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Extended exponential distribution based on order statistics

Author

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  • Devendra Kumar
  • Sanku Dey
  • Saralees Nadarajah

Abstract

The extended exponential distribution due to Nadarajah and Haghighi (2011) is an alternative to and always provides better fits than the gamma, Weibull, and the exponentiated exponential distributions whenever the data contain zero values. We establish recurrence relations for the single and product moments of order statistics from the extended exponential distribution. These recurrence relations enable computation of the means, variances, and covariances of all order statistics for all sample sizes in a simple and efficient manner. By using these relations, we tabulate the means, variances, and covariances of order statistics and derive best linear unbiased estimates of the extended exponential distribution. Finally, a data application is provided.

Suggested Citation

  • Devendra Kumar & Sanku Dey & Saralees Nadarajah, 2017. "Extended exponential distribution based on order statistics," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(18), pages 9166-9184, September.
    • Handle: RePEc:taf:lstaxx:v:46:y:2017:i:18:p:9166-9184
    DOI: 10.1080/03610926.2016.1205625
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    Cited by:

    1. Mansoor Rashid Malik & Devendra Kumar, 2019. "Generalized Pareto Distribution Based On Generalized Order Statistics And Associated Inference," Statistics in Transition New Series, Polish Statistical Association, vol. 20(3), pages 57-79, September.
    2. Mansour Shrahili & Naif Alotaibi & Devendra Kumar & Salem A. Alyami, 2020. "Inference for the Two Parameter Reduced Kies Distribution under Progressive Type-II Censoring," Mathematics, MDPI, vol. 8(11), pages 1-20, November.
    3. Devendra Kumar & Neetu Jain & Mazen Nassar & Osama Eraki Abo-Kasem, 2021. "Parameter Estimation for the Exponentiated Kumaraswamy-Power Function Distribution Based on Order Statistics with Application," Annals of Data Science, Springer, vol. 8(4), pages 785-811, December.
    4. Devendra Kumar & Anju Goyal, 2019. "Order Statistics from the Power Lindley Distribution and Associated Inference with Application," Annals of Data Science, Springer, vol. 6(1), pages 153-177, March.
    5. Ibrahim Elbatal & Naif Alotaibi & Salem A. Alyami & Mohammed Elgarhy & Ahmed R. El-Saeed, 2022. "Bayesian and Non-Bayesian Estimation of the Nadaraj ah–Haghighi Distribution: Using Progressive Type-1 Censoring Scheme," Mathematics, MDPI, vol. 10(5), pages 1-16, February.
    6. Devendra Kumar & Maneesh Kumar & J. P. Singh Joorel, 2022. "Estimation with Modified Power Function Distribution Based on Order Statistics with Application to Evaporation Data," Annals of Data Science, Springer, vol. 9(4), pages 723-748, August.
    7. Malik Mansoor Rashid & Kumar Devendra, 2017. "Relations for Moments of Progressively Type-II Right Censored Order Statistics From Erlang-Truncated Exponential Distribution," Statistics in Transition New Series, Polish Statistical Association, vol. 18(4), pages 651-668, December.
    8. Malik Mansoor Rashid & Kumar Devendra, 2019. "Generalized Pareto Distribution Based On Generalized Order Statistics And Associated Inference," Statistics in Transition New Series, Polish Statistical Association, vol. 20(3), pages 57-79, September.
    9. repec:exl:29stat:v:20:y:2019:i:3:p:57-80 is not listed on IDEAS
    10. Mansoor Rashid Malik & Devendra Kumar, 2017. "Relations For Moments Of Progressively Type-Ii Right Censored Order Statistics From Erlang-Truncated Exponential Distribution," Statistics in Transition New Series, Polish Statistical Association, vol. 18(4), pages 651-668, December.
    11. Devendra Kumar & Anju Goyal, 2019. "Generalized Lindley Distribution Based on Order Statistics and Associated Inference with Application," Annals of Data Science, Springer, vol. 6(4), pages 707-736, December.

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