An intermolecular parameter estimation procedure is incorporated into a model of a static cell vapor-liquid equilibrium experiment where only the total pressure and temperature are measured, so that compositions are not available experimentally. The coexistence compositions are often obtained from the raw experimental measurements by data reduction, in which a (mostly empirical) thermodynamic description must be assumed to represent the liquid and vapor phases. The molecular interaction parameters inherent in a more advanced equation of state treatment are then estimated from this pretreated data for the coexistence compositions. This can lead to a bias in the development of the mixture model and does not allow a statistical analysis to be applied to the model. To overcome these limitations, an integrated self-consistent approach is developed in this work. The pure component model parameters are used with an equation of state to calculate the amount of substance in the experimental apparatus, and the mixture parameters are obtained from parameter estimation based on a model of the experimental setup and the representation of the vapor-liquid equilibrium. This type of integrated approach, best achieved by close integration of detailed experimental information and the theoretical treatment, is tested on three well-studied and characterized binary mixtures: xenon + diborane; xenon + cyclopropane; and xenon + boron trifluoride. The statistical associating fluid theory for potentials of variable range (SAFT-VR) is the equation of state used in this work; the molecular models inherent in the approach are associating chain molecules formed from square-well segments. Excellent agreement between SAFT-VR calculations of the fluid phase equilibrium and experimental data is obtained for all three mixtures, without a priori knowledge of the compositions of the coexisting phases. In the case of xenon + boron trifluoride, the region of liquid-liquid immiscibility and the vapor-liquid-liquid three-phase line are accurately predicted. The effect of experimental error is incorporated into the parameter estimation procedure so that the confidence in the optimal parameters can be evaluated providing guidance in choosing which parameters to estimate with confidence. For comparison, SAFT-VR models are also developed using the reduced data for the coexistence compositions. The description of the fluid phase equilibrium and the values of the intermolecular parameters are found to be similar to those obtained from the integrated approach. The integrated approach presented is general and can be modified to specific static cell apparatus or applied to other types of mixtures or with other equations of state.