lmomco (version 1.7.3)

x2xlo: Conversion of a Vector through a Left-Hand Threshold to Setup Conditional Probability Computations

Description

This function takes a vector of numerical values and subselects the values above and those equal to or less than the leftout argument and assigns plodding positions based on the a argument (passed into the pp function) and returns a list providing helpful as well as necessary results needed for conditional probability adjustment for general magnitude and frequency analysis. This function only performs very simple vector of selection of patient. The real features for conditional probability application are found in the f2flo and f2flo functions.

Usage

x2xlo(x, leftout=0, a=0)

Arguments

x

A vector of values.

leftout

The lower threshold for which to leave out. The default of zero sets up for conditional probability adjustments for values equal (or less than) zero.

a

The plotting position coefficient passed to the pp function.

Value

• An R list is returned.
• xin
  The subselection of values greater than the leftout threshold.
• ppin
  The plotting positions of the subselected values greater than the leftout threshold. These plotting positions correspond to those data values in xin.
• xout
  The subselection of values less than or equal to the leftout threshold.
• ppout
  The plotting positions of the subselected values less than or equal to the leftout threshold. These plotting positions correspond to those data values in xout.
• pp
  The plotting position of the largest value left out of xin.
• source
  The source of the parameters: x2xlo.

See Also

f2flo, flo2f

Examples

set.seed(13)
type <- "nor"
parent <- vec2par(c(0,1), type=type)
X <- rlmomco(100, parent); a <- 0
Fs <- seq(0.001,.999, by=.005)
PP <- pp(X, a=a); Xs <- sort(X)
par <- lmom2par(lmoms(X), type=type)
plot(PP, Xs, type="n", xlim=c(0,1),
     xlab="NONEXCEEDANCE PROBABILITY",
     ylab="RANDOM VARIATE")
points(PP, Xs, col=3, cex=2, pch=0)
Xlo <- x2xlo(X, leftout=0, a=a)
parlo <- lmom2par(lmoms(Xlo$xin), type=type)
points(Xlo$ppout, Xlo$xout, pch=4, col=4)
points(Xlo$ppin, Xlo$xin, col=4, cex=.7)
lines(Fs, qlmomco(Fs, parent), lty=2, lwd=2)
lines(Fs, qlmomco(Fs, par), col=2, lwd=4)
lines(sort(c(Xlo$ppin, 0.999)),
      qlmomco(f2flo(sort(c(Xlo$ppin, 0.999)), pp=Xlo$pp), parlo),
      col=4, lwd=3)
# Notice how in the last line plotted that the proper
# plotting positions of the data greater than the threshold
# are passed into the f2flo() function that has the
# effect of mapping conventional nonexceedance probabilities
# into the conditional probability space. These mapped
# probabilities are then passed into the quantile function.
legend(.1,2, c("Simulated random variates",
                "Values to 'leave' (condition) out",
                "Values to 'leave' in",
                "Normal parent",
                "Normal fitted to whole data set",
                "Normal fitted to left-in values"),
       bty="n", cex=.75,
       pch=c(0,  4, 1,  NA, NA, NA),
       col=c(3,  1, 4,  1,  2,  4),
       pt.lwd=c(2,1, 1,1),
       pt.cex=c(2,1, 0.7, 1),
       lwd=c(0,0,0,2,2,3),
       lty=c(0,0,0,2,1,1))

set.seed(62)
type <- "exp"
parent <- vec2par(c(0,1), type=type)
X <- rlmomco(100, parent); a <- 0
Fs <- seq(0.001,.999, by=.005)
PP <- pp(X, a=a); Xs <- sort(X)
par <- lmom2par(lmoms(X), type=type)
plot(PP, Xs, type="n", xlim=c(0,1), log="y",
     xlab="NONEXCEEDANCE PROBABILITY",
     ylab="RANDOM VARIATE")
points(PP, Xs, col=3, cex=2, pch=0, lwd=2)
Xlo <- x2xlo(X, leftout=0.5, a=a)
parlo <- lmom2par(lmoms(Xlo$xin), type=type)
points(Xlo$ppout, Xlo$xout, pch=4, col=1)
points(Xlo$ppin, Xlo$xin, col=4, cex=.7)
lines(Fs, qlmomco(Fs, parent), lty=2, lwd=2)
lines(Fs, qlmomco(Fs, par), col=2, lwd=4)
lines(sort(c(Xlo$ppin,.999)),
      qlmomco(f2flo(sort(c(Xlo$ppin,.999)), pp=Xlo$pp), parlo),
      col=4, lwd=3)
legend(.4,.2, c("Simulated random variates",
                "Values to 'leave' (condition) out",
                "Values to 'leave' in",
                "Exponential parent",
                "Exponential fitted to whole data set",
                "Exponential fitted to left-in values"),
       bty="n", cex=.75,
       pch=c(0,  4, 1,  NA, NA, NA),
       col=c(3,  1, 4,  1,  2,  4),
       pt.lwd=c(2,1, 1,1),
       pt.cex=c(2,1, 0.7, 1),
       lwd=c(0,0,0,2,2,3),
       lty=c(0,0,0,2,1,1))