On the Construction of Preliminary Test Estimators of the Reliability Characteristics for the Exponential Distribution Based on Records

References

• Arnold, B. C., Balakrishan, N., & Nagaraja, H. N. (1992). A First Course in Order Statistics. John Wiley & Sons.
   Google Scholar
• Arashi, M., & Emadi, M. (2008). Evidential inference based on record data and inter-record times. Statistical Papers, 13(8), 380–210.
   Google Scholar
• Awad, A. M., & Gharraf, M. K. (1986). Estimation of P(Y<X) in the Burr case: A Comparative Study. Communications in Statistics - Simulation and Computation, 15(2), 389–403.
   Web of Science ®Google Scholar
• Balakrishan, N., Ahsanullah, M., & Chan, P. S. (1995). On the logistic record values and associated inference. Journal of Applied Statistical Science, 2, 233–248.
   Google Scholar
• Bancroft, T. A. (1944). On Biases in Estimation Due to the Use of Preliminary Tests of Significance. Ann. Math. Stat., 15(2), 190–204.
   Google Scholar
• Bartholomew, D. J. (1957). A problem in life testing. Journal of the American Statistical Association, 52, 350–355.
   Web of Science ®Google Scholar
• Bartholomew, D. J. (1963). The sampling distribution of an estimate arising in life testing. Technometrics, 5, 361–374.
   Web of Science ®Google Scholar
• Basu, A. P. (1964). Estimates of reliability for some distributions useful in life testing. Technometrics, 6, 215–219.
   Web of Science ®Google Scholar
• Belaghi, R. A., Arashi, M., & Tabatabaey, S. M. M. (2014). Improved confidence intervals for the scale parameter of Burr XII model based on record values. Computational Statistics, 29(5), 1153–1173, doi10.1007/s00180-014-0484-3
   Web of Science ®Google Scholar
• Belaghi, R. A., Arashi, M., & Tabatabaey, S. M. M. (2015). On the Construction of Preliminary Test Estimator Based on Record Values for the Burr XII Model. Communications in Statistics - Theory and Methods, 44(1), 1–23, doi:10.1080/03610926.2012.733473
   Web of Science ®Google Scholar
• Chandler, K. N. (1952). The distribution and frequency of record values. Jour. Journal of the Royal Statistical Society, Series B, 14, 220–228.
   Google Scholar
• Chao, A. (1982). On comparing estimators of Pr{X>Y} in the exponential case. IEEE Transactions on Reliability, R-26, 389–392.
   Google Scholar
• Chaturvedi, A., & Kumari, T. (2015). Estimation and testing procedures for the reliability functions of a family of lifetime distributions. interstat.statjournals.net/YEAR/2015/abstracts/1306001.php
   Google Scholar
• Chaturvedi, A., & Malhotra, A. (2016). Estimation and Testing Procedures for the Reliability Functions of a Family of Lifetime Distributions based on Records. International Journal of System Assurance Engineering and Management, doi:10.1007/s13198-016-0531-2
   Web of Science ®Google Scholar
• Chaturvedi, A., & Malhotra, A. (2017). Inference on the Parameters and Reliability Characteristics of three parameter Burr Distribution based on Records. Applied Mathematics & Information Sciences, 11(3), 837–849.
   Google Scholar
• Chaturvedi, A., & Pathak, A. (2012). Estimation of the reliability functions for exponentiated Weibull distribution. Journal of Statistics & Applications, 7, 1–8.
   Google Scholar
• Chaturvedi, A., & Pathak, A. (2013). Bayesian estimation procedures for three parameter exponentiated Weibull distribution under entropy loss function and type II censoring. interstat.statjournals.net/YEAR/2013/abstracts/1306001.php
   Google Scholar
• Chaturvedi, A., & Pathak, A. (2014). Estimation of the Reliability Function for four-Parameter Exponentiated Generalized Lomax Distribution. IJSER, 5(1), 1171–1180.
   Google Scholar
• Chaturvedi, A., & Rani, U. (1997). Estimation procedures for a family of density functions representing various life-testing models. Metrika, 46, 213–219.
   Web of Science ®Google Scholar
• Chaturvedi, A., & Rani, U. (1998). Classical and Bayesian reliability estimation of the generalized Maxwell failure distribution. Journal of Statistical Research, 32, 113–120.
   Google Scholar
• Chaturvedi, A., & Singh, K. G. (2006). Bayesian estimation procedures for a family of lifetime distributions under squared-error and entropy losses. Metron, 64(2), 179–198.
   Google Scholar
• Chaturvedi, A., & Singh, K. G. (2008). A family of lifetime distributions and related estimation and testing procedures for the reliability function. Journal of Applied Statistical Science, 16(2), 35–50.
   Google Scholar
• Chaturvedi, A., & Surinder, K. (1999). Further remarks on estimating the reliability function of exponential distribution under type I and type II censorings. Brazilian Journal of Probability and Statistics, 13, 29–39.
   Google Scholar
• Chaturvedi, A., & Tomer, S. K. (2002). Classical and Bayesian reliability estimation of the negative binomial distribution. Journal of Applied Statistical Science, 11, 33–43.
   Google Scholar
• Chaturvedi, A., & Tomer, S. K. (2003). UMVU estimation of the reliability function of the generalized life distributions. Statistical Papers, 44(3), 301–313.
