A new parameter estimation method for the extended power Lindley distribution based on order statistics, with application

Devendra Kumar; Maneesh Kumar; Sapna Yadav; Anju Goyal

doi:https://doi.org/10.59170/stattrans-2024-020

A new parameter estimation method for the extended power Lindley distribution based on order statistics, with application

Devendra Kumar Department of Statistics, Central University of Haryana and Department of Statistics, Faculty of Mathematical Sciences, University of Delhi, Delhi, India ORCID:https://orcid.org/0000- 0001-5831-3315 , Maneesh Kumar Department of Statistics, Central University of Haryana, India ORCID:https://orcid.org/0000-0002-4186-5962 , Sapna Yadav Department of Statistics, Central University of Haryana, India ORCID:https://orcid.org/0009-0000-3143-3827 , Anju Goyal 4Department of Statistics, Panjab University, Chandigarh, India ORCID:https://orcid.org/0000-0002-0171-3163 Statistics in Transition new series, vol. 25, 2024, 2, pages: 167-184 Published online: 5 June 2024 https://doi.org/10.59170/stattrans-2024-020 Citation: Kumar, D., Kumar, M., Yadav, S., Goyal, A., 2024. A new parameter estimation method for the extended power Lindley distribution based on order statistics, with application.Statistics in Transition new series, 25(2), pp. 167-184. https://doi.org/10.59170/stattrans-2024-020

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ABSTRACT

In this paper, we propose inference procedures for the estimation of parameters by using order statistics. First, we derive some new expressions for single and product moments of the order statistics from the extended power Lindley distribution. We then use these moments to obtain the best linear unbiased estimates (BLUEs) of the location and scale parameters based on Type-II right-censored samples. A real data set is analysed to illustrate the flexibility and importance of the model.

KEYWORDS

extended power Lindley distribution, order statistics, moments, best linear unbiased estimator

REFERENCES

Alkarnil, S. H., (2015). Extended power Lindley distribution: a new statistical model for non-monotone survival data. European Journal of Statistics and Probability, 3, pp. 19–34.

Arnold, B. C., Balakrishnan, N., Nagaraja, H. N., (2003). A First Course in Order Statistics, New York: John Wiley.

Ahsanullah, M., Alzaatreh, A., (2018). Parameter estimation for the log-logistic distribution based on order statistics. REVSTAT Statistical Journal, 16, pp. 429–443.

Balakrishnan, N., Cohan, A. C., (1991). Order Statistics and Inference: Estimation Methods, San Diego: Academic Press.

Balakrishnan, N., Chandramouleeswaran, M. P., (1996). BLUEs of location and scale parameters of Laplace distribution based on Type-II censored samples and associated. Microelectron Reliab, 36, pp. 371–374.

Balakrishnan N., Melas VB, Ermakove S., (2000). Advances in stochastic simulation and methods. Boston, MA: Birkhauser, pp. 245–282.

Bhaumik, D. K., Kapur, K., Gibbons, R. D., (2009). Testing parameters of a gamma distribution for small samples. Technometrics, 51, pp. 326–334.

Bouchahed, L., Zeghdoudi, H., (2018). A new and unified approach in generalizing the Lindley’s distribution with applications. Statistics in Transition new series, 19(1), pp. 61–74.

David, H. A., Nagaraja, H. N., (2003). Order Statistics. Third edition. New York: John Wiley.

Ghitany, M., Atieh, B., Nadarajah, S., (2008), Lindley distribution and its application. Mathematics and Computers in Simulation , 78(4), pp. 493–506.

Jabeen, R., Ahmad, A., Feroze, N. and Gilani, G. M., (2013). Estimation of location and scale parameters of Weibull distribution using generalized order statistics under Type II singly and doubly censored data. Int J Adv Sci Technol., 55, pp. 67–80.

Kumar, D., Dey, S., Nadarajah, S., (2017). Extended exponential distribution based on order statistics. Communication in Statistics-Theory and Methods, 46(18), pp. 9166–9184.

Kumar, D., Dey, S., (2017a). Power generalized Weibull distribution based on order statistics. Journal of Statistical Research, 51(1), pp. 61–78.

Kumar, D., Dey, S., (2017b). Relations for Moments of Generalized Order Statistics from Extended Exponential Distribution. American Journal of Mathematical and Management Sciences. 36, pp. 378–400.

Kumar, D., Goyal, A., (2019a). Order Statistics from the power Lindley distribution and associated inference with application. Annals of data Science, 6, pp. 153–177.

Kumar, D., Goyal, A., (2019b). Generalized Lindley Distribution Based on Order Statistics and Associated Inference with Application. Annals of data Science, 6, pp. 707–736.

Kumar, D., Kumar, M., Joorel, J. P. S., (2020a). Estimation with modified power function distribution based on order statistics with application to evaporation data. Annals of data Science, 9, pp. 723–748.

Kumar, D., Kumar, M., Dey, S., (2020b). Inferences for the type-II exponentiated loglogistic distribution based on order statistics with application. Journal of Statistical Theory and Methods, 13(3), pp. 352–367.

Lindley, D., (1958). Fiducial distributions and bayes theorem. J. R. Statist. Soc. Ser. B, 20, pp. 102–107.

Mahmoud, M. A.W., Sultan, K. S., Moshref, M. E., (2005). Inference based on order statistics from the generalized Pareto distribution and application. Commun. Stat. Simul. Comput., 34, pp. 267–282.

Sanmel, P., Thomas, P. Y., (1997). Estimation of location and scale parameters of U-shaped distribution. J Int. Soc. Agric. Stat., 50, pp. 75–94.

Sultan K. S, Childs A, Balakrishnan, N., (2000). Higher order moments of order statistics from the power function distribution and Edgeworth approximate inference.

Sultan, K. S., Balakrishnan, N., (2000). Higher order moments of order statistics from the power function distribution and edgeworth approximate inference. Advances in Stochastic Simulation Methods, pp. 245–282 , Springer, New York.

Sultan, K. S., Al-Thubyani, W. S., (2016). Higher order moments of order statistics from the Lindley distribution and associated inference. Journal of Statistical Computation and Simulation, 86, pp. 3432–3445.

Zeghdoudi, H., Nouar, L., Yahia, D., (2018). Lindley Pareto Distribution. Statistics in Transition new series, 19(4), pp. 671–692.