New Shrinkage Entropy Estimator for Mean of Exponential Distribution under Different Loss Functions




Exponential distribution, Entropy function, Shrinkage estimation, Progressive type-II censored sample, Squared error loss function and LINEX loss function


In this paper, a new shrinkage estimator of entropy function for mean of an exponential distribution is proposed. A progressive type censored sample is taken to obtain the estimator. For the new estimator, risk functions and relative risk functions are developed under symmetric and asymmetric loss functions, viz. squared error loss function and LINEX loss function, and new estimator is shown to have better performance than a classical estimator in terms of relative risk.


Download data is not yet available.


N. Balakrishnan and R. Aggarwala, Progressive Censoring: Theory, Methods, and Applications, Birkhäuser, Boston, MA, xv + 248 (2000), DOI: 10.1007/978-1-4612-1334-5.

J. O. Berger, Statistical Decision Theory and Bayesian Analysis, 2nd edition, Springer-Verlag, New York, xvi + 618 (1985), DOI: 10.1007/978-1-4757-4286-2.

E. S. Jeevanand and E. I. Abdul-Sathar, Estimation of residual entropy function for exponential distribution from censored samples, ProbStat Forum 2 (2009), 68 – 77, URL:

A. K. Jiheel and A. Shanubhogue, Shrinkage estimation of the entropy function for the exponential distribution under different loss functions using progressive type II censored sample, International Journal of Mathematics and Computer Research 2(4) (2014), 394 – 402, URL:

N. S. Kambo, B. R. Handa and Z. A. Al-Hemyari, On shrunken estimators for exponential scale parameter, Journal of Statistical Planning and Inference 24(1) (1990), 87 – 94, DOI: 10.1016/0378-3758(90)90019-Q.

S. Kayal and S. Kumar, Estimating the entropy of an exponential population under the LINEX loss function, Journal of the Indian Statistical Association 49(1) (2011), 91 – 112.

A. V. Lazo and P. Rathie, On the entropy of continuous probability distributions (Corresp.), IEEE Transactions on Information Theory 24(1) (1978), 120 – 122, DOI: 10.1109/TIT.1978.1055832.

H. F. Martz, Bayesian Reliability Analysis, in: Wiley StatsRef: Statistics Reference Online (editors: N. Balakrishnan, T. Colton, B. Everitt, W. Piegorsch, F. Ruggeri and J. L. Teugels), John Wiley & Sons, New York (2014), DOI: 10.1002/9781118445112.stat03957.

N. Misra, H. Singh and E. Demchuk, Estimation of the entropy of multivariate normal distribution, Journal of Multivariate Analysis 92(2) (2005), 324 – 342, DOI: 10.1016/j.jmva.2003.10.003.

C. E. Shannon, A mathematical theory of communication, The Bell System Technical Journal 27(3) (1948), 379 – 423, DOI: 10.1002/j.1538-7305.1948.tb01338.x.

J. R. Thompson, Some shrinkage techniques for estimating the mean, Journal of the American Statistical Association 63(321) (1968), 113 – 122, DOI: 10.1080/01621459.1968.11009226.

H. R. Varian, A Bayesian approach to real estate assessment, in: Studies in Bayesian Econometrics and Statistics: in Honor of L. J. Savage, L. J. Savage, S. E. Feinberg and A. Zellner (eds.), North-Holland Publishing Company, Amsterdam (1975), pp. 195 – 208.




How to Cite

Sahni, P., & Kumar, R. (2023). New Shrinkage Entropy Estimator for Mean of Exponential Distribution under Different Loss Functions. Communications in Mathematics and Applications, 14(1), 175–187.



Research Article