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A New Generalization of the Extended Exponential Distribution with an Application

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  • Devendra Kumar

    (Central University of Haryana)

  • Manoj Kumar

    (Central University of Haryana)

Abstract

We introduce a new lifetime distribution namely, transmuted extended exponential distribution which generalizes the extended exponential distribution proposed by Nadarajah and Haghighi (Statistics 45:543–558, 2011) with an additional parameter using the quadratic rank transmutation map which was studied by Shaw and Buckley (The alchemy of probability distributions: beyond Gram-Charlier expansions, and a skew-kurtotic-normal distribution from a rank transmutation map, 2009. arXiv:0901.0434) to provide greater flexibility in modeling data from a practical point of view. In this paper, our main focus is on estimation from frequentist point of view, yet, some statistical and reliability characteristics for the model are derived. We briefly describe different estimation procedures namely, the method of maximum likelihood estimation, maximum product of spacings estimation and least square estimation. Monte Carlo simulations are performed to compare the performance of the proposed methods of estimations for both small and large samples. Finally, the potentiality of the model is analyzed by means of one real data set.

Suggested Citation

  • Devendra Kumar & Manoj Kumar, 2019. "A New Generalization of the Extended Exponential Distribution with an Application," Annals of Data Science, Springer, vol. 6(3), pages 441-462, September.
    • Handle: RePEc:spr:aodasc:v:6:y:2019:i:3:d:10.1007_s40745-018-0181-0
    DOI: 10.1007/s40745-018-0181-0
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    References listed on IDEAS

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    1. Robert King & Irene Lena Hudson & Muhammad Shuaib Khan, 2016. "Transmuted Kumaraswamy Distribution," Statistics in Transition new series, Główny Urząd Statystyczny (Polska), vol. 17(2), pages 183-210, June.
    2. Ferreira, Jose T.A.S. & Steel, Mark F.J., 2006. "A Constructive Representation of Univariate Skewed Distributions," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 823-829, June.
    3. M. Jones, 2004. "Families of distributions arising from distributions of order statistics," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 13(1), pages 1-43, June.
    4. Kundu, Debasis & Raqab, Mohammad Z., 2005. "Generalized Rayleigh distribution: different methods of estimations," Computational Statistics & Data Analysis, Elsevier, vol. 49(1), pages 187-200, April.
    5. Wanbo Lu & Daimin Shi, 2012. "A new compounding life distribution: the Weibull--Poisson distribution," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(1), pages 21-38, March.
    6. H. Barakat, 2015. "A new method for adding two parameters to a family of distributions with application to the normal and exponential families," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 24(3), pages 359-372, September.
    7. William T. Shaw & Ian R. C. Buckley, 2009. "The alchemy of probability distributions: beyond Gram-Charlier expansions, and a skew-kurtotic-normal distribution from a rank transmutation map," Papers 0901.0434, arXiv.org.
    8. Muhammad Shuaib Khan & Robert King & Irene Lena Hudson, 2016. "Transmuted Kumaraswamy Distribution," Statistics in Transition New Series, Polish Statistical Association, vol. 17(2), pages 183-210, June.
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