Shrinkage Estimators of the Reliability Characteristics of a Family of Lifetime Distributions
DOI:
https://doi.org/10.6092/issn.1973-2201/5458Keywords:
Family of lifetime distributions, shrinkage estimation, type I and type II censorings, p-valueAbstract
A family of distributions is considered, which covers many lifetime distributions as specific cases. Two measures of reliability are considered, R(t) = P(X>t) and P = P(X>Y). Shrinkage estimators are considered for the powers of parameter, R(t) and 'P' under type I and type II censorings. Simulation study is conducted to judge the performance of estimators.References
Ahsanullah, M. (1980): Linear prediction of record values for the two parameter exponential distribution. Ann. Inst. Statist. Math., 32, Part A, 363-368.
Awad, A. M. and Gharraf, M. K. (1986): Estimation of P(Y
Baklizi, A. (2003): Shrinkage estimation of the exponential reliability with censored data. Focus on Applied Statistics, p.195-204.
Baklizi, A. and Dayyeh, W. A. (2003): Shrinkage Estimation of P(Y
Bartholomew, D. J. (1957): A problem in life testing. Jour. Amer. Statist. Assoc., 52, p. 350-355.
Bartholomew, D. J. (1963): The sampling distribution of an estimate arising in life testing. Technometrics, 5, p. 361-374.
Basu, A. P. (1964): Estimates of reliability for some distributions useful in life testing. Technometrics, 6, p. 215-219.
Burr, I. W. (1942): Cumulative frequency functions. Ann. Math. Statist., 13, p.215-232.
Chao, A. (1982): On comparing estimators of Pr{X>Y} in the exponential case. IEEE Trans. Reliability, R-26, p. 389-392.
Chaturvedi, A., Chauhan, K. and Alam, M. W. (2009): Estimation of the reliability function for a family of lifetime distributions under type I and type II censorings. Journal of reliability and statistical studies, 2(2), p. 11-30.
Chaturvedi, A. and Rani, U. (1997): Estimation procedures for a family of density functions representing various life-testing models. Metrika, 46, 213-219.
Chaturvedi, A. and Rani, U. (1998): Classical and Bayesian reliability estimation of the generalized Maxwell failure distribution. Jour. Statist. Res., 32, 113-120.
Chaturvedi, A. and Surinder, K. (1999): Further remarks on estimating the reliability function of exponential distribution under type I and type II censorings. Brazilian Jour. Prob. Statist., 13, p. 29-39.
Chen, Z. (2000): A new two- parameter lifetime distribution with bathtub shape or increasing failure rate function. Statistics & Probability Letters, 49, 155-161.
Cislak, P. J. and Burr, I. W. (1968): On a general system of distributions; I. Its curve-shape characteristics; II. The sample median. Jour. Amer. Statist. Assoc., 63. p. 627-635.
Constantine, K., Karson, M. and Tse, S. K. (1986): Estimation of P(Y
Erdélyi, A. (1954): Tables of Integral Transformations, Vol. 1. McGraw-Hill.
Johnson, N. L. (1975): Letter to the editor. Technometrics, 17, p. 393.
Johnson, N. L., Kotz, S. and Balakrishnan, N. (1994): Continuous Univariate Distributions-Vol. 1. John Wiley & Sons, New York.
Khan, R.U. and Zia, B. (2009): Recurrence Relations for single and Product moments of record values from Gompertz distribution and a characterization. World Applied Sciences Journal, 7(10), 1331-1334.
Kelly, G. D., Kelly, J.A. and Schucany, W. R. (1976): Efficient estimation of P(Y
Lai, C. D., Xie, M. and Murthy, D. N. P. (2003): Modified Weibull model. IEEE Trans. Reliability, 52, 33-37.
Ljubo, M. (1965): Curves and concentration indices for certain generalized Pareto distributions. Statist. Rev., 15, 257-260.
Lomax, K. S. (1954): Business failures. Another example of the analysis of failure data. Jour. Amer. Statist. Assoc., 49, 847-852.
Mahmoud, M. A. W. and Al-Nagar, H. SH. (2009): On generalized order statistics from linear exponential distribution and its characterization. Stat Papers, 50, 407-418.
Nikulin, M. and Haghighi, F. (2006): A chi-squared test for the generalized power weibull family for the head-and-neck cancer censored data, Journal of Mathematical sciences, Vol. 133(3), 1333-1341.
Pandey, M. (1983): Shrinkage estimation of the exponential scale parameter. IEEE Trans. Rel. , 2, 203-205.
Philipson, C. (1963): A note on moments of a Poisson probability distribution. Scandinavian Actuarial Journal, Vol. 1963, Issue 3-4, p. 243-244.
Pugh, E.L. (1963): The best estimate of reliability in the exponential case. Operations Research, 11, p. 57-61.
Sathe, Y. S. and Shah, S. P. (1981): On estimating P(X
Sinha, S. K. (1986): Reliability and Life Testing. Wiley Eastern Limited, New Delhi.
Tadikamalla, P. R. (1980): A look at the Burr and related distributions. Inter. Statist. Rev., 48, 337-344.
Thompson, J. (1968): Some shrinkage techniques for estimating the mean. JASA, 63, p. 113-122.
Tong, H. (1974): A note on the estimation of P(Y
Tong, H. (1975): Letter to the editor. Technometrics, 17, p. 393.
Tse, S. and Tso, G. (1996): Shrinkage estimation of reliability for exponentially distributed lifetmes. Communications in Statistics, Simulation and Computation, 25(2), p.415-430.
Tyagi, R. K. and Bhattacharya, S. K.(1989): A note on the MVU estimation of reliability for the Maxwell failure distribution. Estadistica, 41, p. 73-79.
Watson, G. N. (1952): Treatise on the theory of Bessell Functions (2nd ed.). Cambridge University Press, London.
Xie, M., Tang, Y. and Goh, T. N. (2002): A modified Weibull extension with bathtub-shaped failure rate function. Reliability Eng. Sys. Safety, 76, 279-285.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2016 Statistica
This journal is licensed under a Creative Commons Attribution 3.0 Unported License (full legal code).
Authors accept to transfer their copyrights to the journal.
See also our Open Access Policy.