   Web of Science ®Google Scholar
• Constantine, K., Karson, M., & Tse, S. K. (1986). Estimation of P(Y<X) in the gamma case. Commun. Statist.—Simul., 15(2), 365–388.
   Web of Science ®Google Scholar
• Epstein, B., & Sobel, M. (1953). Life Testing. Journal of the American Statistical Association, 48, 486–502.
   Web of Science ®Google Scholar
• Glick, N. (1978). Breaking records and breaking boards. American Mathematical Monthly, 85, 543–551.
   Web of Science ®Google Scholar
• Habibi Rad, A., Arghami, N. R., & Ahmadi, J. (2006). Statistical evidence in experiments and in record values. Communications in Statistics-Theory and Methods, 35(11), 1971–1983.
   Web of Science ®Google Scholar
• Johnson, N. L. (1975). Letter to the editor. Technometrics, 17, 393.
   Web of Science ®Google Scholar
• Kelly, G. D., Kelly, J. A., & Schucany, W. R. (1976). Efficient estimation of P(Y<X) in the exponential case. Technometrics, 18, 359–360.
   Web of Science ®Google Scholar
• Kibria, B. M. G. (2004). Performance of the shrinkage preliminary tests ridge regression estimators based on the conflicting of W, LR and LM tests. Journal of Statistical Computation and Simulation, 74(11), 793–810.
   Web of Science ®Google Scholar
• Kibria, B. M. G., & Saleh, A. K. M. E. (1993). Performance of shrinkage preliminary test estimator in regression analysis. Jahangrinagar Review, A17, 133–148.
   Google Scholar
• Kibria, B. M. G., & Saleh, A. K. M. E. (2004). Preliminary test ridge regression estimators with Student's t errors and conflicting test-statistics. Metrika., 59(2), 105–124.
   Web of Science ®Google Scholar
• Kibria, B. M. G., & Saleh, A. K. M. E. (2005). Comparison between Han-Bancroft and Brook method to determine the optimum significance level for pre-test estimator. Journal of Probability and Statistical Science, 3, 293–303.
   Google Scholar
• Kibria, B. M. G., & Saleh, A. K. M. E. (2006). Optimum critical value for pre-test estimators. Communications in Statistics-Theory and Methods, 35(2), 309–320.
   Web of Science ®Google Scholar
• Kibria, B. M. G., & Saleh, A. K. M. E. (2010). Preliminary test estimation of the parameters of exponential and Pareto distributions for censored samples. Statistical Papers, 51, 757–773.
   Web of Science ®Google Scholar
• Kotz, S., Lumelskii, Y., & Pensky, M. (2003). The Stress-Strength Model and its Generalizations, Theory and Applications. New York: World Scientific.
   Google Scholar
• Nagaraja, H. N. (1988a). Record values and related statistics—A review. Commun. Statist.—Theo. Meth., 17, 2223–2238.
   Web of Science ®Google Scholar
• Nagaraja, H. N. (1988b). Some characterizations of continuous distributions based on regressions of adjacent order statistics and record values. Sankhya, Series A, 50, 70–73.
   Google Scholar
• Pugh, E. L. (1963). The best estimate of reliability in the exponential case. Operations Research, 11, 57–61.
   Web of Science ®Google Scholar
• Razmkhah, M., & Ahmadi, J. (2011). Comparing two sampling schemes based on entropy of record statistics. Statist. Papers, 53, 95–106.
   Web of Science ®Google Scholar
• Saleh, A. K. M. E. (2006). Theory of preliminary test and Stein-type estimation with applications., Hoboken, NJ: John Wiley & Sons, Inc..
   Google Scholar
• Saleh, A. K. M. E., & Kibria, B. M. G. (1993). Performance of some new preliminary test ridge regression estimators and their properties. Communications in Statistics-Theory and Methods, 22(10), 2747–2764.
   Web of Science ®Google Scholar
• Sen, P. K., & Saleh, A. K. M. E. (1978). Nonparametric estimation of location parameter after a preliminary test on regression in the multivariate case. Journal of Multivariate Analysis, 9(2), 322–331.
   Web of Science ®Google Scholar
• Sinha, S. K. (1986). Reliability and Life Testing. New Delhi, India: Wiley Eastern Limited.
   Google Scholar
• Sathe, Y. S., & Shah, S. P. (1981). On estimating P(X > Y) for the exponential distribution. Commun. Stat. - Theory. Methods., 10(1):39–47.
   Web of Science ®Google Scholar
• Tong, H. (1974). A note on the estimation of P(Y<X) in the exponential case. Technometrics, 16, 625.
   Web of Science ®Google Scholar
• Tong, H. (1975). Letter to the editor. Technometrics, 17, 393.
   Web of Science ®Google Scholar
• Tyagi, R. K., & Bhattacharya, S. K. (1989). A note on the MVU estimation of reliability for the Maxwell failure distribution. Estadistica, 41, 73–79.
   Google Scholar
• Watson, R. I. (1952). Research design and methodology in evaluating the results of psychotherapy. Journal of Clinical Psychology, 8, 29–33. doi:10.1002/1097-4679(195201)8:1<29::AID-JCLP2270080107>3.0.CO;2-O
   PubMed Web of Science ®Google Scholar