# bvNormalContour: Bivariate Normal Contour Ellipse In douglaswhitaker/MVQuickGraphs: Quick Multivariate Graphs

## Description

Draws a contour of constant density at the (1-`alpha`)100% level for a bivariate normal distribution using the eigendecomposition of the covariance matrix. This is likely more interesting for learning about the bivariate normal distribution than as a practical tool, for which other functions already exist (e.g. `link[graphics]{contour}`).

## Usage

 ``` 1 2 3 4 5 6 7 8 9 10 11 12``` ```bvNormalContour( mu = c(0, 0), Sigma = NULL, eig = NULL, xl = NULL, yl = NULL, axes = TRUE, center = FALSE, lim.adj = 0.02, alpha = 0.05, ... ) ```

## Arguments

 `mu` a vector giving the mean of the bivariate normal distribution. This is the center of the ellipse. `Sigma` a matrix giving the covariance matrix of the bivariate normal distribution. Either `Sigma` or `eig` must be specified. `eig` the eigenvalues and eigenvectors of the covariance matrix. This should be of the same form as the output of `eigen`, namely a list with two components: `values` and `vectors`. It is assumed that the largest eigenvalue is given first. Either `Sigma` or `eig` must be specified. `xl` a vector giving the lower and upper limits of the x-axis for plotting. If `xl = NULL` (default), then reasonable values are computed automatically. `yl` a vector giving the lower and upper limits of the y-axis for plotting. If `yl = NULL` (default), then reasonable values are computed automatically. `axes` logical. If `axes = TRUE` (default) then the major and minor axes of the ellipse are plotted. `center` logical. If `axes = TRUE` then the center of the ellipse is indicated with a point and dashed lines are drawn to the x-axis and y-axis. `lim.adj` a value giving an adjustment to the x-axis and y-axis limits computed if either `xl = NULL` or `yl = NULL`. Essentially this is a way to have some coarse control over these limits for quick graphing: positive values will increase the distance between the upper and lower limits (making the ellipse appear smaller) while negative values will decrease the distance (and make the ellipse appear larger). `alpha` a value giving the value of alpha to be used when computing the contour. Contours are drawn at the `1-alpha` level. `...` other arguments to be passed to the graphing functions.

None

## References

Johnson, R. A., & Wichern, D. W. (2007). Applied multivariate statistical analysis (6th ed). Pearson Prentice Hall.

## Examples

 ```1 2 3 4``` ```mu <- c(-1,8) Sigma <- matrix(c(3,2,2,4), ncol = 2) # Draw a 90% contour bvNormalContour(mu = mu, Sigma = Sigma, alpha = 0.10) ```

douglaswhitaker/MVQuickGraphs documentation built on Aug. 26, 2020, 11:51 p.m.