Abstract Characterization of diffuse alcoholic disease is being attempted by estimating the slope of the acoustic attenuation coefficient with frequency, a parameter denoted by β, from reflected ultrasound signals. The ultrasound signals reflected from within the body are distorted by the non-ideal properties of tissues. Two distorting mechanisms are considered: the propagation through nonhomogeneous media and the reflection from irregularly shaped interfaces. The mechanisms are modeled as random filters and their effect on estimating the value of β are considered. The variances of three β estimators are derived from the model. Clinical results on normals and patients with alcoholic liver disease are presented to verify the model.