Inferences for generalized Topp-Leone distribution under order statistics with application to polyester bers data


Abstract


In this note, we obtain recurrence relations for the moments of order statis-tics from generalized Topp-Leone distribution without any restriction for theshape parameter. Several relations are also derived when the shape parame-ter is an integer. These expressions will be useful for computational purposes. In addition, we use these moments to obtain the best linear unbiased esti-mates of the location and scale parameters based on Type-II right-censoredsamples. In addition, we carry out some numerical illustrations throughMonte Carlo simulations to show the usefulness of the findings. Finally, weapply the ndings of the paper to some real data set.

DOI Code: 10.1285/i20705948v16n2p208

Keywords: Generalized Topp-Leone distribution, moments, order statis- tics, best linear unbiased estimators.

References


Ahsanullah, M. and Alzaatreh, A. (2018). Parameter estimation for the Log-logistic distribution based on order statistics. REVSTAT Statistical Journal, 16(4), 429443.

Arnold, B. C., Balakrishnan, N.and Nagaraja, H. N. (1992). A rst course in order statistics. New York:Wiley.

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

Balakrishnan, N., Zhu, X. and Al-Zaharani, B. (2015). Recursive computation of the single and product moments of order statistics for the complementary exponential-geometric distribution. J. Stat. Comput. Simul., 85, 2187-2201.

Genc, A. I_. (2012). Moments of Order Statistics of Topp-Leone Distribution. Statistical Papers, 53, 117131.

Kamps, U. (1991). A general recurrence relation for moments of order statistics in a class of probability distributions and characterizations. Metrika, 38, 215-225.

Kumar, D. (2015). Exact moments of generalized order statistics from type II exponentiated log-logistic distribution. Hacettepe Journal of Mathematics and Statistics, 44(3), 715 733.

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

Kumar, D. and Dey, S. (2017). Relations for Moments of Generalized Order Statistics from Extended Exponential Distribution. American Journal of Mathematical and

Management Sciences, 36, 378-400.

Kumar, D. and Goyal, A. (2019a). Order Statistics from the Power Lindley Distribution and Associated Inference with Application. Annals of Data Science, 6, 153-177.

Kumar, D. and Goyal, A. (2019b). Generalized Lindley distribution based on order statistics and associated inference with application. Annals of Data Science, 6, 707-736.

Kumar, D., Kumar, M. and Joorel, J. P. S. (2020). Estimation with modied power function distribution based on order statistics with application to evaporation data. Annals of Data Science, doi.org/10.1007/s40745-020-00244-6.

Mahmoud, M. A. W., Sultan, K. S. and Moshref, M. E. (2005). Inference based on order statistics from the generalized Paret distribution and application. Commun Stat

Simul Comput., 34, 267-282.

Mohie El-Din, M. M., Mahmoud, M. A. W., and Abu-Youssef, S. E. (1991). Moments of order statistics from parabolic and skewed distributions and characterization of Weibull distribution. Commun. Stat. Simul. Comput., 20, 639-645.

Navarro, J., Ruiz, J.M. and Sandoval, C.J. (2007). Properties of Coherent Systems with Dependent Components. Communications in Statistics - Theory and Methods, 36, 175-191.

Quesenberry, C. and Hales, C. (1980). Concentration bands for uniformity plots. Journal of Statistical Computation and Simulation, 11, 4153.

Samaniego, F.J. (1985). On Closure of the IFR Class Under Formation of Coherent Systems. IEEE Transactions On Reliability, 34, 6972.

Shekhawat, K. and Sharma, V. K. (2020). An extension of J-shaped distribution with application to tissue damage proportions in blood. Sankhya B: The Indian Journal of

Statistics, https://doi.org/10.1007/s13571-019-00218-6.

Sultan, K. S. and Balakrishnan, N. (2000a). Higher order moments of order statistics from the Pareto distribution and edgeworth approximate inference. Advances in

Stochastic Simulation Methods, Springer, New York, 207-244.

Sultan, K. S. and Balakrishnan, N. (2000b). Higher order moments of order statistics from the power function distribution and edgeworth approximate inference. Advances

in Stochastic Simulation Methods, Springer, New York, 245-282.

Sultan, K. S. and AL-Thubyani, W. S. (2016). Higher order moments of order statistics from the Lindley distribution and associated inference. J. of Stat. Compu. Simul., 86,

-3445.

Thomas, P.Y. and Samuel, P. (2008). Recurrence Relations for the Moments of Order Statistics from a Beta Distribution. Statistical Papers, 49, 139-146.


Full Text: pdf
Bookmark and Share


Creative Commons License
This work is licensed under a Creative Commons Attribuzione - Non commerciale - Non opere derivate 3.0 Italia License.