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$$\alpha $$ α Logarithmic Transformed Family of Distributions with Application

Author

Listed:
  • Sanku Dey

    (St. Anthony’s College)

  • Mazen Nassar

    (Zagazig University)

  • Devendra Kumar

    (Central University of Haryana)

Abstract

In this paper, a new three-parameter distribution, called $$\alpha $$ α logarithmic transformed generalized exponential distribution ( $$\alpha LTGE$$ α L T G E ) is proposed. Various properties of the proposed distribution, including explicit expressions for the moments, quantiles, moment generating function, mean deviation about the mean and median, mean residual life, Bonferroni curve, Lorenz curve, Gini index, Rényi entropy, stochastic ordering and order statistics are derived. It appears to be a distribution capable of allowing monotonically increasing, decreasing, bathtub and upside-down bathtub shaped hazard rates depending on its parameters. The maximum likelihood estimators of the unknown parameters cannot be obtained in explicit forms, and they have to be obtained by solving non-linear equations only. The asymptotic confidence intervals for the parameters are also obtained based on asymptotic variance covariance matrix. Finally, two empirical applications of the new model to real data are presented for illustrative purposes.

Suggested Citation

  • Sanku Dey & Mazen Nassar & Devendra Kumar, 2017. "$$\alpha $$ α Logarithmic Transformed Family of Distributions with Application," Annals of Data Science, Springer, vol. 4(4), pages 457-482, December.
    • Handle: RePEc:spr:aodasc:v:4:y:2017:i:4:d:10.1007_s40745-017-0115-2
    DOI: 10.1007/s40745-017-0115-2
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    References listed on IDEAS

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    1. 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.
    2. Ayman Alzaatreh & Carl Lee & Felix Famoye, 2013. "A new method for generating families of continuous distributions," METRON, Springer;Sapienza Università di Roma, vol. 71(1), pages 63-79, June.
    3. Miroslav Ristić & Debasis Kundu, 2015. "Marshall-Olkin generalized exponential distribution," METRON, Springer;Sapienza Università di Roma, vol. 73(3), pages 317-333, December.
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    Cited by:

    1. Sandeep Kumar Maurya & Saralees Nadarajah, 2021. "Poisson Generated Family of Distributions: A Review," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(2), pages 484-540, November.

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