Kth Smallest/Largest Values

Find the kth smallest, resp. largest values from a vector x and return the values and their frequencies.

Usage

large(x, k = 5L, unique = FALSE, na.last = NA)

small(x, k = 5L, unique = FALSE, na.last = NA)

highLow(x, nlow = 5L, nhigh = nlow, na.last = NA)

Arguments

x

a numeric vector

k

a positive integer defining how many extreme values are returned. Default is k = 5. If k > length(x), all values will be returned.

unique

logical, defining if unique values should be considered or not. If this is set to TRUE, a list with the k extreme values and their frequencies is returned. Default is FALSE (as unique is a rather expensive function).

na.last

for controlling the treatment of NAs. If TRUE, missing values in the data are put last; if FALSE, they are put first; if NA, they are removed.

nlow

number of smallest values included in the formatted output; defaults to 5

nhigh

number of largest values included in the formatted output; defaults to nlow

Value

for large() and small(), a vector of extreme values when unique = FALSE, otherwise a list with components:

value

extreme values

frequency

corresponding frequencies

highLow() returns a character scalar containing formatted lowest and highest values with frequencies.

Details

This does not seem to be a difficult problem at first sight. We could simply tabulate and sort the vector and finally take the first or last k values. However sorting and tabulating the whole vector when we're just interested in the few smallest values is a considerable waste of resources. This approach becomes already impracticable for medium vector lengths (~10⁵). There are several points and solutions of this problem discussed out there. The present implementation is based on highly efficient C++ code and proved to be very fast.

highLow() combines the two upper functions and reports the k extreme values on both sides together with their frequencies in parentheses. It is used for describing univariate variables and is interesting for checking the ends of the vector, where in real data often wrong values accumulate. In essence this is nothing more than a combine printing routine for large() and small().

Note

Based on C++ code by Nathan Russell and Romain Francois, adapted to conform to package standards.

References

StackOverflow: Largest n unique values

Rcpp Gallery article

See also

max(), min(), sort(), rank()

Other quantile: quantileX()

Examples

x <- sample(1:10, 1000, rep=TRUE)
large(x, 3)
#> [1] 10 10 10
large(x, k=3, unique=TRUE)
#> $value
#> [1]  8  9 10
#> 
#> $frequency
#> [1]  94 107 108
#> 

# works fine up to x ~ 1e6
x <- runif(1000000)
small(x, 3, unique=TRUE)
#> $value
#> [1] 1.548324e-07 5.243346e-07 1.089182e-06
#> 
#> $frequency
#> [1] 1 1 1
#> 
small(x, 3, unique=FALSE)
#> [1] 1.548324e-07 5.243346e-07 1.089182e-06

# Both ends
cat(highLow(bedrock::Pizza$temperature, na.last=NA))
#> lowest : 19.3, 19.4, 20, 20.2 (2), 20.35
#> highest: 63.8, 64.1, 64.6, 64.7, 64.8