Characterization of biological tissues in ultrasound images is often tackled using empirical pre-Rayleigh distributions. However, the absence of a theoretical explanation to these distributions hinders their improvement and clinical interpretation. This paper presents a novel model that extends classic statistical theories to speckle in biological tissues and explains the existing pre-Rayleigh distributions. Furthermore, statistics derived from the proposed model outperform the state of the art in skin tissue characterization. Finally, promising results in characterization of skin melanoma tumors set the basis for the development of reliable ultrasound-based diagnosis techniques.