Moments and Distributions of Ratios of Quadratic Forms Using Recursion

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Documentation for package ‘qfratio’ version 1.1.1

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

qfratio-package qfratio: Moments and Distributions of Ratios of Quadratic Forms

-- A --

a1_pk Recursion for a_{p,k}
ABDpqr_int_E Internal C++ functions
ABpq_int_E Internal C++ functions
ApBDqr_int_Ec Internal C++ functions
ApBDqr_int_Ed Internal C++ functions
ApBDqr_int_El Internal C++ functions
ApBDqr_npi_Ec Internal C++ functions
ApBDqr_npi_Ed Internal C++ functions
ApBDqr_npi_El Internal C++ functions
ApBIqr_int_cEd Internal C++ functions
ApBIqr_int_nEc Internal C++ functions
ApBIqr_int_nEd Internal C++ functions
ApBIqr_int_nEl Internal C++ functions
ApBIqr_npi_Ec Internal C++ functions
ApBIqr_npi_Ed Internal C++ functions
ApBIqr_npi_El Internal C++ functions
ApBq_int_E Internal C++ functions
ApBq_npi_Ec Internal C++ functions
ApBq_npi_Ed Internal C++ functions
ApBq_npi_El Internal C++ functions
ApIq_int_cE Internal C++ functions
ApIq_int_nE Internal C++ functions
ApIq_npi_cE Internal C++ functions
ApIq_npi_nEc Internal C++ functions
ApIq_npi_nEd Internal C++ functions
ApIq_npi_nEl Internal C++ functions
Ap_int_E 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
dqfr Probability distribution of ratio of quadratic forms
dqfr_A1I1 Probability distribution of ratio of quadratic forms
dqfr_broda Probability distribution of ratio of quadratic forms
dqfr_butler Probability distribution of ratio of quadratic forms
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
d_A1I1_Ed Internal C++ functions
d_broda_Ed Internal C++ functions
d_butler_Ed Internal C++ functions

-- G --

gen_eig Get range of ratio of quadratic forms
gsl_wrap Internal C++ wrappers for GSL

-- 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
hyperg_1F1_vec_b Internal C++ wrappers for GSL
hyperg_2F1_mat_a_vec_c Internal C++ wrappers for GSL

-- I --

IpBDqr_gen_Ec Internal C++ functions
IpBDqr_gen_Ed Internal C++ functions
IpBDqr_gen_El 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
pqfr Probability distribution of ratio of quadratic forms
pqfr_A1B1 Probability distribution of ratio of quadratic forms
pqfr_butler Probability distribution of ratio of quadratic forms
pqfr_davies Probability distribution of ratio of quadratic forms
pqfr_imhof Probability distribution of ratio of quadratic forms
print.qfpm Methods for qfrm and qfpm objects
print.qfrm Methods for qfrm and qfpm objects
p_A1B1_Ec Internal C++ functions
p_A1B1_Ed Internal C++ functions
p_A1B1_El Internal C++ functions
p_butler_Ed Internal C++ functions
p_imhof_Ed Internal C++ functions

-- 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
qqfr Probability distribution of ratio of quadratic forms

-- R --

range_qfr Get range of ratio of quadratic forms
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