plotCDF1: Create a marginal CDF (or survival function) plot of the MLE

Description

This function plots the MLE for a marginal (sub)-CDF (or survival function) for one of the two variables of interest. To be precise, it can plot the MLE for P(X<=x, a<Y<=b) (or 1-P(X<=x, a<Y<=b)) as a function of x, and the MLE for P(a<X<=b, Y<=y) (or 1-P(a<X<=b, Y<=y)) as a function of y, where a and b may take the values -infinity and infinity. The values of these estimates are computed by summing all probability mass of the MLE that falls in the regions (-infinity,x] x (a,b] and (a,b] x (-infinity,y], respectively.

Usage

plotCDF1(mle, margin, bound="b", int=NULL, surv=FALSE,
         add=FALSE, col=1, lty=1, xlim=NULL, 
         ylim=NULL, xlab="", ylab="", main="", sub="")

Value

No value is returned.

Arguments

mle: List with elements 'p' and 'rects', as outputted by computeMLE.
margin: Indicates which margin should be plotted: 1 = x-margin, 2 = y-margin. So if margin=1, the MLE for P(X<=x, a<Y<=b) is plotted, and if margin=2, then the MLE for P(a<X<=b, Y<=y) is plotted.
bound: Parameter taking the values "u", "l" and "b". 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. Option "b" (both) indicates that both the upper and the lower bound should be plotted. The default value is "b".
int: This indicates the range of interest of the variable that was not chosen in margin. If int is specified, it should be of the form c(a,b), with a<b. If margin=1, the MLE for P(X<=x, a<Y<=b) is plotted as a function of x. If margin=2, the MLE for P(a<X<=b, Y<=y) is plotted as a function of y. This parameter defaults to (-infinity,infinity), yielding plots of the estimates for P(X<=x) and P(Y<=y).
surv: Logical. The default value is FALSE. If TRUE, the function 1-P(X<=x, a<Y<=b) is plotted instead of P(X<=x, a<Y<=b), and the function 1-P(a<X<=b, Y<=y) is plotted instead of P(a<X<=b, Y<y).
add: Logical, indicating if the lines should be added to an existing plot. The default value is FALSE.
col: Line color. The default value is 1="black".
lty: Line type. The default value is 1="solid".
xlim: Range for the horizontal axis, defaulting to the range of x-coordinates (if margin=1) or y-coordinates (if margin=2) of the relevant corners of maximal interesctions.
ylim: Range for the vertical axis, defaulting to the range of values of the estimate.
xlab,ylab: Labels of the x- and y-axis. The default values are empty.
main: Title of the plot.
sub: Sub title of the plot.

Author

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

Examples

Run this code

# Load example data:
data(ex)

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

# Plot marginal CDF for X
par(mfrow=c(2,2))
plotCDF1(mle, margin=1, xlim=c(min(ex[,1])-1,max(ex[,2])+1), 
 bound="b", xlab="x", ylab="P(X<=x)", main="MLE for P(X<=x)")

# Plot marginal survival function for X
plotCDF1(mle, margin=1, surv=TRUE, xlim=c(min(ex[,1])-1,max(ex[,2])+1), 
 bound="b", xlab="x", ylab="P(X>x)", main="MLE for P(X>x)")

# Plot marginal CDF for Y
plotCDF1(mle, margin=2, xlim=c(min(ex[,3])-1,max(ex[,4])+1), 
 bound="b", xlab="y", ylab="P(Y<=y)", main="MLE for P(Y<=y)")

# Plot marginal survival function for Y
plotCDF1(mle, margin=2, surv=TRUE, xlim=c(min(ex[,3])-1,max(ex[,4])+1), 
 bound="b", xlab="y", ylab="P(Y>y)", main="MLE for P(Y>y)")