Comparison of different estimation methods for the inverse weighted Lindley distribution
In this paper, different estimation methods are considered for the parameters of the inverse weighted Lindley (IWL) distribution introduced by Ramos et al.(2019). Parameters of the IWL are estimated by the method of maximum likelihood (ML), least squares (LS), weighted least squares (WLS), Cram´er-von Mises (CVM) and Anderson Darling (AD). The performances of the estimators are compared using Monte Carlo simulation study via bias, mean square error and deficiency (Def) criteria. Finally, a real data set is analyzed for illustrative purposes.
Keywords:
Parameter estimation, Bias, efficiency, Monte Calo simulation Inverse weighted Lindley distribution,
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- Bakouch, H. S., Al-Zahrani, B. M., Al-Shomrani, A. A., Marchi, V. A., Louzada, F., An extended Lindley distribution, Journal of the Korean Statistical Society, 41 (2012),75–85. https://doi.org/10.1016/j.jkss.2011.06.002
- D’Agostino, R., Stephens M. Goodness-of-Fit Techniques, Marcel Dekker, New York, NY, USA, 1986.
- Ghitany, M., Al-Mutairi, D., Balakrishnan, N., Al-Enezi, L. Power Lindley distribution and associated inference, Computational Statistics Data Analysis, 64 (2013), 20–33. https://doi.org/10.1016/j.csda.2013.02.026
- Ghitany, M. E., Alqallaf, F., Al-Mutairi, D. K., Husain, H. A. A two-parameter weighted Lindley distribution and its applications to survival data. Mathematics and Computers in Simulation, 81(6) (2011), 1190-1201. https://doi.org/10.1016/j.matcom.2010.11.005
- Ghitany, M. E., Atieh, B., Nadarajah, S. Lindley distribution and its application, Mathematics and Computers in Simulation, 78(4) (2008), 493-506. https://doi.org/10.1016/j.matcom.2007.06.007
- Kantar, Y. M., Senoglu, B. A comparative study for the location and scale parameters of the Weibull distribution with given shape parameter, Computers Geosciences, 34(12) (2008), 1900-1909. https://doi.org/10.1016/j.cageo.2008.04.004
- Lindley, D. V., Fiducial distributions and Bayes’ theorem, Journal of the Royal Statistical Society, Ser. B 20 (1985), 102–107.
- Luceno, A., Fitting the generalized Pareto distribution to data using maximum goodnessof-fit estimators, Computational Statistics Data Analysis, 51(2) (2006), 904–917. https://doi.org/10.1016/j.csda.2005.09.011
- Mazucheli, J., Louzada, F., Ghitany, M. E., Comparison of estimation methods for the parameters of the weighted Lindley distribution, Applied Mathematics and Computation, 220 (2013), 463-471. https://doi.org/10.1016/j.amc.2013.05.082
- Miller, L.H., Table of percentage points of Kolmogorov statistics,J. Am. Stat. Assoc. 51 (1956), 111–121. https://doi/abs/10.1080/01621459.1956.10501314
- Patil, G. P., Rao, C. R., Weighted distributions and size-biased sampling with applications to wildlife populations and human families, Biometrics, (1978), 179–89. https://doi.org/10.2307/2530008
- Ramos, P. L., Louzada, F., Shimizu, T. K., Luiz, A. O., The inverse weighted Lindley distribution: Properties, estimation and an application on a failure time data, Communications in Statistics-Theory and Methods, 48(10) (2019), 2372-2389. https://doi.org/10.1080/03610926.2018.1465084
- Ramos, P. L., Louzada, F., The generalized weighted Lindley distribution: Properties, estimation, and applications, Cogent Mathematics Statistics, 3(1) (2016), 1256022. http://dx.doi.org/10.1080/23311835.2016.1256022
- Wang, M., Wang, W., Bias-corrected maximum likelihood estimation of the parameters of the weighted Lindley distribution, Communications in Statistics-Simulation and Computation, 46(1) (2017), 530-545. https://doi.org/10.1080/23311835.2016.1256022
- Zakerzadeh, H., Dolati, A., Generalized Lindley distribution, Journal of Mathematical Extensions, (2009), 13-25.
- ISSN: 1303-5991
- Yayın Aralığı: Yılda 4 Sayı
- Başlangıç: 1948
- Yayıncı: Ankara Üniversitesi