| Title: | Approximation to the Survival Functions of Quadratic Forms of Gaussian Variables |
|---|---|
| Description: | Calculates the right-tail probability of quadratic forms of Gaussian variables using the skewness-kurtosis ratio matching method, modified Liu-Tang-Zhang method and Satterthwaite-Welch method. The technical details can be found in Hong Zhang, Judong Shen and Zheyang Wu (2020) <arXiv:2005.00905>. |
| Authors: | Hong Zhang |
| Maintainer: | Hong Zhang <[email protected]> |
| License: | GPL-2 |
| Version: | 0.2.0 |
| Built: | 2024-12-30 07:06:46 UTC |
| Source: | https://github.com/cran/Qapprox |
Right-tail probability of quadratic forms of centered Gaussian variables.
Qapprox(q, Sigma, A = NULL, method = "MR")Qapprox(q, Sigma, A = NULL, method = "MR")
q |
- quantile, could be a vector. |
Sigma |
- covariance matrix of Gaussian variables. |
A |
- a positive-semi-definite matrix that defines the quadratic form. |
method |
- "MR": moment-ratio (skewness-kurtosis) matching method; "SW": Satterthwaite-Welch method that matches mean and variance; "LTZ4": Liu-Tang-Zhang method that matches the kurtosis. |
The right-tail probability of a quadratic form (Q = X'AX) of centered Gaussian variables.
1. Hong Zhang, Judong Shen and Zheyang Wu. "An efficient and accurate approximation to the distribution of quadratic forms of Gaussian variables", arXiv:2005.00905.
n <- 100 Sigma <- toeplitz(1/(1:n)) thr <- 180 Qapprox(thr, Sigma, method="SW") Qapprox(thr, Sigma, method="LTZ4") Qapprox(thr, Sigma, method="MR")n <- 100 Sigma <- toeplitz(1/(1:n)) thr <- 180 Qapprox(thr, Sigma, method="SW") Qapprox(thr, Sigma, method="LTZ4") Qapprox(thr, Sigma, method="MR")
Right-tail probability of quadratic forms (Q = X'AX) of noncentral Gaussian variables.
Qapprox_nc(q, mu, Sigma, A = NULL, method = "MR")Qapprox_nc(q, mu, Sigma, A = NULL, method = "MR")
q |
- quantile, could be a vector. |
mu |
- mean vector of Gaussian variables. |
Sigma |
- covariance matrix of Gaussian variables. |
A |
- a positive-semi-definite matrix that defines the quadratic form. |
method |
- "MR": moment-ratio (skewness-kurtosis) matching method; "SW": Satterthwaite-Welch method that matches mean and variance; "LTZ4": Liu-Tang-Zhang method that matches the kurtosis. |
The right-tail probability of a quadratic form (Q = X'AX) of noncentral Gaussian variables.
1. Hong Zhang, Judong Shen and Zheyang Wu. "An efficient and accurate approximation to the distribution of quadratic forms of Gaussian variables", arXiv:2005.00905.
n <- 100 Sigma <- toeplitz(1/(1:n)) mu <- rep(1, n) thr <- 500 Qapprox_nc(thr, mu, Sigma, method="SW") Qapprox_nc(thr, mu, Sigma, method="LTZ4") Qapprox_nc(thr, mu, Sigma, method="MR")n <- 100 Sigma <- toeplitz(1/(1:n)) mu <- rep(1, n) thr <- 500 Qapprox_nc(thr, mu, Sigma, method="SW") Qapprox_nc(thr, mu, Sigma, method="LTZ4") Qapprox_nc(thr, mu, Sigma, method="MR")