SOMETIMES POOL TESTIMATION OF SCALE PARAMETER FOR NEGATIVE EXPONENTIAL MODEL UNDER GENERAL ENTROPY LOSS FUNCTION
Keywords:
Negative exponential distribution, Scale Parameter, Type – II Censored Samples, Preliminary Test, Level of Significance, General Entropy Loss Function, Life Ratio, Euler’s Psi Function, Relative Risk.Abstract
The present paper proposes a sometimes pool testimator of scale parameter (mean life) of negative exponential distribution under general entropy loss function, when it is assume that both the guarantees are known If a real life situation is modeled by this distribution having mean life time of certain items as θ1 and now it is suspected that the mean life may change due to some technological advances and assumes the value θ2 then we may have conditional information on θ1 as θ1≥θ2(however θ1 may be less than or equal to θ2).This uncertainty can be resolved by using preliminary testing and then a sometimes pool testimator is proposed for θ1The risk properties of this estimator have been studied under General entropy loss function and it is claimed that the estimator dominates the never pool estimator (in terms of having smaller risk) in certain range of life ratio. Use of a general entropy loss function facilitates to control the risk of proposed estimators for various directions and degrees of asymmetry.
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References
Basu, A. P. and Ebrahimi, N. (1991). Bayesian approach to life testing and
reliability estimation using asymmetric loss function, J. Statist. Plann. Inf., 29,
p. 21 – 31.
Canfield, R. V. (1970). A Bayesian approach to reliability estimation using
loss function. IEEE Trans, Reliab., 19, p. 13 – 16.
Calabria, R. and Pulcini, G. (1994a). An engineering approach to Bayes
estimation for the Weibull distribution, Microelectronics and Reliability, 34, p.
– 802.
Davis, D. J. (1952). The analysis of some failure data, J. Amer. Stat. Assoc.,
, p. 113 – 160.
Dey, D. K. and Peri – San Liao Lin (1992). On comparison of estimators in a
generalized life model, Microdectron. Reliab., 32, p. 207 – 221.
Epstein, B. and Sobel, M. (1953). Life testing, J. Amer. Stat. Assoc., 48, p.
– 502.
Govindrajulu, Z. (1964). A supplement to a bibliography on life testing and
related topics, J. Amer. Stat. Assoc., 59, p. 1231 – 1241.
. Mendenhall, W. (1958). A bibliography on life testing and related topics,
Biometrika, 45, p. 521 – 543.
Parsian, A. and Sanjari Farsipour, N. (1993). On the admissibility of estimator
of scale parameters using an asymmetric loss function, Comm. Stat. – Theory
and methods, 22, p. 2877 – 2901.
Ramkaran and Bhattacharya, S. K. (1984). A sometimes pool estimator of the
mean life, Biom. J., 26, p. 383 – 387.
Rai, O. (1996). A sometimes pool estimator of the mean life under Linex loss
function, Comm. Stat. – Theory and methods, 25, p. 2057 – 2067.
Schabe, H. (1991). Bayes estimators under asymmetric loss, IEEE., 40, p. 63
– 67.
Srivastava, R. (1996). Bayesian estimation of scale parameter and reliability in
Weibull distribution using asymmetric loss function, IAPQR Trans., 21, p.
– 148.
Srivastava, R. and Tank, H. B. (2001). Sometimes pool testimtion of a scale
parameter under asymmetric loss function, Calcutta Statist. Association
Bulletin, 51, p. 105 – 111.
Srivastava, R. and Tanna, V. (2001). An estimation procedure for error
variance incorporating PTS for random effects model under LINEX loss
function, Comm. Stat. - Theory and Methods, 30(15), p. 2583 – 2599.
Srivastava,R.and Tanna,V.(2005). Improved testimation procedure for error
variance in Random models incorporating PTS: Under Linex loss function,
.JISAS 59(2), p. 104-111.
Srivastava,R and Tanna,V.(2007). Double stage shrinkage testimator for scale
parameter in Exponential distribution under General Entropy loss function,
Comm. Stat. – Theory and methods, 36(2), p. 283-295.
Srivastava,R and Tanna,V.(2011). Pooling procedures for
incompletelySpecified random models under asymmetric loss functions,
Jour.of Indian Stat.Assoc. 49(2), p. 231-251.
Tanna, V. and Srivastava, R. (2012). A pretest double stage shrunken
testimator of the mean life of exponential life model under asymmetric loss
function, Aligarh Journal of Statistics, 32, p. 11-28.
Varde, S. D. (1969). Life testing and reliability estimation for the two
parameter exponential distribution, J. Amer. Statist. Assoc., 64, p. 621 – 631.
Varian, H. R. (1975). A Bayesian approach to real estate assessment. In
studies in Bayesian econometrics and statistics in honour of L. J. Savage, Eds.
S. E. Feinberge and A. Zellner, Amsterdam North Holland, p. 195 – 208.
Zellner, A. (1986). Bayesian estimation and predictions using asymmetric loss
function. J. Amer. Statist. Assoc., 61, p. 446 – 451.
