# NOT RUN {
# A simple example
PM <- pmoms(rnorm(1000)) # n standard normal values as a fake data set.
cat(c(PM$moments[1],PM$moments[2],PM$ratios[3],PM$ratios[4],"\n"))
# As sample size gets very large the four values returned should be
# 0,1,0,0 by definition of the standard normal distribution.
# A more complex example
para <- vec2par(c(100,500,3),type='pe3') # mean=100, sd=500, skew=3
# The Pearson type III distribution is implemented here such that
# the "parameters" are equal to the mean, standard deviation, and skew.
simDATA <- rlmomco(100,para) # simulate 100 observations
PM <- pmoms(simDATA) # compute the product moments
p.tmp <- c(PM$moments[1],PM$moments[2],PM$ratios[3])
cat(c("Sample P-moments:",p.tmp,"\n"))
# This distribution has considerable variation and large skew. Stability
# of the sample product moments requires LARGE sample sizes (too large
# for a builtin example)
# Continue the example through the L-moments
lmr <- lmoms(simDATA) # compute the L-moments
epara <- parpe3(lmr) # estimate the Pearson III parameters. This is a
# hack to back into comparative estimates of the product moments. This
# can only be done because we know that the parent distribution is a
# Pearson Type III
l.tmp <- c(epara$para[1],epara$para[2],epara$para[3])
cat(c("PearsonIII by L-moments:",l.tmp,"\n"))
# The first values are the means and will be identical and close to 100.
# The second values are the standard deviations and the L-moment to
# PearsonIII will be closer to 500 than the product moment (this
# shows the raw power of L-moment based analysis---they work).
# The third values are the skew. Almost certainly the L-moment estimate
# of skew will be closer to 3 than the product moment.
# }
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