Main Article Content
The Lindley distribution may serve as a useful reliability model. Applications of this distribution are presented in statistical literature. In this article, a powerful goodness of fit test for the Lindley distribution is proposed. In order to compute the proposed test statistic, we use the maximum likelihood estimate (MLE) suggested by Ghitany et al. (2008), which is simple explicit estimator. By Monte Carlo simulation, critical points of the proposed test statistic for different sample sizes are obtained. Power values of the proposed test are compared with the competing tests against various alternatives via simulations. Finally, two real data are presented and analyzed.
This work is licensed under a Creative Commons Attribution 4.0 International License.
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
- Ali, S., Aslam, M., Kazmi, S. (2013). A study of the effect of the loss function on Bayes Estimate, posterior risk and hazard function for Lindley distribution. Applied Mathematical Modelling, 37, 6068–6078.
- Alizadeh Noughabi, H. (2021). A new goodness of fit test for the logistic distribution. Sankhya B, https://doi.org/10.1007/s13571-021-00262-1.
- Alizadeh Noughabi, H. (2019). A new estimator of Kullback–Leibler information and its application in goodness of fit tests. Journal of Statistical Computation and Simulation, 89, 1914-1934.
- Alizadeh Noughabi, H. and Balakrishnan, N. (2015). Goodness of fit using a new estimate of Kullback-Leibler information based on type II censored data. IEEE Transactions on Reliability, 64, 627-635.
- Al-Mutairi, D.K., Ghitany, M.E., Kundu, D. (2013). Inferences on the stress-strength reliability from Lindley distributions. Communications in Statistics-Theory and Methods, 42, 1443–1463.
- Altun, E. (2019). Two-sided Lindley distribution with inference and applications. Journal of the Indian Society for Probability and Statistics, 20, 255–279.
- Anderson, T.W. and Darling, D.A. (1954). A test of goodness of fit. Journal of American Statistical Association, 49, 765-769.
- Balakrishnan, N., Habibi Rad, A. and Arghami, N.R. (2007). Testing exponentiality based on Kullback–Leibler information with progressively type-II censored data. IEEE Transactions on Reliability, 56, 301–307.
- Balakrishnan, N., Ng, H.K.T. and Kannan, N. (2004). Goodness-of-fit tests based on spacings for progressively type-II censored data from a general location-scale distribution. IEEE Transactions on Reliability, 53, 349–356.
- D’Agostino, R.B. and Stephens, M.A. (Eds.) (1986). Goodness-of-fit Techniques. New York: Marcel Dekker.
- Ghitany, M.E., Atieh, B. and Nadarajah, S. (2008). Lindley distribution and its application. Mathematics Computing and Simulation, 78, 493-506.
- Gupta, PK, Singh, B. (2013). Parameter estimation of Lindley distribution with hybrid censored data. International Journal of System Assurance Engineering and Management, 4, 378–385.
- Habibi Rad, A., Yousefzadeh, F. and Balakrishnan, N. (2011). Goodness-of-fit test based on Kullback–Leibler information for progressively Type-II censored data. IEEE Transactions on Reliability, 60, 570–579.
- Huber-Carol, C., Balakrishnan, N., Nikulin, M. S. and Mesbah, M. (2002). Goodness-of-fit tests and model validity. Boston, Basel, Berlin: Birkhäuser.
- Ibrahim M., Yadav, A.S., Yousof, H.M., Goual, H., Hamedani, G. (2019). A new extension of Lindley distribution: modified validation test, characterizations and different methods of estimation. Communications for Statistical Applications and Methods, 26:473-495.
- Kolmogorov, A.N. (1933). Sulla Determinazione Empirica di une legge di Distribuzione. Giornale dell’Intituto Italiano degli Attuari, 4, 83-91.
- Krishna, H. and Kumar, K. (2011). Reliability estimation in Lindley distribution with progressively type II right censored sample. Mathematics and Computers in Simulation, 82, 281–294.
- Kuiper, N.H. (1960). Tests concerning random points on a circle. Proceedings of the Koninklijke Nederlandse Akademie van Wetenschappen, Series A, 63, 38-47.
- Kumar, C.S. and Jose, R. (2019). On double Lindley distribution and some of its properties. American Journal of Mathematical and Management Sciences, 38, 23-43.
- Kumar, K., Krishna, H. and Garg, R. (2015). Estimation of P(Y < X) in Lindley distribution using progressively first failure censoring. International Journal of System Assurance Engineering and Management, 6, 330–341.
- Lawless, J.F. (1982). Statistical models and methods for lifetime data. In: John Wiley & Sons (Ed.), New York, USA.
- Lin, C-T., Huang, Y-L. and Balakrishnan, N. (2008). A new method for goodness-of-fit testing based on Type-II right censored samples. IEEE Transactions on Reliability, 57, 633–642.
- Lindley, D.V. (1958). Fiducial distribution and Bayes’ theorem. Journal of the Royal Statistical Society, 20, 102–107.
- Mazucheli, J. and Achcar, J.A. (2011). The Lindley distribution applied to competing risks lifetime data. Computer Methods and Programs in Biomedicine, 2011, 104, 188- 192.
- Pakyari, R. and Balakrishnan, N. (2012). A general purpose approximate goodness-of-fit test for progressively Type-II censored data. IEEE Transactions on Reliability, 61, 238–244.
- Pakyari, R. and Balakrishnan, N. (2013). Goodness-of-fit tests for progressively Type-II censored data from location-scale distributions. Journal of Statistical Computation and Simulation, 83, 167-178.
- Shanker, R., Hagos, F., Sujatha, S. (2015). On modeling of Lifetimes data using exponential and Lindley distributions. Biometrics & Biostatistics International Journal, 2, 1–9.
- Singh, B. and Gupta, P.K. (2012). Load-sharing system model and its application to the real data set. Mathematics and Computers in Simulation, 82, 1615–1629.
- Valiollahi, R., Asgharzadeh, A. and Ng, H.K.T. (2017). Prediction for Lindley distribution based on type-II right censored samples. Journal of The Iranian Statistical Society, 16, 1-19.
- von Mises, R. (1931). Wahrscheinlichkeitsrechnung und ihre Anwendung in der Statistik und theoretischen Physik. Leipzig and Vienna: Deuticke.
- Wang, M. (2013). A new three-parameter lifetime distribution and associated inference. arXiv:1308.4128 [stat.ME].
- Watson, G.S. (1961). Goodness of fit tests on a circle. Biometrika, 48, 109-114.