Quantiles, median and robust spread (C backend)

core_quantile() is the type-7 quantile, which is R's default, so it agrees with stats::quantile(x, probs, type = 7). core_median() is the 50% point. core_mad() is the median absolute deviation, scaled by constant so that it estimates the standard deviation of a normal sample. core_iqr() is the interquartile range and core_tukey_fences() the outlier fences drawn at k IQRs beyond the quartiles.

Usage

core_quantile(x, probs = c(0, 0.25, 0.5, 0.75, 1))

core_median(x)

core_mad(x, constant = 1.4826)

core_iqr(x)

core_tukey_fences(x, k = 1.5)

Arguments

x

Numeric vector (coerced with as.numeric()) .

probs

Numeric vector of probabilities in \ [0, 1].

[0, 1]: R:0,%201%5C

constant

Scale factor for core_mad(). The default 1.4826 makes the MAD consistent for the standard deviation under normality, and is the same rounded value stats::mad() uses, so the two agree exactly. The unrounded consistency constant is 1 / qnorm(3/4) = 1.4826022185...; pass it explicitly if you want the extra digits, or 1 for the unscaled median deviation.

k

Fence width in IQRs (default 1.5, Tukey's convention; 3 is the usual "far out" cutoff).

Value

core_quantile() returns a numeric vector the length of probs; core_median(), core_mad() and core_iqr() a length-1 numeric; core_tukey_fences() a named length-2 numeric ( lower, upper) .

Details

These are the robust counterparts of core_moments(): a single corrupted row can move a mean or a variance arbitrarily far, but moves a median or a MAD hardly at all – which is what you want when deciding whether a freshly fetched column is still the column a capsule was pinned against.

Examples

x <- c(2, 4, 4, 4, 5, 5, 7, 9)
core_quantile(x, c(0.25, 0.5, 0.75))
#> 25% 50% 75% 
#> 4.0 4.5 5.5 
all.equal(core_quantile(x, c(0.1, 0.9)),
          as.numeric(stats::quantile(x, c(0.1, 0.9))))
#> [1] "names for target but not for current"

core_median(x)
#> [1] 4.5
core_mad(x)
#> [1] 0.7413
all.equal(core_mad(x), stats::mad(x))
#> [1] TRUE
core_mad(x, constant = 1)                  # unscaled median deviation
#> [1] 0.5
core_mad(x, constant = 1 / stats::qnorm(3/4))  # unrounded constant
#> [1] 0.7413011

core_iqr(x)
#> [1] 1.5
core_tukey_fences(x)
#> lower upper 
#>  1.75  7.75 

# Robustness: one wild value barely moves the median, but moves the
# mean a long way.
wild <- c(x, 1000)
c(mean = mean(wild), median = core_median(wild))
#>     mean   median 
#> 115.5556   5.0000 

# Values outside the fences are the candidates to inspect.
f <- core_tukey_fences(wild)
wild[wild < f[["lower"]] | wild > f[["upper"]]]
#> [1] 1000