Moments and Distributions of Ratios of Quadratic Forms Using Recursion
Recursion for a_{p,k}
Coefficients in polynomial expansion of generating function---single m...
Coefficients in polynomial expansion of generating function---for rati...
Coefficients in polynomial expansion of generating function---for rati...
Coefficients in polynomial expansion of generating function---for prod...
Internal C++ wrappers for
Calculate hypergeometric series
Is this matrix diagonal?
Are these vectors equal?
Matrix square root and generalized inverse
Methods for qfrm and qfpm objects
Construct qfrm object
Probability distribution of ratio of quadratic forms
Moment of multiple ratio of quadratic forms in normal variables
Moment of (product of) quadratic forms in normal variables
qfratio: Moments and Distributions of Ratios of Quadratic Forms
Moment of ratio of quadratic forms in normal variables
Internal C++ functions
Get range of ratio of quadratic forms
Monte Carlo sampling of ratio/product of quadratic forms
Make covariance matrix from eigenstructure
Summing up counter-diagonal elements
Matrix trace function
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.