The sampling distributions for the activity coefficient gamma and distribution ratio (or K-value) in binary fluid mixtures are derived from the assumptions that the pressure errors are negligible, and that the vapor and liquid composition measurements from which they are derived are normally distributed with known mean and variance. The distribution of K is shown to be not normal, with deviations from normality becoming particularly pronounced at the extremes of the composition range. The dispersion of this distribution is considerably greater than that predicted by the classic error-propagation formula. Deviation from normality invalidates the most important assumption implicit in the use of the least-squares criterion as the basis for parameter estimation from activity-coefficient data. This has important implications for the estimation of Henry's law constants for solutes in very dilute solutions, as well as for Raoult's law-based infinite-dilution activity coefficients. The use of the exact distributions of gamma and K as the basis for a more rigorous maximum-likelihood method for parameter estimation in excess Gibbs energy models based on either Henry's law or Raoult's law standard states is demonstrated.