| Type: | Package |
| Title: | Approximation to the Survival Functions of Quadratic Forms of Gaussian Variables |
| Version: | 0.2.0 |
| Author: | Hong Zhang |
| Maintainer: | Hong Zhang <hzhang@wpi.edu> |
| 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) <doi:10.48550/arXiv.2005.00905>. |
| License: | GPL-2 |
| Imports: | stats |
| Encoding: | UTF-8 |
| RoxygenNote: | 6.1.0 |
| NeedsCompilation: | no |
| Packaged: | 2021-07-07 03:12:57 UTC; consi |
| Repository: | CRAN |
| Date/Publication: | 2021-07-07 04:30:05 UTC |
Right-tail probability of quadratic forms of centered Gaussian variables.
Description
Right-tail probability of quadratic forms of centered Gaussian variables.
Usage
Qapprox(q, Sigma, A = NULL, method = "MR")
Arguments
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. |
Value
The right-tail probability of a quadratic form (Q = X'AX) of centered Gaussian variables.
References
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.
Examples
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.
Description
Right-tail probability of quadratic forms (Q = X'AX) of noncentral Gaussian variables.
Usage
Qapprox_nc(q, mu, Sigma, A = NULL, method = "MR")
Arguments
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. |
Value
The right-tail probability of a quadratic form (Q = X'AX) of noncentral Gaussian variables.
References
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.
Examples
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")