quantileMean: Average of R's quantile methods

In berryFunctions: Function Collection Related to Plotting and Hydrology

Average of R's quantile methods

Description

Weighted average of R's quantile methods

Usage

quantileMean(
  x,
  probs = seq(0, 1, 0.25),
  weights = rep(1, 9),
  names = TRUE,
  truncate = 0,
  ...
)

Arguments

x	Numeric vector whose sample quantiles are wanted
probs	Numeric vector of probabilities with values in [0,1]. DEFAULT: seq(0, 1, 0.25)
weights	Numeric vector of length 9 with weight for each quantile method. Recycled if shorter. DEFAULT: unweighted mean. DEFAULT: rep(1,9)
names	If TRUE, the resulting vector has a names attribute. DEFAULT: TRUE
truncate	Number between 0 and 1. Censored quantile: fit to highest values only (truncate lower proportion of x). Probabilities are adjusted accordingly. DEFAULT: 0
...	further arguments passed to quantile, except for type

Details

weights are internally normalized to sum 1

Value

numeric named vector, as returned by apply

Author(s)

Berry Boessenkool, [e-mail], Sept 2014

See Also

quantile

Examples

exDat <- rnorm(30,sd=5)
quantile(exDat, probs=c(0.9, 0.99), type=1)
quantile(exDat, probs=c(0.9, 0.99), type=2)
round( sapply(1:9, function(m) quantile(exDat, probs=0.9, type=m)) , 3)
# and now the unweighted average:
quantileMean(exDat, probs=c(0.9, 0.99))
quantileMean(exDat, probs=0.9)
# say I trust type 2 and 3 especially and want to add a touch of 7:
quantileMean(exDat, probs=c(0.9, 0.99), weights=c(1,5,5,0,1,1,3,1,1))

# quantile sample size dependency simulation:
qbeta(p=0.999, 2, 9) # dist with Q99.9% = 0.62
betaPlot(2, 9, cumulative=FALSE, keeppar=TRUE)
abline(v=qbeta(p=0.999, 2, 9), col=6, lwd=3)
qm <- function(size) quantileMean(rbeta(size, 2,9), probs=0.999, names=FALSE)
n30  <- replicate(n=500, expr=qm(30))
n1000 <- replicate(n=500, expr=qm(1000))
lines(density(n30)) 
lines(density(n1000), col=3) 
# with small sample size, high quantiles are systematically
# underestimated. for Q0.999, n must be > 1000


## Not run: 
# #Excluded from CRAN Checks because of the long computing time

# Parametrical quantiles can avoid sample size dependency!
library2("extremeStat")
library2("pbapply")

dlq <- distLquantile(rbeta(1000, 2,9), probs=0.999, list=TRUE, gpd=FALSE)
plotLquantile(dlq, nbest=10) # 10 distribution functions
select <- c("wei","wak","pe3","gno","gev","gum","gpa","gam")

# median of 10 simulations:
nsim <- 10 # set higher for less noisy image (but more computing time)
qmm <- function(size, truncate=0) median(replicate(n=nsim,
       expr=quantileMean(rbeta(size, 2,9), probs=0.999, names=FALSE, 
                         truncate=truncate)                            ))

pqmm <- function(size, truncate=0) median(replicate(n=nsim,
       expr=mean(distLquantile(rbeta(size, 2,9), probs=0.999, selection=select,
                 progbars=FALSE, time=FALSE, truncate=truncate, gpd=FALSE, 
                 weighted=FALSE, empirical=FALSE, ssquiet=TRUE)[1:8, 1])   ))
                 
n <- round(  logSpaced(min=10, max=1000, n=15, base=1.4, plot=FALSE)  )

medians_emp <- pbsapply(n, qmm)  # medians of regular quantile average
# with truncation, only top 20% used for quantile estimation (censored quant):
medians_emp_trunc <- sapply(n, qmm, truncate=0.8) 
# medians of parametrical quantile estimation
medians_param       <- pbsapply(n, pqmm)              # takes ~60 secs
medians_param_trunc <- pbsapply(n, pqmm, truncate=0.8)

plot(n, medians_emp, type="l", ylim=c(0.45, 0.7), las=1)
abline(h=qbeta(p=0.999, 2, 9), col=6) # real value
lines(n, medians_emp_trunc, col=2) #  don't help!
# In small samples, rare high values, on average, simply do not occur 
lines(n, medians_param, col=4) # overestimated, but not dependent on n
# with truncation, only top 20% used for quantile estimation
lines(n, medians_param_trunc, col="orange", lwd=3) # much better!

## End(Not run)

berryFunctions documentation built on May 29, 2024, 4:01 a.m.