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

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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.

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Authors and Affiliations

  1. Department of Statistics, Bartin University, 74100, Bartin, Turkey

    Emrah Altun

  2. Department of Mathematics, Bartin University, 74100, Bartin, Turkey

    Emrah Altun

  3. Department of Statistics, Federal University of Pernambuco, Recife, Brazil

    Gauss M. Cordeiro

Authors
  1. Emrah Altun
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  2. Gauss M. Cordeiro
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Correspondence to Emrah Altun.

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Appendix

Appendix

The data for Sect. 6.2 are given below:

  1. 1.

    Long term interest (LTI) rate (%): 2.640 0.596 0.680 2.190 4.560 2.140 0.410 0.530 0.750 0.280 4.390 3.390 5.190 0.800 2.160 2.640 0.060 2.549 0.930 0.310 0.540 7.750 0.470 2.810 1.760 3.170 1.760 1.010 0.990 1.318 0.550 0.040 1.374 2.890

  2. 2.

    Foreign Direct Investment (FDI) stocks (Outward) (% GDP): 30.78 57.87 121.52 90.17 45.39 11.08 55.92 51.54 56.31 43.34 11.64 20.85 21.99 276.22 28.81 27.56 30.6 21.02 5.93 7.24 380.1 15.76 305.44 8.94 48.05 5.41 23.68 3.56 14.53 41.9 71.7 162.75 61.86 40.43

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Altun, E., Cordeiro, G.M. The unit-improved second-degree Lindley distribution: inference and regression modeling. Comput Stat 35, 259–279 (2020). https://doi.org/10.1007/s00180-019-00921-y

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  • DOI: https://doi.org/10.1007/s00180-019-00921-y

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