DOUBLE STAGE SHRINKAGE TESTIMATION IN EXPONENTIAL TYPE-II CENSORED DATA

Gyan Prakash; D. C. Singh

Gyan Prakash Department of Statistics, Harish Chandra P. G. College, Varanasi, U. P., India , D. C. Singh Department of Statistics, Harish Chandra P. G. College, Varanasi, U. P., India. Statistics in Transition new series, vol. 10, 2009, 2, pages: 235-250 Published online: 1 October 2009

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ABSTRACT

The present paper investigates the properties of the shrinkage testimators for mean and variance of an Exponential distribution in double stage samples, by using the cost function when Type – II censored data are available.

KEYWORDS

Type-II censored data; Shrinkage factor; Shrinkage testimator; Level of significance; Effective Interval; Cost function.

REFERENCES

ADKE, S. R., WAIKAR, V. B. and SCHUURMANN, F. J. (1987). A two stage shrinkage testimator for the mean of an exponential distribution. Communication in Statistics – Theory and Methods, 16, 1821–1834.

AL-BAYYATI, H. A. and ARNOLD, J. C. (1969). Double stage shrunken estimator of the variance. Ind. Statist. Theory Meth. Assoc., 7, 175–184.

AL-BAYYATI, H. A. and ARNOLD, J. C. (1972). On double stage estimation in simple liner regression using prior knowledge. Technometrices, 14, 405–414.

AL-BAYYATI, H. A. and ARNOLD, J. C. (1970). On double stage estimation of mean using prior knowledge. Biometrics, 26, 787–800.

BANCROFT, T. A. and HAN, C. P. (1977). Inference based on conditional specification. A note and a bibliography. International Statistical Review, 15, 117–127.

BASU, A. P. and EBRAHIMI, N. (1991). Bayesian approach to life testing and reliability estimation using asymmetric loss function. Journal of Statistical Planning and Inferences, 29, 21–31.

CHAPMAN, D. G. (1960). Some two sample test. Annals of Mathematical Statistics, 21, 601–606.

EBRAHIMI, N. and HOSMANE, B. (1987). On shrinkage estimation of the Exponential parameter. Communications in Statistics –Theory and Methods, 16, 2623–2637.

EPSTEIN, B. and SOBEL, M. (1953). Life Testing. Journal of American Statistical Association, 48, 486–507.

HAN, C. P., RAO, C. V. and RAVICHANDRAN, J. (1988). Inference based on the condition specification: A second bibliography. Communications in Statistics –Theory and Methods, A–17, 1–21.

KATTI, S. K. (1962). Use of some apriori knowledge in the estimation of mean from double samples. Biometrics, 18, 139–147.

PANDEY, B. N. (1979). Double stage estimation of population variance. Annals of Institute of Statistics Mathematical, 31, 225–233.

PANDEY, B. N. (1983). Shrinkage estimation of the Exponential scale parameter. IEEE Transaction on Reliability, R–32, 203–205.

PANDEY, B. N. (1997). Testimator of the scale parameter of the Exponential distribution using LINEX loss function. Communication in Statistics – Theory and Methods, 26, 2191–2200.

PANDEY, B. N and SRIVASTAVA, R. (1987). A shrinkage testimator for scale parameter of an exponential distribution. Microelectron Reliability, 27 (16), 949–951.

SHAH, S. M. (1964). Use a prior knowledge in the estimation of a parameter from double samples. Journal of Indian Statistical Association, 2, 41–51.

STEIN, C. (1945). A two-stage sample test for a linear hypothesis whose power is independent of the variance. Annals of Mathematical Statistics, 16, 243–258.

THOMPSON, J. R. (1968) Some Shrunken techniques for estimating the Mean. Journal of the American Statistical Association, 63, 113–122.

WAIKAR, V. B., SCHUURMANN, F. J. and RAGHUNATHAN, T. E. (1984). On a two stage shrunken testimator of the mean of a normal distribution. Communications in Statistics – Theory and Methods, 13, 1901–1913.

WEISS, L. (1945). On confidence intervals of given length for the mean of a Normal distribution with unknown variance. Annals of Mathematical Statistics, 16, 348–352.