As a common starting point for the interpretation of SnowMicroPenetrometer (SMP) data the penetration force is interpreted as a superposition of spatially uncorrelated ruptures of structural elements which follow an ideal elastic-brittle response. We re-state this idea and describe the fluctuating penetration force as a Poisson shot noise process. This allows us to derive simple analytical expressions for the cumulants and the co-variance of the penetration force in terms of the micromechanical, force-displacement parameters of individual elements. Vice versa, the micromechanical parameters can be estimated from the statistics of the penetration force. We test our method with simulated shot noise processes and real snow profiles and reveal potential limitations of the underlying assumptions. Our model unifies different previous approaches to snow classification which are based on snow penetration resistance.