qfratio
Moments and Distributions of Ratios of Quadratic Forms Using Recursion
Last update: 9 February 2024
Copyright license: GNU General Public License
Software version identifier: 1.0.0, 1.0.1, 1.1.0, 1.1.1
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.
- On the moments of ratios of quadratic forms in normal random variables
- GENERATING FUNCTIONS AND SHORT RECURSIONS, WITH APPLICATIONS TO THE MOMENTS OF QUADRATIC FORMS IN NONCENTRAL NORMAL VECTORS
- Exact expressions and numerical evaluation of average evolvability measures for characterizing and comparing $$\textbf{G}$$ matrices
