Aids for Fitting the Gamma Distribution by Maximum Likelihood

Evaluation of the rainfall component of a weather generator for climate impact studies

“…This is expected as Geng et al (1986) based their linear model for b on estimates using the ML approximation method of Greenwood and Durand (1960). This also agrees with the literature (e.g.…”

Analysis of extreme precipitation over Europe from different reanalyses: a comparative assessment

“…For a fixed mean precipitation, the growing scale parameter implies increasing of the percentile for a relatively large (more than 10 mm/day) precipitation value. Quantitative estimation of the shape and scale parameters was performed using maximum likelihood method of Greenwood and Durand (1960), based on ln(hxi)Àhln(x)i, hi being the averaging operator, which is more effective than the traditional moment estimators (Wilks, 1990(Wilks, , 1995 and more accurate for the data used than the Thom (1958) method. From the Gamma distribution, we have derived the other statistical characteristics of daily precipitation, such as different percentiles and others.…”

Inferences concerning the Mean of the Gamma Distribution

“…as a function of In (g/x), and Wilk, Gnanadesikan, and Huyett (1962) give tables of I? as a function of Q = [l -(a/2)-l]-l. Greenwood and Durand (1960) also provide rational approximations for I?.…”