qfratio

Evaluates moments of ratios (and products) of quadratic forms in normal variables, specifically using recursive algorithms developed by Bao and Kan (2013) doi:10.1016/j.jmva.2013.03.002 and Hillier et al. (2014) doi:10.1017/S0266466613000364. Also provides distribution, quantile, and probability density functions of simple ratios of quadratic forms in normal variables with several algorithms. Originally developed as a supplement to Watanabe (2023) doi:10.1007/s00285-023-01930-8 for evaluating average evolvability measures in evolutionary quantitative genetics, but can be used for a broader class of statistics. Generating functions for these moments are also closely related to the top-order zonal and invariant polynomials of matrix arguments.