In many oceanic waveguides, acoustic propagation is characterized by a parameter called waveguide invariant. This property is used in many passive and active sonar applications where knowledge of the waveguide invariant value is required. The waveguide invariant is classically considered as scalar but several studies show that it is better modeled by a distribution because of its dependence on frequency and mode pairs. This paper presents a new method for estimating the waveguide invariant distribution. Using the noise radiated by a distant ship and a single hydrophone, the proposed methodology allows estimating the waveguide invariant for each pair of modes in shallow water. Performance is evaluated on simulated data.