The inference procedure for any elliptical configuration density is set out in this work in terms of published efficient algorithms involving infinite confluent hypergeometric type series of zonal polynomials. The polynomial configuration density study is proposed and then applied in a subfamily of the Kotz configuration densities, including the normal distribution; the inference procedure is then based on polynomial densities, which can be computed easily. Finally, the polynomial distributions are applied to the type of experiment readily available in other publications on shape literature.