We investigate the feasibility of quantifying properties of a composite dielectric material through the reflectance, where the permittivity is described by the Lorentz model in which an unknown probability measure is placed on the model parameters. We summarize the computational and theoretical framework (the Prohorov Metric Framework) developed by our group in the past two decades for nonparametric estimation of probability measures using a least-squares method, and point out the limitation of the existing computational algorithms for this particular application. We then demonstrate the feasibility of our proposed methods by numerical results obtained for both simulated data and experimental data for inorganic glass when considering the resonance wavenumber as a distributed parameter. This research represents joint efforts with colleagues at NCSU (Jared Catenacci and Dr. Shuhua Hu) and collaborative research efforts of our group with scientists at AFRL (Materials State Awareness and Supportability Branch, Air Force Research Lab, WPAFB 45433, USA) led by Amanda K. Criner and Adam T. Cooney. In these efforts, the goal is to develop a noninvasive technique to characterize the degradation of a complex nonmagnetic dielectric material (e.g., ceramic matrix composites, which are used in a wide range of applications such as high temperature engines) by assessing the small physical and chemical changes in the material using reflectance spectroscopy. This involves determining the components of the permittivity of the composite dielectric medium using the measured spectral responses.