Package: qfratio 1.1.1.9000
qfratio: Moments and Distributions of Ratios of Quadratic Forms Using Recursion
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.
Authors:
qfratio_1.1.1.9000.tar.gz
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qfratio.pdf |qfratio.html✨
qfratio/json (API)
NEWS
| # Install 'qfratio' in R: |
| install.packages('qfratio', repos = c('https://watanabe-j.r-universe.dev', 'https://cloud.r-project.org')) |
Bug tracker:https://github.com/watanabe-j/qfratio/issues
quadratic-formsrcpprcppeigenzonal-polynomials
Last updated 2 months agofrom:a2ccd27726. Checks:OK: 9. Indexed: yes.
| Target | Result | Date |
|---|---|---|
| Doc / Vignettes | OK | Nov 23 2024 |
| R-4.5-win-x86_64 | OK | Nov 23 2024 |
| R-4.5-linux-x86_64 | OK | Nov 23 2024 |
| R-4.4-win-x86_64 | OK | Nov 23 2024 |
| R-4.4-mac-x86_64 | OK | Nov 23 2024 |
| R-4.4-mac-aarch64 | OK | Nov 23 2024 |
| R-4.3-win-x86_64 | OK | Nov 23 2024 |
| R-4.3-mac-x86_64 | OK | Nov 23 2024 |
| R-4.3-mac-aarch64 | OK | Nov 23 2024 |
Exports:dqfrpqfrqfm_Ap_intqfmrmqfmrm_ApBDqr_intqfmrm_ApBDqr_npiqfmrm_ApBIqr_intqfmrm_ApBIqr_npiqfmrm_IpBDqr_genqfpm_ABDpqr_intqfpm_ABpq_intqfrmqfrm_ApBq_intqfrm_ApBq_npiqfrm_ApIq_intqfrm_ApIq_npiqqfrrqfmrrqfprqfr
qfratio: Moments of Ratios of Quadratic Forms
Rendered fromqfratio.Rmdusingknitr::rmarkdownon Nov 23 2024.Last update: 2023-07-15
Started: 2023-02-16
Probability Distribution Functions in Package qfratio
Rendered fromqfratio_distr.Rmdusingknitr::rmarkdownon Nov 23 2024.Last update: 2023-10-20
Started: 2023-07-12
Readme and manuals
Help Manual
| Help page | Topics |
|---|---|
| Recursion for a_{p,k} | a1_pk |
| Coefficients in polynomial expansion of generating function-single matrix | d1_i dtil1_i dtil1_i_m dtil1_i_v |
| Coefficients in polynomial expansion of generating function-for ratios with two matrices | d2_1j d2_1j_m d2_1j_v d2_ij d2_ij_m d2_ij_v d2_pj d2_pj_m d2_pj_v h2_ij h2_ij_m h2_ij_v hhat2_1j hhat2_1j_m hhat2_1j_v hhat2_pj hhat2_pj_m hhat2_pj_v htil2_1j htil2_1j_m htil2_1j_v htil2_pj htil2_pj_m htil2_pj_v |
| Coefficients in polynomial expansion of generating function-for ratios with three matrices | d3_ijk d3_ijk_m d3_ijk_v d3_pjk d3_pjk_m d3_pjk_v h3_ijk h3_ijk_m h3_ijk_v hhat3_pjk hhat3_pjk_m hhat3_pjk_v htil3_pjk htil3_pjk_m htil3_pjk_v |
| Probability distribution of ratio of quadratic forms | dqfr dqfr_A1I1 dqfr_broda dqfr_butler pqfr pqfr_A1B1 pqfr_butler pqfr_davies pqfr_imhof qqfr |
| Coefficients in polynomial expansion of generating function-for products | dtil2_1q_m dtil2_1q_v dtil2_pq dtil2_pq_m dtil2_pq_v dtil3_pqr dtil3_pqr_m dtil3_pqr_v |
| Calculate hypergeometric series | hgs hgs_1d hgs_2d hgs_3d |
| Internal C++ wrappers for GSL | gsl_wrap hyperg_1F1_vec_b hyperg_2F1_mat_a_vec_c |
| Is this matrix diagonal? | is_diagonal |
| Are these vectors equal? | iseq |
| Matrix square root and generalized inverse | KiK |
| Construct qfrm object | new_qfpm new_qfrm |
| Internal C++ functions | ABDpqr_int_E ABpq_int_E ApBDqr_int_Ec ApBDqr_int_Ed ApBDqr_int_El ApBDqr_npi_Ec ApBDqr_npi_Ed ApBDqr_npi_El ApBIqr_int_cEd ApBIqr_int_nEc ApBIqr_int_nEd ApBIqr_int_nEl ApBIqr_npi_Ec ApBIqr_npi_Ed ApBIqr_npi_El ApBq_int_E ApBq_npi_Ec ApBq_npi_Ed ApBq_npi_El ApIq_int_cE ApIq_int_nE ApIq_npi_cE ApIq_npi_nEc ApIq_npi_nEd ApIq_npi_nEl Ap_int_E d_A1I1_Ed d_broda_Ed d_butler_Ed IpBDqr_gen_Ec IpBDqr_gen_Ed IpBDqr_gen_El p_A1B1_Ec p_A1B1_Ed p_A1B1_El p_butler_Ed p_imhof_Ed qfrm_cpp rqfpE |
| Methods for qfrm and qfpm objects | methods.qfrm plot.qfrm print.qfpm print.qfrm |
| Moment of multiple ratio of quadratic forms in normal variables | qfmrm qfmrm_ApBDqr_int qfmrm_ApBDqr_npi qfmrm_ApBIqr_int qfmrm_ApBIqr_npi qfmrm_IpBDqr_gen |
| Moment of (product of) quadratic forms in normal variables | qfm_Ap_int qfpm qfpm_ABDpqr_int qfpm_ABpq_int |
| Moment of ratio of quadratic forms in normal variables | qfrm qfrm_ApBq_int qfrm_ApBq_npi qfrm_ApIq_int qfrm_ApIq_npi |
| Get range of ratio of quadratic forms | gen_eig range_qfr |
| Monte Carlo sampling of ratio/product of quadratic forms | rqfmr rqfp rqfr |
| Make covariance matrix from eigenstructure | S_fromUL |
| Summing up counter-diagonal elements | sum_counterdiag sum_counterdiag3D |
| Matrix trace function | tr |
