NOTE SIMPLIFIED METHOD-OF-MOMENTS ESTIMATION FOR THE WEIBULL DISTRIBUTION

It is often necessary to find a Weibull distribution with specified mean, variance, and location parameter (e.g., Ek et al. 1975; Goulding & Shirley 1979). The usual approach involves the use of some iterative numerical procedure for computing the parameters. An approximation which simplifies the computation and makes it less costly is presented here. This method can be used with a pocket calculator. Greenwood & Durand (I960) used a similar method for maximum likelihood estimation of Gamma parameters. The (three-parameters) Weibull distribution is F(x) = 1- exp V-a(x-c)hr\, c^x< oo, with density f(x) = abix-cj^1 V-a(x-c)hl. The mean and variance are fji = c + ir1/ * T (l + l/b) (Ia) er2 = a-2/b |T (1+2/b)- r 2 ( l + l / £ ) ] (Ib) The moment estimators of a and b (c assumed known) are obtained by solving Equation