QF: pQF_depratio – R documentation

Become an expert in R — Interactive courses, Cheat Sheets, certificates and more!

pQF_depratio

Cumulative Distribution Function of the Dependent QFs Ratio

The function computes the CDF of the ratio of two dependent and possibly indefinite quadratic forms.

pQF_depratio(
  q = NULL,
  lambdas = NULL,
  A = NULL,
  B = NULL,
  eps = 1e-06,
  maxit_comp = 1e+05,
  lambdas_tol = NULL
)

`q`	vector of quantiles.
`lambdas`	vector of eigenvalues of the matrix (A-qB).
`A`	matrix of the numerator QF. If not specified but `B` is passed, it is assumed to be the identity.
`B`	matrix of the numerator QF. If not specified but `A` is passed, it is assumed to be the identity.
`eps`	requested absolute error.
`maxit_comp`	maximum number of iterations.
`lambdas_tol`	maximum value admitted for the weight skewness for both the numerator and the denominator. When it is not NULL (default), elements of lambdas such that the ratio max(lambdas)/lambdas is greater than the specified value are removed.

The distribution function of the following ratio of dependent quadratic forms is computed:

P≤ft(\frac{Y^TAY }{Y^TBY}<q\right),

where Y\sim N(0, I).

The transformation to the following indefinite quadratic form is exploited:

P≤ft(Y^T(A-qB)Y <0\right).

The following inputs can be provided:

vector lambdas that contains the eigenvalues of the matrix (A-qB). Input q is ignored.
matrix A and/or matrix B: in these cases q is required to be not null and an eventual missing specification of one matrix make it equal to the identity.

The values of the CDF at quantiles q.

Density, Cumulative and Quantile Functions of Quadratic Forms

v0.0.4

GPL-3

Authors

Aldo Gardini [aut, cre], Fedele Greco [aut], Carlo Trivisano [aut]

Initial release

2021-02-17