Four anhysteretic polarization models that have been used in the literature to evaluate data acquired from lead magnesium niobate (PMN) are analyzed and compared. Derivations of two of the models from assumed spatial distributions of dipole energy states, using first physical principles, are presented. A third model is derived from a suitable integral averaging calculation. These derivations are used as the basis for developing an integral equation for determining an energy-state distribution that produces a fourth model, which was not originally formulated in terms of an assumed distribution. A new polarization function is also presented. Excellent approximations to each of the four polarization functions of interest can be deduced from this new polarization function by adjusting the numerical value of just a single parameter. An application of two of the models to data is presented. It is shown that it can be necessary to consider a sample to be an admixture of two distinct species of poles, in the sense that two polarization functions must be added together in order to accommodate the data.