Optimal B-robust estimators for the parameters of the power Lindley distribution

References

• D. Bhati, M.A. Malik, and H.J. Waman, Lindley-Exponential distribution: properties and applications. Metron. 73(3) (2015), pp. 335–357.
   Web of Science ®Google Scholar
• Y.M. Bulut, J. Ahad, F.Z. Dogru, and O. Arslan, The generalized half-t distribution. Stat. Interface. 10(4) (2017), pp. 727–734.
   Web of Science ®Google Scholar
• F. Chapeau-Blondeau, and A. Monir, Numerical evaluation of the Lambert W function and application to generation of generalized Gaussian noise with exponent 1/2. IEEE Trans. Signal Process. 50(9) (2002), pp. 2160–2165.
   Web of Science ®Google Scholar
• B. Çakmak, and F.Z. Doğru, Robust estimators for the parameters of the power Lindley distribution. International Conference on Data Science, Machine Learning and Statistics 2019 (DMS-2019), Van/Turkey, 2019a.
   Google Scholar
• B. Çakmak, and F.Z. Doğru, Robust regression method for parameters of power lindley distribution. 11th International Statistics Congress (ISC2019), Bodrum/Turkey, 2019b.
   Google Scholar
• B. Çakmak, Parameter estimation of the power lindley distribution with the optimal B-Robust estimation method. Master’s thesis, Giresun University, Giresun, Turkey, 2020.
   Google Scholar
• F.Z. Doğru, and O. Arslan, Optimal B-robust estimators for the parameters of the Burr XII distribution. J. Stat. Comput. Simul. 86(6) (2016), pp. 1133–1149.
   Web of Science ®Google Scholar
• F.Z. Doğru, Y.M. Bulut, and O. Arslan, Optimal B-robust estimators for the parameters of the generalized half-normal distribution. REVSTAT-Statistical Journal 15(3) (2017), pp. 445–471.
   Web of Science ®Google Scholar
• M.E. Ghitany, D.K. Al-Mutairi, N. Balakrishanan, and L.J. Al-Enezi, Power Lindley distribution and associated inference. Comput. Stat. Data Anal. 64 (2013), pp. 20–33.
   Web of Science ®Google Scholar
• M.E. Ghitany, B. Atieh, and S. Nadarajah, Lindley distribution and its application. Math. Comput. Simul. 78(4) (2008), pp. 493–506.
   Web of Science ®Google Scholar
• Y. Güney, S. Ozdemir, Y. Tuaç, and O. Arslan, Optimal B-Robust estimation for the parameters of the Marshall-Olkin extended Burr XII distribution with an application to pharmacokinetics, REVSTAT-Statistical Journal, forthcoming paper, 2020.
   Google Scholar
• F.R. Hampel, Optimally bounding the gross-error-sensitivity and the influence of position in factor space. Proceedings of the ASA Statistical Computing Section, ASA, Washington, D.C., 59-64, 1978.
   Google Scholar
• F.R. Hampel, E.M. Ronchetti, P.J. Rousseeuw, and W.A. Stahel, Robust Statistics: The Approach Based on Influence Functions, Wiley, New York, 1986.
   Google Scholar
• P.W. Holland, and R.E. Welsch, Robust regression using iteratively reweighted least-squares. Communications in Statistics-Theory and Methods 6 (1977), pp. 813–827.
   Web of Science ®Google Scholar
• P.J. Huber, Robust estimation of a location parameter. The Annals of Mathematical Statistics 35 (1964), pp. 73–101.
   Google Scholar
• P.J. Huber, Robust regression: Asymptotics, conjectures, and Monte Carlo. The Annals of Statistics 1(5) (1973), pp. 799–821.
   Web of Science ®Google Scholar
• P.J. Huber, Robust Statistics, John Wiley & Sons. New York, 1981.
   Google Scholar
• P. Jodra, Computer generation of random variables with Lindley or Poisson–Lindley distribution via the Lambert W function. Math. Comput. Simul. 81 (2010), pp. 851–859.
   Web of Science ®Google Scholar
• W.S. Krasker, Estimation in linear regression models with disparate data points. Econometrica 48(6) (1980), pp. 1333–1346.
   Web of Science ®Google Scholar
• W.S. Krasker, and R.E. Welsch, Efficient bounded-influence regression estimation. J. Am. Stat. Assoc. 77(379) (1982), pp. 595–604.
   Web of Science ®Google Scholar
• Lee, E.T., and Wang, J.W. (2003). Statistical Methods for Survival Data Analysis, 3 rd ed., John Wiley & Sons, Inc., Hoboken, NJ.
   Google Scholar
• D.V. Lindley, Fiducial distributions and Bayes’ theorem. J. Royal Stat. Society 20(1) (1958), pp. 102–107.
   Google Scholar
• C.L. Mallows, On Some Topics in Robustness. Technical Memorandum, Bell Telephone Laboratories, Murray Hill, NJ, 1975.
   Google Scholar
• R.A. Maronna, R.D. Martin, and V.J. Yohai, Robust Statistics: Theory and Methods, Wiley, New York, 2006.
   Google Scholar
• P.J. Rousseeuw, Least median of squares regression. J. Am. Stat. Assoc. 79(388) (1984), pp. 871–880.
   Web of Science ®Google Scholar
• P.J. Rousseeuw, and V.J. Yohai, Robust regression by means of S-estimators, in Robust and Nonlinear Time Series (Lecture, Notes in Statistics No 26), J. Frankc, W. Härdle, and R.D. Martin, eds., Springer-Verlag, Berlin, 1984, pp. 256–272.
   Google Scholar
• N.V. Smirnov, Table for estimating the goodness of fit of empirical distributions. Ann. Math. Stat. 19(2) (1948), pp. 279–281.
   Google Scholar
• M.P. Victoria-Feser, Robust methods for personal income distribution models, Ph.D. thesis in Econometrics and Statistics, Faculty of Economic and Social Sciences, University of Geneva, Switzerland. (GE-archives), 1993.
   Google Scholar
• M.P. Victoria-Feser, and E. Ronchetti, Robust methods for personal-income distribution models. The Canadian Journal of Statistics 22(3) (1994), pp. 247–258.
   Web of Science ®Google Scholar
• V.J. Yohai, High breakdown-point and high efficiency robust estimates for regression. The Annals of Statistics 15(2) (1987), pp. 642–656.
   Web of Science ®Google Scholar