statistics & Data Analysis, Elsevier, vol. 62(C), pages 149-170.
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    6. M. C. Jones, 2015. "On Families of Distributions with Shape Parameters," International Statistical Review, International Statistical Institute, vol. 83(2), pages 175-192, August.
    7. Steve Bennett, 1983. "Log‐Logistic Regression Models for Survival Data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 32(2), pages 165-171, June.
    8. Amal S. Hassan & M. Elgarhy & Rokaya E. Mohamd & Sharifah Alrajhi, 2019. "On the Alpha Power Transformed Power Lindley Distribution," Journal of Probability and Statistics, Hindawi, vol. 2019, pages 1-13, January.
    9. Kus, Coskun, 2007. "A new lifetime distribution," Computational Statistics & Data Analysis, Elsevier, vol. 51(9), pages 4497-4509, May.
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