Record data from Kies distribution and related statistical inferences

Nesreen M. Al-Olaimat; Husam A. Bayoud; Mohammad Z. Raqab

doi:10.21307/stattrans-2021-043

Record data from Kies distribution and related statistical inferences

Nesreen M. Al-Olaimat Department of Mathematics, The University of Jordan, Amman 11942, Jordan ORCID:https://orcid.org/0000-0003-2862-3739 , Husam A. Bayoud College of Sciences and Humanities, Fahad Bin Sultan University, Tabuk, Saudi Arabia ORCID:https://orcid.org/0000-0002-0066-7206 , Mohammad Z. Raqab Department of Mathematics, The University of Jordan, Amman 11942, Jordan ORCID:https://orcid.org/0000-0002-3047-1466 Statistics in Transition new series, vol. 22, 2021, 4, pages: 153–170 Published online: 8 December 2021 DOI 10.21307/stattrans-2021-043

1200 Views 33 Downloads

ARTICLE

(English) PDF

ABSTRACT

The Kies probability model was proposed as an alternative to the extendedWeibull models as it provides a more efficient fit to some real-life data sets in comparison to the aforementioned models. The paper proposes classical and Bayesian inferences for the Kies distribution based on records. Maximum likelihood estimates are studied jointly with asymptotic and bootstrap confidence intervals. Moreover, Bayes estimates, along with credible intervals are discussed assuming squared and LINEX loss functions. The proposed estimation methods have been investigated and compared via simulation studies. A real data set has been analysed for illustrative purposes.

KEYWORDS

Bayesian estimates, Kies distribution, maximum likelihood estimation, records

REFERENCES

Ahmed, E. A., (2014). Bayesian estimation based on progressive Type-II censoring from two parameter bathtub-shaped lifetime model: an Markov chain Monte Carlo approach, Journal of Applied Statistics, 41:4, pp. 752–768.

Ahsanullah, M., (2004). Record values theory and applications, University Press of America, USA.

Ahsanullah, M. and Nevzorov, V. B., (2015). Records via probability theory, Springer, Berlin.

Ahsanullah, M. and Raqab, M. Z., (2006). Bounds and characterizations of record statistics, Nova Publishers, USA.

Arnold, B. C., Balakrishnan, N. and Nagaraja, H. N., (1998). Records, Wiley, New york.

Bayoud, H. A., (2016). Estimating the shape parameter of Topp-Leone distribution based on progressive Type-II censored samples, REVSTAT-Stat. J, 14, pp. 415–431.

Chandler, K. N., (1952). The distribution and frequency of record values, Journal of the Royal Statistical Society: Series B (Methodological), 14(2), pp. 220–228.

Chen, M. H. and Shao, Q. M., (1999). Monte Carlo estimation of Bayesian credible and HPD intervals, Journal of Computational and Graphical Statistics, 8(1), pp. 69–92.

Chen, M. H., Shao, Q. M. and Ibrahim, J. G., (2000). Monte Carlo methods in Bayesian computation, Springer-Verlag, New York.

Genc, A. I., (2013). Estimation of P(X >Y) with Topp-Leone distribution, Journal of Statistical Computation and Simulation, 83(2), pp. 326–339.

Houchens, R. L., (1984). Record value theory and inference, Ph.D. thesis, University of California, Riverside.

Kies, J. A., (1958). The strength of glass performance, Naval Research Lab Report, No. 5093, Washington, D. C., USA.

Kumar, C. S. and Dharmaja, S. H. S., (2013). On reduced Kies distribution, Collection of Recent Statistical Methods and Applications, 111-123, Department of Statistics, Univercity of Kerala Publishers, Trivandrum.

Kumar, C. S. and Dharmaja, S. H. S., (2014). On some properties of Kies distribution, Metron, 72(1), pp. 97–122.

Kumar, C. S. and Dharmaja, S. H. S., (2017a). On modified Kies distribution and its applications, Journal of Statistical Research, 51(1), pp. 41–60.

Kumar, C. S. and Dharmaja, S. H. S., (2017b). The exponentiated reduced Kies distribution: properties and applications, Communications in Statistics-Theory and Methods, 46(17), pp. 8778-8790.

Kundu, D. and Pradhan, B., (2009). Bayesian inference and life testing plans for generalized exponential distribution, Science in China Series A: Mathematics, 52(6), pp. 1373–1388.

Lehmann, E. L. and Casella, G., (1998). Theory of point estimation, New York: Wiley.

Papke, L. E. and Wooldridge, J. M., (1996). Econometric methods for fractional response variables with an application to 401(K) plan participation rates, Journal of Applied Econometrics, 11, pp. 619–632.

Pradhan, B. and Kundu, D., (2009). On progressively censored generalized exponential distribution, Test, 18(3), pp. 497–515.

Pradhan, B. and Kundu, D., (2011). Bayes estimation and prediction of the two-parameter gamma distribution, Journal of Statistical Computation and Simulation, 81(9), pp. 1187–1198.

Ren, J. and Gui, W., (2020). Inference and optimal censoring scheme for progressively Type-II censored competing risk model for generalized Rayleigh distribution, Computational Statistics, pp. 1–35.

Tarvirdizade, B. and Ahmadpour, M., (2016). Estimation of the stress-strength reliability for the two-parameter bathtub-shaped lifetime distribution based on upper record values, Statistical Methodology, 31, pp. 58–72.

Zellner, A., (1986). Bayesian estimation and prediction using asymmetric loss functions, Journal of the American Statistical Association, 81(394), pp. 446–451.