Weibull distribution

The Weibull distribution models the long-term distribution of wave heights and wave-induced load peaks, with cumulative form F(x) = 1 minus exp of minus (x over lambda) to the power k, defined by a shape parameter k and a scale lambda (a three-parameter version adds a location shift). The Rayleigh distribution of short-term wave heights is the special case k = 2. Fitting load peaks to a Weibull tail lets the extreme response at a design probability, for instance 10-to-the-minus-8 per cycle over the ship life, be read off by extrapolation, which is how IACS Common Structural Rules set the wave bending moment and how fatigue stress ranges are characterized for spectral and equivalent-design-wave methods.