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

Abstract

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).