Estimation of the smallest scale parameter of two-parameter exponential distributions

References

• Ahsanullah, M. 1995. Record statistics. New York, NY: Nova Science Publishers.
   Google Scholar
• Arnold, B. C. 1970. Inadmissibility of the usual scale estimate for a shifted exponential distribution. Journal of the American Statistical Association 65:1260–4.
   Web of Science ®Google Scholar
• Arnold, B. C., N. Balakrishnan, and H. N. Nagaraja. 1998. Records. New York, NY: Wiley.
   Google Scholar
• Balakrishnan, N., and R. Aggarwala. 2000. Progressive censoring: Theory, methods and applications. Boston, MA: Birkhäuser.
   Google Scholar
• Bobotas, P., and S. Kourouklis. 2009. Strawderman-type estimators for a scale parameter with application to the exponential distribution. Journal of Statistical Planning and Inference 139:3001–12.
   Web of Science ®Google Scholar
• Bobotas, P., and S. Kourouklis. 2011. Improved estimation of the scale parameter, the hazard rate parameter and the ratio of the scale parameters in exponential distributions: An integrated approach. Journal of Statistical Planning and Inference 141:2399–416.
   Web of Science ®Google Scholar
• Bobotas, P., and S. Kourouklis. 2017. Estimation of the smallest normal variance with applications to variance components models. Statistics & Probability Letters 131:38–45.
   Web of Science ®Google Scholar
• Brewster, J. F. 1974. Alternative estimators for the scale parameter of the exponential distribution with unknown location. The Annals of Statistics 2:553–7.
   Web of Science ®Google Scholar
• Brewster, J. F., and J. V. Zidek. 1974. Improving on equivariant estimators. The Annals of Statistics 2:21–38.
   Web of Science ®Google Scholar
• Cramer, E., and G. Iliopoulos. 2010. Adaptive progressive Type-II censoring. Test 19:342–58.
   Web of Science ®Google Scholar
• Fearnhead, P., and L. Meligkotsidou. 2004. Exact filtering for partially observed continuous time models. Journal of the Royal Statistical Society: Series B 66:771–89.
   Google Scholar
• Goutis, C., and G. Casella. 1991. Improved invariant confidence intervals for a normal variance. The Annals of Statistics 19:2015–31.
   Web of Science ®Google Scholar
• Iliopoulos, G., and S. Kourouklis. 2000. Interval estimation for the ratio of scale parameters and for ordered scale parameters. Statistics & Decisions 18:169–184.
   Google Scholar
• Kubokawa, T. 1994a. A unified approach to improving equivariant estimators. The Annals of Statistics 22:290–9.
   Web of Science ®Google Scholar
• Kubokawa, T. 1994b. Double shrinkage estimation of ratio of scale parameters. Annals of the Institute of Statistical Mathematics 46:95–116.
   Web of Science ®Google Scholar
• Kushary, D., and A. Cohen. 1989. Estimating ordered location and scale parameters. Statistics & Decisions 7:201–13.
   Google Scholar
• Lehmann, E. L., and J. P. Romano. 2005. Testing statistical hypotheses. 3rd ed. New York, NY: Springer.
   Google Scholar
• Madi, M. 2002. On the invariant estimation of an exponential scale using doubly censored data. Statistics & Probability Letters 56:77–82.
   Web of Science ®Google Scholar
• Madi, M. 2006. Decision theoretic estimation using record statistics. Metrika 63:91–8.
   Web of Science ®Google Scholar
• Madi, M. 2010. A note on the equivariant estimation of an exponential scale using progressively censored data. Journal of Statistical Planning and Inference 140:1437–40.
   Web of Science ®Google Scholar
• Mathai, A. M. 1982. Storage capacity of a dam with gamma type inputs. Annals of the Institute of Statistical Mathematics 34:591–7.
   Web of Science ®Google Scholar
• Maruyama, Y. 1998. Minimax estimators of a normal variance. Metrika 48:209–14.
   Web of Science ®Google Scholar
• Petropoulos, C., and S. Kourouklis. 2002. A class of improved estimators for the scale parameter of an exponential distribution with unknown location. Communications in Statistics—Theory Methods 31:325–35.
   Web of Science ®Google Scholar
• Petropoulos, C., and S. Kourouklis. 2012. New classes of improved confidence intervals for the variance of a normal distribution. Metrika 75:491–506.
   Web of Science ®Google Scholar
• Robertson, T., F. T. Wright, and R. L. Dykstra. 1988. Order restricted statistical inference. New York, NY: Wiley.
   Google Scholar
• Stein, C. 1964. Inadmissibility of the usual estimator for the variance of a normal distribution with unknown mean. Annals of the Institute of Statistical Mathematics 16:155–60.
   Web of Science ®Google Scholar
• Strawderman, W. E. 1974. Minimax estimation of powers of the variance of a normal population under squared error loss. The Annals of Statistics 2:190–8.
   Web of Science ®Google Scholar
• Vijayasree, G., N. Misra, and H. Singh. 1995. Componentwise estimation of order parameters of k (≥ 2) exponential populations. Annals of the Institute of Statistical Mathematics 47:287–307.
   Web of Science ®Google Scholar
• Zidek, J. V. 1973. Estimating the scale parameter of the exponential distribution with unknown location. The Annals of Statistics 1:264–78.
   Web of Science ®Google Scholar