•We propose a general unit hydrography (GUH) distribution for wind speed statistics.•The GUH distribution is a generalized logistic distribution with a closed form.•The GUH model removes the limitation of a zero initial condition in the Weibull model. We here introduce a simple, general, and analytical method based on the general unit hydrograph (GUH) theory proposed by Guo (2022a, 2022b, 2022c) to describe wind speed marginal distribution. Wind speed probability is generally described by the Weibull distribution; however, its accuracy depends on the contribution made by null wind speed (owing to its zero initial condition). To overcome this disadvantage, we propose a three-parameter GUH distribution with significant flexibility in modeling symmetric heavy-tailed distributions as well as skewed distributions. We show that our proposed GUH distribution corresponds to a generalized logistic distribution that contains both type I and type II generalized logistic distributions. The shape properties of the GUH distribution are discussed along with a simple method for estimating parameters by means of least squares methods. The flexibility of the proposed GUH distribution was assessed by applying it to a well reconstructed global gridded wind speed dataset. Subsequently, we quantify the changes caused by a reversal in global surface wind speed stilling using our GUH distribution. Finally, we confirm that our proposed GUH model agrees with reconstructed wind speed data better than conventional Weibull distribution models, which suggests that the new distribution can be a useful tool for sustainable development of wind energy.