On a Detection Estimator Related to Entropy
The paper discusses the problem of estimation of parameters in a Rayleigh distribution modified to take into account the additional information. Madan and Guild  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.
KeywordsFalse Alarm Random Noise Rayleigh Distribution Linear Detector Entropy Estimator
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