The 2-parameter Weibull distribution is the hypothesis that is widely used in the fitting studies of random series of wind speeds. Several procedures are used to find the set of the two fitting parameters k and c. From an experimental study, the fitting parameters were first determined by the regression method. The basic ideas of the Eigen-coordinates method were reported by previous works, in the case of the 4-parameter Stauffer distribution. In the present paper, the new method is applied to identify the 2-parameter Weibull distribution. The differential equation was identified. Then the study disclosed a linear relationship with two Eigen-coordinates. Two complemental errors epsilon(j) and e(j) were introduced, as criteria to assess the goodness-of-fit of the distribution. e(j) was linked to the linear relationship. epsilon(j) was used to test the goodness-of-fit between the observed and Weibull cumulative distribution functions. Then the fitting parameters were determined using the Eigen-coordinates method. The results showed a better reliability. (C) 2004 Elsevier Ltd. All rights reserved.