Moments of Ratios of Quadratic Forms Using Recursion

---

Documentation for package ‘qfratio’ version 1.0.1

• DESCRIPTION file.
• User guides, package vignettes and other documentation.
• Package NEWS.

Help Pages

A D H I K M N P Q R S T

qfratio-package

qfratio: Moments of Ratios of Quadratic Forms Using Recursion

-- A --

a1_pk	Recursion for a_p,k
ABDpqr_int_cmE	Internal C++ functions
ABDpqr_int_cvE	Internal C++ functions
ABDpqr_int_nmE	Internal C++ functions
ABDpqr_int_nvE	Internal C++ functions
ABpq_int_cmE	Internal C++ functions
ABpq_int_cvE	Internal C++ functions
ABpq_int_nmE	Internal C++ functions
ABpq_int_nvE	Internal C++ functions
ApBDqr_int_cmE	Internal C++ functions
ApBDqr_int_cmEc	Internal C++ functions
ApBDqr_int_cmEl	Internal C++ functions
ApBDqr_int_cvE	Internal C++ functions
ApBDqr_int_cvEc	Internal C++ functions
ApBDqr_int_cvEl	Internal C++ functions
ApBDqr_int_nmE	Internal C++ functions
ApBDqr_int_nmEc	Internal C++ functions
ApBDqr_int_nmEl	Internal C++ functions
ApBDqr_int_nvE	Internal C++ functions
ApBDqr_int_nvEc	Internal C++ functions
ApBDqr_int_nvEl	Internal C++ functions
ApBDqr_npi_cmE	Internal C++ functions
ApBDqr_npi_cmEc	Internal C++ functions
ApBDqr_npi_cmEl	Internal C++ functions
ApBDqr_npi_cvE	Internal C++ functions
ApBDqr_npi_cvEc	Internal C++ functions
ApBDqr_npi_cvEl	Internal C++ functions
ApBDqr_npi_nmE	Internal C++ functions
ApBDqr_npi_nmEc	Internal C++ functions
ApBDqr_npi_nmEl	Internal C++ functions
ApBDqr_npi_nvE	Internal C++ functions
ApBDqr_npi_nvEc	Internal C++ functions
ApBDqr_npi_nvEl	Internal C++ functions
ApBIqr_int_cmE	Internal C++ functions
ApBIqr_int_cvE	Internal C++ functions
ApBIqr_int_nmE	Internal C++ functions
ApBIqr_int_nmEc	Internal C++ functions
ApBIqr_int_nmEl	Internal C++ functions
ApBIqr_int_nvE	Internal C++ functions
ApBIqr_int_nvEc	Internal C++ functions
ApBIqr_int_nvEl	Internal C++ functions
ApBIqr_npi_cmE	Internal C++ functions
ApBIqr_npi_cmEc	Internal C++ functions
ApBIqr_npi_cmEl	Internal C++ functions
ApBIqr_npi_cvE	Internal C++ functions
ApBIqr_npi_cvEc	Internal C++ functions
ApBIqr_npi_cvEl	Internal C++ functions
ApBIqr_npi_nmE	Internal C++ functions
ApBIqr_npi_nmEc	Internal C++ functions
ApBIqr_npi_nmEl	Internal C++ functions
ApBIqr_npi_nvE	Internal C++ functions
ApBIqr_npi_nvEc	Internal C++ functions
ApBIqr_npi_nvEl	Internal C++ functions
ApBq_int_cmE	Internal C++ functions
ApBq_int_cvE	Internal C++ functions
ApBq_int_nmE	Internal C++ functions
ApBq_int_nvE	Internal C++ functions
ApBq_npi_cmE	Internal C++ functions
ApBq_npi_cmEc	Internal C++ functions
ApBq_npi_cmEl	Internal C++ functions
ApBq_npi_cvE	Internal C++ functions
ApBq_npi_cvEc	Internal C++ functions
ApBq_npi_cvEl	Internal C++ functions
ApBq_npi_nmE	Internal C++ functions
ApBq_npi_nmEc	Internal C++ functions
ApBq_npi_nmEl	Internal C++ functions
ApBq_npi_nvE	Internal C++ functions
ApBq_npi_nvEc	Internal C++ functions
ApBq_npi_nvEl	Internal C++ functions
ApIq_int_cmE	Internal C++ functions
ApIq_int_nmE	Internal C++ functions
ApIq_npi_cvE	Internal C++ functions
ApIq_npi_nvE	Internal C++ functions
ApIq_npi_nvEc	Internal C++ functions
ApIq_npi_nvEl	Internal C++ functions
Ap_int_cmE	Internal C++ functions
Ap_int_nmE	Internal C++ functions

