Johnson 4-parameter distribution

The Johnson four-parameter distribution is a member of the Johnson translation system (the SB bounded, SU unbounded, and SL lognormal families), fitted by transforming the variate to a standard normal through z = gamma plus delta times a function of (x minus xi) over lambda, with two shape parameters gamma and delta, a location xi, and a scale lambda. Its flexibility in skewness and kurtosis lets it fit measured short-term wave-crest, wave-height, or nonlinear-response data that depart from the Rayleigh form, by matching the first four moments. In ocean and structural engineering it is used to model non-Gaussian peaks where a two-parameter Rayleigh or Weibull fit is inadequate.