The Folded Normal Distribution: Two Methods of Estimating Parameters from Moments

Abstract

The general formula for the rth moment of the folded normal distribution is obtained, and formulae for the first four non-central and central moments are calculated explicitly. To illustrate the mode of convergence of the folded normal to the normal distribution, as μ/σ = θ increases, the shape factors β f1 and β f2 were calculated and the relationship between them represented graphically. Two methods, one using first and second moments (Method I) and the other using second and fourth moments (Method II) of estimating the parameters μ and σ of the parent normal distribution are presented and their standard errors calculated. The accuracy of both methods, for various values of θ, are discussed.