Resampling with replacement to approximate the sampling distribution of a statistic and quantify uncertainty.
Arguments
- x
a numeric vector. The sample of interest
- Stat
the function (to calculate the statistic) to be applied to the bootstrapped samples. For example mean, max, or median.
- n
the number of bootstrapped samples (default 500). i.e. the size of the derived sampling distribution.
- Conf
the confidence level of the intervals (default 0.95). Must be between 0 and 1.
- ReturnSD
Logical argument with a default of FALSE. If true the bootstrapped sampling distribution is returned.
- ...
further arguments for the Stat function. For example if you use the GEVAM function you might want to add RP = 50 to derive a sampling distribution for the 50-year quantile.
Value
If ReturnSD is FALSE a data.frame is returned with one row and three columns; Mean, lower, and upper (statistics of the bootsrapped sampling distribution). If ReturnSD is TRUE, the sampling distribution is returned.
Details
The bootstrapping procedure resamples from a sample length(x) * n times with replacement. After splitting into n samples of size length(x), the statistic of interest is calculated on each.
Examples
# Extract an AMAX sample and quantify uncertainty for the Gumbel estimated 50-year flow
am_203018 <- GetAM(203018)
Bootstrap(am_203018$Flow, Stat = GumbelAM, RP = 50)
#> Mean Lower Upper
#> 1 156 130 186
# Quantify uncertainty for the sample standard deviation at the 90% confidence level
Bootstrap(am_203018$Flow, Stat = sd, Conf = 0.90)
#> Mean Lower Upper
#> 1 28.6 20.4 36.6
# Return the sampling distribution of the mean and plot an associated histogram
samp_dist <- Bootstrap(am_203018$Flow, Stat = mean, ReturnSD = TRUE)
hist(samp_dist)
