Relations for moments of progressively Type-II right  censored order statistics from Erlang-truncated exponential distribution

Mansoor Rashid  Malik; Devendra  Kumar

Relations for moments of progressively Type-II right censored order statistics from Erlang-truncated exponential distribution

Mansoor Rashid Malik Department of Statistics, Amity University, Noida, India. , Devendra Kumar Corresponding Author: Department of Statistics, Central University of Haryana. Statistics in Transition new series, vol. 18, 2017, 4, pages: 651-668 Published online: 29 December 2017

116 Views 4 Downloads

ARTICLE

(English) PDF

ABSTRACT

In this paper, we establish some new recurrence relations for the single and product moments of progressively Type-II right censored order statistics from the Erlangtruncated exponential distribution. These relations generalize those established by Aggarwala and Balakrishnan (1996) for standard exponential distribution. These recurrence relations enable computation of mean, variances and covariances of all progressively Type-II right censored order statistics for all sample sizes in a simple and efficient manner. Further an algorithm is discussed which enable us to compute all the means, variances and covariances of Erlang-truncated exponential progressive Type-II right censored order statistics for all sample sizes n and all censoring schemes (R1, R2,..., Rm), m < n. By using these relations, we tabulate the means and variances of progressively Type-II right censored order statistics of the Erlangtruncated exponential distribution

KEYWORDS

Censoring, progressive Type-II right censored order statistics, single moments, product moments, recurrence relations, Erlang-truncated exponential distribution.

REFERENCES

ARNOLD, B. C., BALAKRISHNAN, N., NAGARAJA, H. N., (1992). A First Course in Order Statistics. John Wiley and Sons, New York.

AGGARWALA, R., BALAKRISHNAN, N., (1996). Recurrence relations for sin gle and product moments of progressively Type-II censored order statistics from a exponential and truncated exponential distribution. Ann. Inst. Statist.Math., 48, pp. 757–771.

BALAKRISHNAN, N., MALIK, H. J., (1986). Order statistics from the linear exponential distribution, part I: Increasing hazard rate case. Comm. Stat. The ory Meth., 15, pp. 179–203.

BALAKRISHNAN, N., CRAMER, H. J., (2014). The art of progressive censoring:Applications to reliability and quality. Springer Science Business Media New York.

BALAKRISHNAN, N., Sandhu, R. A., (1995). A simple simulational algorithm for generating progressive Type-II censored samples. Amer. Statist., 49, pp.229–230.

BALAKRISHNAN, N., AGGARWALA, R. (1998). Recurrence relations for single and product moments of order statistics from a generalized logistic distribution with applications to inference and generalizations to double truncation. Hand book of Statistics, 17, pp. 85–126.

BALAKRISHNAN, N., SULTAN, K. S., (1998). Recurrence relations and identi ties for moments of order statistics. In: N. Balakrishnan and C. R. Rao, eds.Handbook of Statistics, 16, pp. 149–228, Order Statistics: Theory and Meth ods, North-Holland, Amsterdam, The Netherlands.

BALAKRISHNAN, N. AGGARWALA, R., (2000). Progressive Censoring: The ory, Method and Applications, Birkhauser, Bosto.

BALAKRISHNAN, N., KANNAN, N., LIN, C. T., WU, S. J. S., (2004). Inference for the extreme value distribution under progressive Type-II censoring, Journal of Statistical Computation and Simulation, 74, pp. 25–45.

BALAKRISHNAN, N., (2007). Progressive Censoring Methodology. An Ap praisal Test. 16, pp. 211–296.

BALAKRISHNAN, N., AL-HUSSAINI, E. K., SALEH, H. M., (2011). Recur rence relations for moments of progressively censored order statistics from logistic distribution with applications to inference. Journal of Statistical Plan ning and Inference, 14, pp. 17–30.

BALAKRISHNAN, N., SALEH, H. M., (2012). Relations for moments of pro gressively Type-II censored order statistics from log-logistic distribution with applications to inference. Comm. Stat. Theory Meth., 41, pp. 880–906.

BALAKRISHNAN, N., SALEH, H. M., (2013). Recurrence relations for single and product moments of progressively Type-II censored order statistics from a generalized halflogistic distribution with application to inference., Journal of Statistical Computation and Simulation, 83, 1704–1721.

COHEN, A. C., (1963). Progressively censored samples in life testing, Technomet rics, 5, pp. 327–329.

DAVID, H. A., NAGARAJA, H. N., (2003). Order Statistics, Third Edition. John Wiley and Sons, New York.

EL-BASET, A., AHMED, A., FAWZY, A. M., (2003). Recurrence relations for sin gle moments of generalized order statistics from doubly truncated distribution.Journal of Statistical Planning and Inference, 117, pp. 241–249.

El-Alosey, A. R., (2007). Random sum of new type of mixture of distribution.International Journal of Statistics and Systems, 2, pp. 49–57.

FERNANDEZ, A. J., (2004). On estimating exponential parameters with general type II progressive censoring. Journal of Statistical Planning and Inference,121, pp. 135–147.

JOSHI, P. C., (1978). Recurrence relations between moments of order statistics from exponential and truncated exponential distributions. Sankhya Ser. B, 39,pp. 362–371.

KHAN, R. U., KUMAR, D., HASEEB, A., (2010). Moments of generalized order statistics from Erlang-truncated exponential distribution and its characteriza tion. International Journal of Statistics and Systems, 5, pp. 455–464.

KUMAR, D., (20014). Relations of generalized order statistics from Erlang-Truncated exponential distribution. Pacific Journal of Applied Statistics, 6, pp. 55–77.

KUMAR, D., DEY, S., NADARAJAH, S., (2017). Extended exponential distribu tion based on order statistics. Communications in Statistics-Theory and Meth ods, 46, pp. 9166–9184.

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

KULSHRESTHA, A., KHAN, R. U., KUMAR, D., (2013). On moment generat ing functions of generalized order statistics from Erlang-truncated exponential distribution. Open Journal of Statistics, 2, pp. 557–564.

MAHMOUD, R. M., SULTAN, K. S., SALEH, H. M., (2006). Progressively cen sored data from the linear exponential distribution, moments and estimation.METRON, LXIV(2), pp. 99–215.

MANN, N. R., (1971). Best linear invariant estimation for Weibull parameters under progressive censoring, Technometrics, 13, pp. 521–534.

NADARAJAH, S., HAGHIGHI, F., (2011). An extension of the exponential distri bution. Statistics, 45, pp. 543–558.

NIKULIN, M., HAGHIGHI, F., (2006). A chi-squared test for the generalized power Weibull family for the head-and-neck cancer censored data. Journal of Mathematics Sciences, 133, pp. 1333–1341.

SALAH, M. M., RAQAB, M. Z., AHSANULLAH, M., (2008). Marshall-Olkin Exponential Distribution: Moments of Order Statistics. Journal of Applied Statistical Science, 17, pp. 81–92.

SULTAN, K. S., MAHMOUD, M. R., SALEH, H. M., (2006). Moments of estima tion from progressively censored data of the half logistic distribution. Interna tional Journal of Reliability and Applications, 7, pp. 187–201.

THOMAS, D. R., WILSON, W. M., (1972). Linear order statistic estimation for the two-parameter Weibull and extreme-value distributions from Type-II pro gressively censored samples. Technometrics, 14, pp. 679–691.

VIVEROS, R., BALAKRISHNAN, N., (1994). Interval estimation of life charac teristics from progressively censored data. Technometric