Parviz Nasiri

© Parviz Nasiri. Article available under the CC BY-SA 4.0 licence


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In this paper, we studied estimators based on an interval shrinkage with equal weights point shrinkage estimators for all individual target points θ ∈ (θ01) for exponentially distributed observations in the presence of outliers drawn from a uniform distribution. Estimators obtained from both shrinkage and interval shrinkage were compared, showing that the estimators obtained via the interval shrinkage method perform better. Symmetric and asymmetric loss functions were also used to calculate the estimators. Finally, a numerical study and illustrative examples were provided to describe the results.


interval information, mean square error, shrinkage estimator, exponential distribution, uniform distribution, outliers, Linex loss function


Basu, A. P., & Ebrahimi, N., (1991). Bayesian approach to life testing and reliability estimation using asymmetric loss function. Journal of statistical planning and inference, 29(1–2), pp. 21–31.

Berger, J., (1985). Statistical decision theory and Bayesian analysis. Springer, second edition.

Bhattacharya, S. K., & Srivastava, V. K., (1974). A preliminary test procedure in life testing. Journal of the American Statistical Association, 69(347), pp. 726–729.

Dixit, U. J. & Nasiri, P., (2001). Estimation of parameters of the exponential distribution in the presence of outlier generated from uniform distribution, Metron 49, (3-4), pp. 187–198.

Epstein, B., & Sobel, M., (1954). Some theorems relevant to life testing from an exponential distribution. The Annals of Mathematical Statistics, pp. 373–381.

Golosnoy, V., & Liesenfeld, R., (2011). Interval shrinkage estimators. Journal of Applied Statistics, 38(3), pp. 465–477.

Hawkins, D. M., (1980). Identification of outliers (Vol. 11). London: Chapman and Hall.

Nasiri, P. & Ebrahimi, F., (2019), Interval Shrinkage Estimators of Scale Parameter of Exponential Distribution in the Presence of Outliers, Malaysian Journal of Mathematical Sciences, 13(1), pp. 75–85.

Nasiri, P., & Jabbari Nooghabi, M., (2009). Estimation of P[Y < X] for generalized exponential distribution in presence of outlier. Iranian Journal of Numerical Analysis and Optimization, 2(1), pp. 69–80.

Nelson, W. B., (1982). Applied life Data Analysis. Wiley, New York.

Pandey, B. N., (1997). Testimator of the scale parameter of the exponential distribution using LINEX loss function. Communications in statistics-theory and methods, 26(9), pp. 2191–2202.

Roio, J., (1987). On the admissibility of c[Xbar]+d with respect to the LINEX loss function. Communications in Statistics-Theory and Methods, 16(12), pp. 3745–3748.

Soliman, A. A., (2000). Comparison of LINEX and quadratic Bayes estimators for the Rayleigh distribution. Communications in Statistics-theory and Methods, 29(1), pp. 95–107.

Stein, C., (1956). Inadmissibility of the usual estimator for the mean of a multivariate normal distribution. In Proceedings of the Third Berkeley symposium on mathematical statistics and probability, Vol. 1, No. 1, pp. 197–206.

Thompson, J. R., (1968). Accuracy borrowing in the estimation of the mean by shrinkage to an interval. Journal of the American Statistical Association, 63(323), pp. 953–963.

Varian, H. R., (1975). A Bayesian approach to real estate assessment. Studies in Bayesian econometric and statistics in Honor of Leonard J. Savage, pp. 195–208.

Zellner, A., (1986). Bayesian estimation and prediction using asymmetric loss functions. Journal of the American Statistical Association, 81(394), pp. 446–451.

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