Using the King and Wells method, we present experimental data on the dependence of the sticking of molecular hydrogen and deuterium on the beam temperature onto nonporous amorphous solid water ice surfaces of interstellar interest. A statistical model that explains the isotopic effect and the beam temperature behavior of our data is proposed. This model gives an understanding of the discrepancy between all known experimental results on the sticking of molecular hydrogen. Moreover, it is able to fit the theoretical results of Buch et al. [Astrophys. J. 379, 647 (1991)] on atomic hydrogen and deuterium. For astrophysical applications, an analytical formula for the sticking coefficients of H, D, H₂, D₂, and HD in the case of a gas phase at thermal equilibrium is also provided at the end of the article.