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The acoustic attenuation coefficient of soft biological tissue has been observed to have an increasing linear-with-frequency attenuation characteristic with a slope, denoted by β, that varies with the disease condition of the liver. Hence, it would be diagnostically useful to estimate the value of β from reflected ultrasound signals. Two approaches for estimating β are examined: the spectral-shift approach, which estimates β from the downward shift experienced by the propagating pulse spectrum with penetration into the liver, and the spectral-difference approach, which estimates β from the slope of the log spectral differences. While the spectral-shift approach requires the propagating pulse to have a Gaussian-shaped spectrum, the spectral-difference method does not require a specific spectral form. A mathematical model is developed to simulate the random ultrasound signals reflected from the liver. The bias and variance properties of the β estimators are determined by using the simulated signals and compared as a function of the data window size. The results indicate that, while the accuracy of both approaches is equivalent for large data windows, the frequency-shift approach is more accurate than the spectral-difference approach for most practical cases.