The beta distribution - A statistical model for world cloud cover

Considerable work has been performed in developing empirical global cloud cover models. This investigation was made to determine a theoretical statistical distribution to represent worldwide cloud cover. The beta distribution with probability density function ƒ(x) = [Γ(γ + η)/Γ(γ)Γ(η)]xγ−1(1 − x)η−1, where 0 ≤ x ≤ 1, γ > 0, and η > 0, and ƒ (x) = 0 elsewhere is presented to represent the variability of this random variable. It is shown that the beta distribution possesses the versatile statistical characteristics necessary to assume the wide variety of shapes exhibited by cloud cover. A total of 160 representative empirical cloud cover distributions were investigated, and the conclusion is reached that this study provides sufficient statistical evidence to accept the beta probability distribution as an adequate model for world cloud cover.