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.
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.
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.
Gedik Balay, I. (2021). Comparison of different estimation methods for the inverse weighted Lindley distribution. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 70(2), 1085-1098. https://doi.org/10.31801/cfsuasmas.915412
AMA
Gedik Balay I. Comparison of different estimation methods for the inverse weighted Lindley distribution. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. December 2021;70(2):1085-1098. doi:10.31801/cfsuasmas.915412
Chicago
Gedik Balay, Iklim. “Comparison of Different Estimation Methods for the Inverse Weighted Lindley Distribution”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 70, no. 2 (December 2021): 1085-98. https://doi.org/10.31801/cfsuasmas.915412.
EndNote
Gedik Balay I (December 1, 2021) Comparison of different estimation methods for the inverse weighted Lindley distribution. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 70 2 1085–1098.
IEEE
I. Gedik Balay, “Comparison of different estimation methods for the inverse weighted Lindley distribution”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 70, no. 2, pp. 1085–1098, 2021, doi: 10.31801/cfsuasmas.915412.
ISNAD
Gedik Balay, Iklim. “Comparison of Different Estimation Methods for the Inverse Weighted Lindley Distribution”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 70/2 (December 2021), 1085-1098. https://doi.org/10.31801/cfsuasmas.915412.
JAMA
Gedik Balay I. Comparison of different estimation methods for the inverse weighted Lindley distribution. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2021;70:1085–1098.
MLA
Gedik Balay, Iklim. “Comparison of Different Estimation Methods for the Inverse Weighted Lindley Distribution”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 70, no. 2, 2021, pp. 1085-98, doi:10.31801/cfsuasmas.915412.
Vancouver
Gedik Balay I. Comparison of different estimation methods for the inverse weighted Lindley distribution. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2021;70(2):1085-98.