-- D --

d1_i	Coefficients in polynomial expansion of generating function-single matrix
d2_1j	Coefficients in polynomial expansion of generating function-for ratios with two matrices
d2_1j_m	Coefficients in polynomial expansion of generating function-for ratios with two matrices
d2_1j_v	Coefficients in polynomial expansion of generating function-for ratios with two matrices
d2_ij	Coefficients in polynomial expansion of generating function-for ratios with two matrices
d2_ij_m	Coefficients in polynomial expansion of generating function-for ratios with two matrices
d2_ij_v	Coefficients in polynomial expansion of generating function-for ratios with two matrices
d2_pj	Coefficients in polynomial expansion of generating function-for ratios with two matrices
d2_pj_m	Coefficients in polynomial expansion of generating function-for ratios with two matrices
d2_pj_v	Coefficients in polynomial expansion of generating function-for ratios with two matrices
d3_ijk	Coefficients in polynomial expansion of generating function-for ratios with three matrices
d3_ijk_m	Coefficients in polynomial expansion of generating function-for ratios with three matrices
d3_ijk_v	Coefficients in polynomial expansion of generating function-for ratios with three matrices
d3_pjk	Coefficients in polynomial expansion of generating function-for ratios with three matrices
d3_pjk_m	Coefficients in polynomial expansion of generating function-for ratios with three matrices
d3_pjk_v	Coefficients in polynomial expansion of generating function-for ratios with three matrices
dtil1_i	Coefficients in polynomial expansion of generating function-single matrix
dtil1_i_m	Coefficients in polynomial expansion of generating function-single matrix
dtil1_i_v	Coefficients in polynomial expansion of generating function-single matrix
dtil2_1q_m	Coefficients in polynomial expansion of generating function-for products
dtil2_1q_v	Coefficients in polynomial expansion of generating function-for products
dtil2_pq	Coefficients in polynomial expansion of generating function-for products
dtil2_pq_m	Coefficients in polynomial expansion of generating function-for products
dtil2_pq_v	Coefficients in polynomial expansion of generating function-for products
dtil3_pqr	Coefficients in polynomial expansion of generating function-for products
dtil3_pqr_m	Coefficients in polynomial expansion of generating function-for products
dtil3_pqr_v	Coefficients in polynomial expansion of generating function-for products

-- H --

h2_ij	Coefficients in polynomial expansion of generating function-for ratios with two matrices
h2_ij_m	Coefficients in polynomial expansion of generating function-for ratios with two matrices
h2_ij_v	Coefficients in polynomial expansion of generating function-for ratios with two matrices
h3_ijk	Coefficients in polynomial expansion of generating function-for ratios with three matrices
h3_ijk_m	Coefficients in polynomial expansion of generating function-for ratios with three matrices
h3_ijk_v	Coefficients in polynomial expansion of generating function-for ratios with three matrices
hgs	Calculate hypergeometric series
hgs_1d	Calculate hypergeometric series
hgs_2d	Calculate hypergeometric series
hgs_3d	Calculate hypergeometric series
hhat2_1j	Coefficients in polynomial expansion of generating function-for ratios with two matrices
hhat2_1j_m	Coefficients in polynomial expansion of generating function-for ratios with two matrices
hhat2_1j_v	Coefficients in polynomial expansion of generating function-for ratios with two matrices
hhat2_pj	Coefficients in polynomial expansion of generating function-for ratios with two matrices
hhat2_pj_m	Coefficients in polynomial expansion of generating function-for ratios with two matrices
hhat2_pj_v	Coefficients in polynomial expansion of generating function-for ratios with two matrices
hhat3_pjk	Coefficients in polynomial expansion of generating function-for ratios with three matrices
hhat3_pjk_m	Coefficients in polynomial expansion of generating function-for ratios with three matrices
hhat3_pjk_v	Coefficients in polynomial expansion of generating function-for ratios with three matrices
htil2_1j	Coefficients in polynomial expansion of generating function-for ratios with two matrices
htil2_1j_m	Coefficients in polynomial expansion of generating function-for ratios with two matrices
htil2_1j_v	Coefficients in polynomial expansion of generating function-for ratios with two matrices
htil2_pj	Coefficients in polynomial expansion of generating function-for ratios with two matrices
htil2_pj_m	Coefficients in polynomial expansion of generating function-for ratios with two matrices
htil2_pj_v	Coefficients in polynomial expansion of generating function-for ratios with two matrices
htil3_pjk	Coefficients in polynomial expansion of generating function-for ratios with three matrices
htil3_pjk_m	Coefficients in polynomial expansion of generating function-for ratios with three matrices
htil3_pjk_v	Coefficients in polynomial expansion of generating function-for ratios with three matrices

