Carlos de la Calle-Arroyo, University of Castilla-La Mancha

• Title: Homoscedastic and Heteroscedastic response in Antoine’s Equation Optimal Designs

• Abstract: Vapor pressure is a temperature-dependent characteristic of pure liquids, and also of their mixtures. This thermodynamic property can be characterized through a wide range of models. Antoine's equation stands out among them for its simplicity and precision. Its parameters are estimated via maximum likelihood with experimental data. Once the parameters of the equation have been estimated, vapor pressures between known values of the curve can be interpolated. Other physical properties such as heat of vaporization can be predicted as well. The probability distribution of a physical phenomenon is often hard to know in advance, as it depends on the phenomenon itself as well as the procedures to carry on the experiments and the measurements. Hence, assuming a probability distribution for such events has to be done with caution, as it affects the Fisher Information Matrix and consequently the optimal designs. This work presents D-, Ds-, A- and I-optimal designs to estimate the unknown parameters of the Antoine's equation as accurately as possible for homoscedastic and heteroscedastic normal distribution of the response, with the characteristic objectives of the different criteria. An online tool to calculate Antoine's optimal designs for the criteria included in this work has been developed.