SEARCH WITHIN CONTENT
Citation Information : Statistics in Transition New Series. Volume 22, Issue 4, Pages 191-212, DOI: https://doi.org/10.21307/stattrans-2021-045
License : (CC BY-NC-ND 4.0)
Received Date : 09-September-2019 / Accepted: 14-October-2020 / Published Online: 08-December-2021
In this paper, we establish several recurrence relations between single and product moments of progressively Type-II right censored order statistics from the power Lomax distribution. The relations enable the computation of all the single and product moments of progressively Type-II right censored order statistics for all sample sizes 𝑛 and all censoring schemes (𝑅1, 𝑅2,…,𝑅𝑚), 𝑚≤𝑛, in a simple recursive manner. The maximum likelihood approach is used for the estimation of the parameters and the reliability characteristic. A Monte Carlo simulation study has been conducted to compare the performance of the estimates for different censoring schemes.
Abdul-Moniem, I. B., Abdel-Hameed, H. F., (2012). On exponentiated Lomax distribution. International Journal of Mathematical Archive, 3, pp. 2144–2150.
Afify, A. Z., Nofal, Z. M., Yousof, H. M., El Gebaly, Y. M., Butt, N. S., (2015). The Transmuted Weibull Lomax Distribution: Properties and Application. Pak. j. stat. oper. res., XI(1), pp. 135–152.
Aggarwala, R., Balakrishnan, N., (1996). Recurrence relations for single and product moments of progressive Type-II right censored order statistics from exponential and truncated exponential distributions. Ann. Inst. Statist. Math., 48(4), pp. 757–771.
Aggarwala, R., Balakrishnan, N., (1998). Some properties of progressive censored order statistics from arbitrary and uniform distributions with applications to inference and simulation. Journal of Statistical planning and Inference, 70(1), pp. 35–49.
Al-Zahrani, B., Sagor, H., (2014). The Poisson-Lomax Distribution. Revista Colombiana de Estadistica, 37(1), pp. 223–243.
Arnold, B. C., Balakrishnan, N., Nagaraja, H. N., (1992). A First Course in Order Statistics. John Wiley, New York.
Athar, H., Akhter, Z., Saran, J., (2014). Moments of Progressive Type-II Right Censored Order Statistics from Lindley Distribution. Statistics Research Letters, 3(1), pp. 01–06.
Balakrishnan, N., Aggarwala, R., (2000). Progressive Censoring – Theory, Methods, and Applications, Birkhauser, Boston.
Balakrishnan, N., Sandhu, R.A., (1995). A simple simulation algorithm for generating progressively Type-II censored samples. American Statistician, 49(2), pp. 229–230.
Bryson, M., (1974). Heavy-tailed distributions: properties and tests. Technometrics, 16, pp. 61–68.
Cohen, A. C., (1963). Progressively censored samples in life testing. Technometrics, 5, pp. 327–329.
Cohen, A. C., (1976). Progressively censored sampling in the three parameter lognormal distribution. Technometrics, 18, pp. 99–103.
Cohen, A. C., (1991). Truncated and Censored Samples: Theory and Applications. Marcel Dekker, New York.
Cohen, A. C., Whitten, B.J., (1988). Parameter Estimation in Reliability and Life Span Models. Marcel Dekker, New York.
Ghitany, M. E., AL-Awadhi, F. A., Alkhalfan, L. A., (2007). Marshall-Olkin extended Lomax distribution and its applications to censored data. Communications in Statistics-Theory and Methods, 36, pp. 1855–1866.
Lomax, K. S., (1954). Business failures: Another example of the analysis of failure data. Journal of the American Statistical Association, 49, pp. 847–852.
Pushkarna, N., Saran, J., Tiwari, R., (2015). L-moments and TL-moments estimation and relationships for moments of progressive Type-II right censored order statistics from Frechet distribution. ProbStat Forum, 08, pp. 112–122.
Rady, E. A., Hassanein, W. A., Elhaddad, T. A., (2016). The power Lomax distribution with an application to bladder cancer data. SpringerPlus, 5, pp. 18–38.
Saran, J., Nain, K., Bhattacharya, A. P., (2018). Recurrence relations for single and product moments of progressive Type-II right censored order statistics from left truncated Logistic distribution with application to inference. International Journal of Mathematics and Statistics, 19(1), pp. 113–136.
Saran, J., Pande, V., (2012). Recurrence relations for moments of progressive Type II right censored order statistics from Half-Logistic distribution. Journal of Statistical Theory and Applications, 11(1), pp. 87–96.
Saran, J., Pushkarna, N., (2001). Recurrence relations for moments of progressive TypeII right censored order statistics from Burr distribution. Statistics, 35(4), pp. 495– 507.
Saran, J., Pushkarna, N., (2014). Moments of Progressive Type-II Right Censored Order Statistics from a General Class of Doubly Truncated Continuous Distributions. Journal of Statistical Theory and Applications, 13(2), pp. 162–174.
Tahir, M. H., Cordeiro, G. M., Mansoor, M., Zubair, M., (2015). The Weibull-Lomax distribution: properties and applications. Hacettepe Journal of Mathematics and Statistics, 44(2), pp. 461–480.
Tahir, M. H., Hussain, M. A., Cordeiro, G. M., Hamedani, G. G., Mansoor, M., Zubair, M., (2016). The Gumbel-Lomax Distribution: Properties and Applications. Journal of Statistical Theory and Applications, 15(1), pp. 61–79.
Thomas, D. R., Wilson, W. M., (1972). Linear order statistics estimation for the two parameter Weibull and extreme value distributions from Type II progressively censored samples. Technometrics, 14, pp. 679–691.