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# pmcm.R -- version 2010-12-05
x <- rnorm(20L)
# mean and probability of loss
theta <- 0.1 # ... or mean(x)
prob.loss <- ecdf(x)(theta)
exponent <- 2
# conditional moment (CM)
(cm <- mean((x[x < theta] - theta)^exponent))
# partial moment (PM)
xx <- x - theta; xx[xx > 0] <- 0
(pm <- mean(xx^exponent))
# relationship between PM and CM
stopifnot(all.equal(cm * prob.loss, pm))
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