The power inverse Lindley distribution: different methods of estimation
DOI:
https://doi.org/10.5902/2179460X27500Keywords:
Outlier, Grouping Analysis, Monte Carlo MethodAbstract
In 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.Downloads
References
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.
Downloads
Published
How to Cite
Issue
Section
License
To access the DECLARATION AND TRANSFER OF COPYRIGHT AUTHOR’S DECLARATION AND COPYRIGHT LICENSE click here.
Ethical Guidelines for Journal Publication
The Ciência e Natura journal is committed to ensuring ethics in publication and quality of articles.
Conformance to standards of ethical behavior is therefore expected of all parties involved: Authors, Editors, Reviewers, and the Publisher.
In particular,
Authors: Authors should present an objective discussion of the significance of research work as well as sufficient detail and references to permit others to replicate the experiments. Fraudulent or knowingly inaccurate statements constitute unethical behavior and are unacceptable. Review Articles should also be objective, comprehensive, and accurate accounts of the state of the art. The Authors should ensure that their work is entirely original works, and if the work and/or words of others have been used, this has been appropriately acknowledged. Plagiarism in all its forms constitutes unethical publishing behavior and is unacceptable. Submitting the same manuscript to more than one journal concurrently constitutes unethical publishing behavior and is unacceptable. Authors should not submit articles describing essentially the same research to more than one journal. The corresponding Author should ensure that there is a full consensus of all Co-authors in approving the final version of the paper and its submission for publication.
Editors: Editors should evaluate manuscripts exclusively on the basis of their academic merit. An Editor must not use unpublished information in the editor's own research without the express written consent of the Author. Editors should take reasonable responsive measures when ethical complaints have been presented concerning a submitted manuscript or published paper.
Reviewers: Any manuscripts received for review must be treated as confidential documents. Privileged information or ideas obtained through peer review must be kept confidential and not used for personal advantage. Reviewers should be conducted objectively, and observations should be formulated clearly with supporting arguments, so that Authors can use them for improving the paper. Any selected Reviewer who feels unqualified to review the research reported in a manuscript or knows that its prompt review will be impossible should notify the Editor and excuse himself from the review process. Reviewers should not consider manuscripts in which they have conflicts of interest resulting from competitive, collaborative, or other relationships or connections with any of the authors, companies, or institutions connected to the papers.
