# NOT RUN {
my.p <- 0.25; y <- runif(nn <- 1000)
(myexp <- qeunif(my.p))
sum(myexp - y[y <= myexp]) / sum(abs(myexp - y)) # Should be my.p
# Equivalently:
I1 <- mean(y <= myexp) * mean( myexp - y[y <= myexp])
I2 <- mean(y > myexp) * mean(-myexp + y[y > myexp])
I1 / (I1 + I2) # Should be my.p
# Or:
I1 <- sum( myexp - y[y <= myexp])
I2 <- sum(-myexp + y[y > myexp])
# Non-standard uniform
mymin <- 1; mymax <- 8
yy <- runif(nn, mymin, mymax)
(myexp <- qeunif(my.p, mymin, mymax))
sum(myexp - yy[yy <= myexp]) / sum(abs(myexp - yy)) # Should be my.p
peunif(mymin, mymin, mymax) # Should be 0
peunif(mymax, mymin, mymax) # Should be 1
peunif(mean(yy), mymin, mymax) # Should be 0.5
abs(qeunif(0.5, mymin, mymax) - mean(yy)) # Should be 0
abs(qeunif(0.5, mymin, mymax) - (mymin+mymax)/2) # Should be 0
abs(peunif(myexp, mymin, mymax) - my.p) # Should be 0
integrate(f = deunif, lower = mymin - 3, upper = mymax + 3,
min = mymin, max = mymax) # Should be 1
# }
# NOT RUN {
par(mfrow = c(2,1))
yy <- seq(0.0, 1.0, len = nn)
plot(yy, deunif(yy), type = "l", col = "blue", ylim = c(0, 2),
xlab = "y", ylab = "g(y)", main = "g(y) for Uniform(0,1)")
lines(yy, dunif(yy), col = "darkgreen", lty = "dotted", lwd = 2) # 'original'
plot(yy, peunif(yy), type = "l", col = "blue", ylim = 0:1,
xlab = "y", ylab = "G(y)", main = "G(y) for Uniform(0,1)")
abline(a = 0.0, b = 1.0, col = "darkgreen", lty = "dotted", lwd = 2)
abline(v = 0.5, h = 0.5, col = "red", lty = "dashed")
# }
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