Universal probability density functions (PDFs) of two-dimensional turbulent velocity fluctuations, Reynolds shear stress and conditional Reynolds shear stresses in flows over smooth and rough beds are obtained using a Gram-Charlier series expansion based on the exponential distribution. To include skewness and kurtosis, the series is truncated up to moments of Order 4. The distributions of PDFs obtained theoretically and from the experimental data are in agreement. The conditional Reynolds shear stresses related to the ejections and sweeps are well represented by the exponential distribution, but those related to the outward and inward interactions depart from the theoretical distributions. © 2010 International Association for Hydro-Environment Engineering and Research.