Abstract
The paper discusses the problem of estimation of parameters in a Rayleigh distribution modified to take into account the additional information. Madan and Guild [1981] have already given the maximum likelihood estimator (MLE) and the minimum mean squared estimator (MMSE) for the problem. Here we propose a new type of estimator called the entropy estimator for finding the mean of the samples from a small number of observations. The entropy estimator is the ratio of the arithmetic mean to the geometric mean multiplied by a normalizing constant. After normalizing the three estimates appropriately, the tightness of the entropy estimator is demonstrated numerically.
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References
Abromowitz, A. and Stegun, I.A. (1965). Handbook of Mathematical Functions, pp. 255–293, Dover Publications, Inc., New York.
Gray, A.H. and Markel, J.D. (1974). “A Spectral-Flatness Measure for Studying the Autocorrelation Method of Linear Prediction of Speech Analysis,” IEEE Transactions on Acoustics, Speech and Signal Processing, ASSP-22, No.3, pp. 207–217.
Madan, R.N. and Guild, J. (1981). “Maximum Likelihood Estimation in Radar Signals,” International Symposium on Information Theory, IEEE, February 9–12, 1981, Santa Monica, CA.
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© 1988 Kluwer Academic Publishers
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Madan, R.N. (1988). On a Detection Estimator Related to Entropy. In: Erickson, G.J., Smith, C.R. (eds) Maximum-Entropy and Bayesian Methods in Science and Engineering. Fundamental Theories of Physics, vol 31-32. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-3049-0_14
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DOI: https://doi.org/10.1007/978-94-009-3049-0_14
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-7871-9
Online ISBN: 978-94-009-3049-0
eBook Packages: Springer Book Archive