plotCDF2: Create a bivariate CDF (or survival function) plot of the MLE

Description

This function plots the MLE for the bivariate CDF of (X,Y) (or the bivariate survival function). The value of the estimate at the point (x,y) is computed by summing all probability mass of the MLE that falls in the region (-infinity,x] x (-infinity,y]. The plot uses colors/shades to represent the value of the MLE, and is generated using the function image.

Usage

plotCDF2(mle, bound, col=gray(seq(0.9,0.3,len=30)), surv=FALSE, 
         key=TRUE, n.key=10, round.key=2, cex.key=0.6, xlim=NULL, 
         ylim=NULL, zlim=NULL, breaks=NULL, xlab="", ylab="", 
         main="", sub="")

Value

No value is returned.

Arguments

mle: List with elements 'p' and 'rects', as outputted by computeMLE.
bound: Parameter taking the values "u" and "l". It indicates how representational non-uniqueness of the MLE should be handled. Option "u" (upper) indicates an upper bound, obtained by assigning all mass to the lower left corners of the maximal intersections. Option "l" (lower) indicates a lower bound, obtained by assigning all mass to the upper right corners of the maximal intersections.
col: Color vector used to represent the values of the MLE. The default value is gray(seq(0.9,0.3,len=30)).
surv: Logical. If FALSE, the bivariate CDF P(X<=x, Y<=y) is plotted. If TRUE, the bivariate survival function 1-P(X<=x,Y<=y) is plotted. The default value is FALSE.
key: Logical, indicating if a color key should be drawn. The default value is TRUE.
n.key: Approximate number of tickmarks for the color key. The default value is 10.
round.key: Number of decimals used for the labels of the color key. The default value is 2.
cex.key: Numerical value giving the amount by which text in the key should be scaled relative to the default. The default value is 0.6.
xlim, ylim: Ranges for the plotted x and y values, defaulting to the ranges of the x- and y-coordinates of the relevant corners of the maximal intersections.
zlim: The minimum and maximum values of the estimate for which colors should be plotted, defaulting to the range of the finite values of the estimate. Each of the given colors will be used to color an equispaced interval of this range. The midpoints of the intervals cover the range, so that values just outside the range will be plotted (see the documentation of image). This parameter is not used if breaks is specified.
breaks: Numeric vector with break points for the colors, satisfying length(breaks)=length(col)+1. This parameter overrides zlim.
xlab, ylab: Labels for the x- and y-axis. The default values are empty.
main: Title of the plot. The default value is empty.
sub: Sub title of the plot. The default value is empty.

Author

Marloes Maathuis: maathuis@stat.math.ethz.ch

Examples

Run this code

# Load example data:
data(ex)

# Compute the MLE:
mle <- computeMLE(ex)

### Bivariate CDF plot of the MLE

# Plot lower bound for representational non-uniqueness
par(mfrow=c(1,1))
plotCDF2(mle, xlim=c(min(ex[,1])-1,max(ex[,2])+1), 
 ylim=c(min(ex[,3])-1, max(ex[,4])+1), bound="l", n.key=4,
 main="Bivariate CDF plot of the MLE,
 lower bound")

# Add observation rectangles and shaded maximal intersections
plotRects(ex, add=TRUE) 
plotRects(mle$rects, density=20, border=NA, add=TRUE) 

# Plot upper bound for representational non-uniqueness
plotCDF2(mle, xlim=c(min(ex[,1])-1,max(ex[,2])+1), 
 ylim=c(min(ex[,3])-1, max(ex[,4])+1), bound="u", n.key=4,
 main="Bivariate CDF plot of the MLE,
 upper bound")

# Add observation rectangles and shaded maximal intersections
plotRects(ex, add=TRUE)
plotRects(mle$rects, density=20, border=NA, add=TRUE)