The power inverse Lindley distribution: different methods of estimation
Keywords:Outlier, Grouping Analysis, Monte Carlo Method
AbstractIn the last years several probability distributions have been proposed in the literature, especially with the aim of obtaining models that are more flexible relative to the behaviors of the density and hazard rate functions. For instance, Ghitany et al. (2013) proposed a new generalization of the Lindley distribution, called power Lindley distribution, whereas Sharma et al. (2015a) proposed the inverse Lindley distribution. From these two generalizations Barco et al. (2017) studied the inverse power Lindley distribution, also called by Sharma et al. (2015b) as generalized inverse Lindley distribution. Considering the inverse power Lindley distribution, in this paper is evaluate the performance, through Monte Carlo simulations, with respect to the bias and consistency of nine different methods of estimations (the maximum likelihood method and eight others based on the distance between the empirical and theoretical cumulative distribution function). The numerical results showed a better performance of the estimation method based on the Anderson-Darling test statistic. This conclusion is also observed in the analysis of two real data sets.
Barco, K. V. P., Mazucheli, J., Janeiro, V. (2017). The inverse power Lindley distribution. Communications in Statistics - Simulation and Computation, 46(8), 6308–6323.
D’Agostino, R. B., Stephens, M. A. (1986). Goodness-of-Fit Techniques. Taylor & Francis.
Dey, S., Mazucheli, J., Nadarajah, S. (2017). Kumaraswamy distribution: Different methods of estimation. Computational and Applied Mathematics, pp. 1–18.
Doornik, J. A. (2007). Object-Oriented Matrix Programming Using Ox, 3rd ed. London: Timberlake Consultants Press and Oxford.
do Espirito-Santo, A. P. J., Mazucheli, J. (2015). Comparison of estimation methods for the Marshall-Olkin extended Lindley distribution. Journal of Statistical Computation and Simulation, 85(17), 3437–3450.
Ghitany, M. E., Atieh, B., Nadarajah, S. (2008). Lindley distribution and its application. Mathematics and Computers in Simulation, 78(4), 493–506.
Ghitany, M. E., Al-Mutairi, D. K., Balakrishnan, N., Al-Enezi, L. J. (2013). Power Lindley distribution and associated inference.
Computational Statistics and Data Analysis, 64, 20–33.
Gupta, R. D., Kundu, D. (2001). Generalized Exponential distribution: Different method of estimations. Journal of Statistical Computation and Simulation, 69(4), 315–337.
Kundu, D., Raqab, M. Z. (2005). Generalized Rayleigh distribution: Different methods of estimations. Computational Statistics & Data Analysis, 49(1), 187–200.
Lehmann, E. J., Casella, G. (1998). Theory of Point Estimation. Springer Verlag.
Lindley, D. V. (1958). Fiducial distributions and Bayes’ theorem. Journal of the Royal Statistical Society, 20(1), 102–107.
Lucenõ, A. (2006). Fitting the Generalized Pareto distribution to data using maximum goodness-of-fit estimators. Computational Statistics & Data Analysis, 51(2), 904–917.
Mahmoud, M. R., Mandouh, R. M. (2013). On the transmuted Fréchet distribution. Journal of Applied Sciences Research, 9(10), 5553–5561.Mazucheli, J., Louzada, F., Ghitany, M. E. (2013). Comparison of estimation methods for the parameters of the weighted Lindley distribution. Applied Mathematics and Computation, 220, 463–471.
Mazucheli, J., Fernandes, L. B., de Oliveira, R. P. (2016). LindleyR: The Lindley Distribution and Its Modifications. URL https://CRAN.R-project.org/package=LindleyR, R package version 1.1.0.
Mazucheli, J., Ghitany, M. E., Louzada, F. (2017). Comparisons of ten estimation methods for the parameters of Marshall-Olkin extended Exponential distribution. Communications in Statistics - Simulation and Computation, 46(7), 5627–5645.
Nadarajah, S., Bakouch, H. S., Tahmasbi, R. (2011). A generalized Lindley distribution. Sankhya B, 73(2), 331–359.
Pawitan, Y. (2001). In All Likelihood: Statistical Modelling and Inference Using Likelihood. Oxford University Press, Oxford.
R Core Team (2017). R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria, URL https://www.R-project.org/.
Rohde, C. A. (2014). Introductory Statistical Inference with the Likelihood Function. Springer-Verlag, New York.
Sharma, V. K., Singh, S. K., Singh, U., Agiwal, V. (2015a). The inverse Lindley distribution: A stress-strength reliability model with application to head and neck cancer data. Journal of Industrial and Production Engineering, 32(3), 162–173.
Sharma, V. K., Singh, S. K., Singh, U., Merovci, F. (2015b). The generalized inverse Lindley distribution: A new inverse statistical model for the study of upside-down bathtub data. Communication in Statistics - Theory and Methods, 45(19), 5709–5729.
Teimouri, M., Hoseini, S. M., Nadarajah, S. (2013). Comparison of estimation methods for the Weibull distribution. Statistics, 47(1), 93–109.
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