The analysis of human movement poses a well-known challenge that has already been addressed in various ways and needs to be adapted to the type of movement being considered. The focus here is on the analysis of hand movement in sign language. This study aims to characterize and model the different variations present in the data to develop a realistic generative model of hand movement in sign language. We identify two types of variations that play a key role in characterizing human movement: temporal variations and shape variations, i.e., variations in the speed of movement and the geometry of movement. However, separating these variations or understanding their relationship is a non-trivial task. A well-known model for the relationship between time, speed, and geometry is the 2/3 power-law demonstrated for several human movements, mainly constrained and planar. We find that the generalization of this law to a three-dimensional motion is not sufficient to explain variations in hand movement in sign language. We develop a new statistical modeling framework that is flexible and can respect the geometry of the movement signals. The two different variations are identified using the Frenet-Serret representation and modeled by mean geometry, mean speed, and their nonlinear transformations. The nonlinear variations in time and geometry are analyzed by functional principal component analysis. Then the generative model for the hand movement in sign language is built by imposing a joint probability model on the principal coefficients of these components. CCS CONCEPTS • Mathematics of computing → Functional analysis; Multivariate statistics.