Author(s)

Siaka Touré

Solar Energy Laboratory, FHB University Abidjan Cocody, Abidjan, Côte d’Ivoire.

The Weibull distribution is a probability density function (PDF) which is widely used in the study of meteorological data. The statistical analysis of the wind speed v by using the Weibull distribution leads to the estimate of the mean wind speed < v >, the variance of v around < v > and the mean power density in the wind. The gamma function Γ is involved in those calculations, particularly Γ (1+1/k), Γ (1+2/k) and Γ (1+3/k). The paper reports the use of the Weibull PDF f(v) to estimate the gamma function. The study was performed by looking for the wind speeds related to the maximum values of f(v), v² f(v) and v³ f(v). As a result, some approximate relationships were obtained for Γ (1+1/k), Γ (1+2/k) and Γ (1+3/k), that use some fitting polynomial functions. Very good agreements were found between the exact and the estimated values of Γ (1+n/k) that can be used for the estimation of the mean wind speed < v >, the variance σ² of the wind speed v; around the mean speed and the average wind power density.

Gamma Function, Weibull Distribution, Beta Function, Mean Wind Speed, Average Wind Power Density

Touré, S. (2019) Investigations into Some Simple Expressions of the Gamma Function in Wind Power Theoretical Estimate by the Weibull Distribution. Journal of Applied Mathematics and Physics, 7, 2990-3002. doi: 10.4236/jamp.2019.712209.