A handwritten signature is the final response to a complex cognitive and neuromuscular process which is the result of the learning process. Because of the many factors involved in signing, it is possible to study the signature from many points of view: graphologists, forensic experts, neurologists and computer vision experts have all examined them. Researchers study written signatures for psychiatric, penal, health and automatic verification purposes. As a potentially useful, multi-purpose study, this paper is focused on the lexical morphology of handwritten signatures. This we understand to mean the identification, analysis, and description of the signature structures of a given signer. In this work we analyze different public datasets involving 1533 signers from different Western geographical areas. Some relevant characteristics of signature lexical morphology have been selected, examined in terms of their probability distribution functions and modeled through a General Extreme Value distribution. This study suggests some useful models for multi-disciplinary sciences which depend on handwriting signatures.