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The unit-improved second-degree Lindley distribution: inference and regression modeling

Author

Listed:
  • Emrah Altun

    (Bartin University
    Bartin University)

  • Gauss M. Cordeiro

    (Federal University of Pernambuco)

Abstract

We define a new one-parameter model on the unit interval, called the unit-improved second-degree Lindley distribution, and obtain some of its structural properties. The methods of maximum likelihood, bias-corrected maximum likelihood, moments, least squares and weighted least squares are used to estimate the unknown parameter. The finite sample performance of these methods are investigated by means of Monte Carlo simulations. Moreover, we introduce a new regression model as an alternative to the beta, unit-Lindley and simplex regression models and present a residual analysis based on Pearson and Cox–Snell residuals. The new models are proved empirically to be competitive to the beta, Kumaraswamy, simplex, unit-Lindley, unit-Gamma and Topp–Leone models by means of two real data sets. Empirical findings indicate that the proposed models can provide better fits than other competitive models when the data are close to the boundaries of the unit interval.

Suggested Citation

  • Emrah Altun & Gauss M. Cordeiro, 2020. "The unit-improved second-degree Lindley distribution: inference and regression modeling," Computational Statistics, Springer, vol. 35(1), pages 259-279, March.
    • Handle: RePEc:spr:compst:v:35:y:2020:i:1:d:10.1007_s00180-019-00921-y
    DOI: 10.1007/s00180-019-00921-y
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    References listed on IDEAS

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    1. M. E. Ghitany & D. K. Al-Mutairi, 2008. "Size-biased Poisson-Lindley distribution and its application," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 299-311.
    2. Gómez-Déniz, Emilio & Sordo, Miguel A. & Calderín-Ojeda, Enrique, 2014. "The Log–Lindley distribution as an alternative to the beta regression model with applications in insurance," Insurance: Mathematics and Economics, Elsevier, vol. 54(C), pages 49-57.
    3. Mustafa Nadar & Alexander Papadopoulos & Fatih Kızılaslan, 2013. "Statistical analysis for Kumaraswamy’s distribution based on record data," Statistical Papers, Springer, vol. 54(2), pages 355-369, May.
    4. Ghitany, M.E. & Atieh, B. & Nadarajah, S., 2008. "Lindley distribution and its application," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 78(4), pages 493-506.
    5. Silvia Ferrari & Francisco Cribari-Neto, 2004. "Beta Regression for Modelling Rates and Proportions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 31(7), pages 799-815.
    6. Saralees Nadarajah & Samuel Kotz, 2003. "Moments of some J-shaped distributions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 30(3), pages 311-317.
    7. Ghitany, M.E. & Al-Mutairi, D.K. & Nadarajah, S., 2008. "Zero-truncated Poisson–Lindley distribution and its application," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(3), pages 279-287.
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    Cited by:

    1. Mustafa Ç. Korkmaz & Emrah Altun & Morad Alizadeh & M. El-Morshedy, 2021. "The Log Exponential-Power Distribution: Properties, Estimations and Quantile Regression Model," Mathematics, MDPI, vol. 9(21), pages 1-19, October.
    2. Abdul Ghaniyyu Abubakari & Suleman Nasiru & Christophe Chesneau, 2024. "A unit Weibull loss distribution with quantile regression and practical applications to actuarial science," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 34(4), pages 1-29.

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