-- I --

IpBDqr_gen_cmE	Internal C++ functions
IpBDqr_gen_cmEc	Internal C++ functions
IpBDqr_gen_cmEl	Internal C++ functions
IpBDqr_gen_cvE	Internal C++ functions
IpBDqr_gen_cvEc	Internal C++ functions
IpBDqr_gen_cvEl	Internal C++ functions
IpBDqr_gen_nmE	Internal C++ functions
IpBDqr_gen_nmEc	Internal C++ functions
IpBDqr_gen_nmEl	Internal C++ functions
IpBDqr_gen_nvE	Internal C++ functions
IpBDqr_gen_nvEc	Internal C++ functions
IpBDqr_gen_nvEl	Internal C++ functions
iseq	Are these vectors equal?
is_diagonal	Is this matrix diagonal?

-- K --

KiK	Matrix square root and generalized inverse

-- M --

methods.qfrm

Methods for qfrm and qfpm objects

-- N --

new_qfpm	Construct qfrm object
new_qfrm	Construct qfrm object

-- P --

plot.qfrm	Methods for qfrm and qfpm objects
print.qfpm	Methods for qfrm and qfpm objects
print.qfrm	Methods for qfrm and qfpm objects

-- Q --

qfmrm	Moment of multiple ratio of quadratic forms in normal variables
qfmrm_ApBDqr_int	Moment of multiple ratio of quadratic forms in normal variables
qfmrm_ApBDqr_npi	Moment of multiple ratio of quadratic forms in normal variables
qfmrm_ApBIqr_int	Moment of multiple ratio of quadratic forms in normal variables
qfmrm_ApBIqr_npi	Moment of multiple ratio of quadratic forms in normal variables
qfmrm_IpBDqr_gen	Moment of multiple ratio of quadratic forms in normal variables
qfm_Ap_int	Moment of (product of) quadratic forms in normal variables
qfpm	Moment of (product of) quadratic forms in normal variables
qfpm_ABDpqr_int	Moment of (product of) quadratic forms in normal variables
qfpm_ABpq_int	Moment of (product of) quadratic forms in normal variables
qfrm	Moment of ratio of quadratic forms in normal variables
qfrm_ApBq_int	Moment of ratio of quadratic forms in normal variables
qfrm_ApBq_npi	Moment of ratio of quadratic forms in normal variables
qfrm_ApIq_int	Moment of ratio of quadratic forms in normal variables
qfrm_ApIq_npi	Moment of ratio of quadratic forms in normal variables
qfrm_cpp	Internal C++ functions

-- R --

rqfmr	Monte Carlo sampling of ratio/product of quadratic forms
rqfp	Monte Carlo sampling of ratio/product of quadratic forms
rqfpE	Internal C++ functions
rqfr	Monte Carlo sampling of ratio/product of quadratic forms

-- S --

sum_counterdiag	Summing up counter-diagonal elements
sum_counterdiag3D	Summing up counter-diagonal elements
S_fromUL	Make covariance matrix from eigenstructure

-- T --

tr	Matrix trace function