Approximation of a normal distribution by a three‐parameter log normal distribution

A procedure is given where mixed normal and log normal populations exist; the normal populations can be approximated with three-parameter log normal (3PLN) distributions to facilitate multivariate stochastic hydrologic disaggregation or generation approaches. Approximations can be made by assuming an arbitrary small value of skew G (0.05-0.01). For G ≤ 0.1 the appropriate parameters for a 3PLN distribution can be approximated as dimensionless location parameter α = a/μx ≃ 1 − CV(3G−l+ G/9); σy ≃ G/3 − 7G3/324; µy ≃ ln (3σx/G) − (G2/54).