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qfratio  

Moments and Distributions of Ratios of Quadratic Forms Using Recursion
View on CRAN: Click here


Download and install qfratio package within the R console
Install from CRAN:
install.packages("qfratio")

Install from Github:
library("remotes")
install_github("cran/qfratio")

Install by package version:
library("remotes")
install_version("qfratio", "1.1.1")



Attach the package and use:
library("qfratio")
Maintained by
Junya Watanabe
[Scholar Profile | Author Map]
All associated links for this package
First Published: 2023-03-16
Latest Update: 2024-02-09
Description:
Evaluates moments of ratios (and products) of quadratic forms in normal variables, specifically using recursive algorithms developed by Bao and Kan (2013) and Hillier et al. (2014) . 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) 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.
How to cite:
Junya Watanabe (2023). qfratio: Moments and Distributions of Ratios of Quadratic Forms Using Recursion. R package version 1.1.1, https://cran.r-project.org/web/packages/qfratio. Accessed 26 Aug. 2026.
Previous versions and publish date:
(2026-07-22 22:20), 1.0.0 (2023-03-16 20:00), 1.0.1 (2023-04-02 16:30), 1.1.0 (2023-10-02 20:40), 1.1.1 (2024-02-09 01:30)
Other packages that cited qfratio R package
View qfratio citation profile
Other R packages that qfratio depends, imports, suggests or enhances
Complete documentation for qfratio
Functions, R codes and Examples using the qfratio R package
Some associated functions: KiK . S_fromUL . a1_pk . d1_i . d2_ij . d3_ijk . dtil2_pq . hgs . is_diagonal . iseq . methods.qfrm . new_qfrm . pqfr . qfmrm . qfpm . qfratio-package . qfrm . qfrm_cpp . rqfr . sum_counterdiag . tr . 
Some associated R codes: RcppExports.R . dist_funs.R . dk_funs.R . hgs_funs.R . methods_qfrm.R . qfratio-package.R . ratio_fun.R . rqf_funs.R . utils.R . zzz.R .  Full qfratio package functions and examples
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