This paper deals with the estimation of total time on test (TTT) for two parameter Lomax distribution. Both the maximum likelihood estimator and the Bayesian estimator of TTT are obtained. The performance of each of the estimators obtained is evaluated using Monte Carlo simulations method.

asymptotic distributions, Bayes estimator, generalized Pareto distribution, Lomax distribution, maximum likelihood estimator, TTT.

Received: November 18, 2020; Accepted: December 7, 2020; Published: February 6, 2021

How to cite this article: Sowbhagya S. Prabhu and E. S. Jeevanand, Estimation of time to test transform for Lomax distribution, Far East Journal of Theoretical Statistics 61(1) (2021), 21-33. DOI: 10.17654/TS061010021

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

References:

[1] R. E. Barlow and R. Campo, Total time on test processes and applications to failure data analysis, Reliability and Fault Tree Analysis, 1975, pp. 451-481.
[2] R. E. Barlow, Geometry of the total time on test transform, Naval Res. Logist. Quart. 26 (1979), 393-402.
[3] M. Chandra and N. D. Singpurwalla, Relationships between some notations which are common to reliability theory and economics, Mathematics of Operations Research 6 (1981), 113-121.
[4] S. Fani, M. A. Pasha and M. Bameni Moghadam, A new approach to optimal design of control charts based on change point estimation and total time on test plot, Comm. Statist. Theory Methods 48 (2019), 5571-5584.
[5] E. S. Jeevanand and E. I. Abdul Sathar, Bayes estimation of time to test transform for classical Pareto distribution in the presence of outliers, J. Indian Statist. Assoc. 48 (2010), 215-230.
[6] B. Klefsjo, Reliability interpretation of some concepts from economics, Naval Res. Logist. Quart. 31 (1984), 301-308.
[7] S. C. Kochar, X. Li and M. Shaked, The total time test transform and the excess wealth stochastic orders of distribution, Adv. Appl. Prob. 34 (2002), 826-845.
[8] K. S. Lomax, Business failures: another example of the analysis of failure data, J. Amer. Stat. Assoc. 49 (1954), 847-852.
[9] T. G. Pham and N. Turkkan, The Lorenz curve and scaled total time on test transfer curves: a unified approach, IEEE Transactions on Reliability 43 (1994), 76-84.
[10] M. Z. Raqab and M. T. Madi, Bayesian prediction of total time on test using doubly censored Rayleigh data, J. Stat. Comput. Simul. 72 (2002), 781-789.