bvNormalContour {MVQuickGraphs}

Bivariate Normal Contour Ellipse

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

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.

Value

None

References

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

Examples

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)