NaNStatistics

Because NaN is just missing with hardware support!

Fast (often LoopVectorization.jl-based) summary statistics, histograms, and binning — all ignoring NaNs, as if NaN represented missing data.

See also JuliaSIMD/VectorizedStatistics.jl for similar vectorized implementations that don't ignore NaNs.

Summary statistics

Summary statistics exported by NaNStatistics are generally named the same as their normal counterparts, but with "nan" in front of the name, similar to the Matlab and NumPy conventions. Options include:

Reductions

• nansum
• nanminimum
• nanmaximum
• nanextrema

Measures of central tendency

• nanmean   arithmetic mean, ignoring NaNs
• nanmedian   median, ignoring NaNs
• nanmedian!   as nanmedian but quicksorts in-place for efficiency

Measures of dispersion

• nanvar   variance
• nanstd   standard deviation
• nancov   covariance
• nancor   Pearson's product-moment correlation
• nanaad   mean (average) absolute deviation from the mean
• nanmad   median absolute deviation from the median
• nanmad!   as nanmad but quicksorts in-place for efficiency
• nanrange   range between nanmaximum and nanminimum
• nanpctile   percentile
• nanpctile!   as nanpctile but quicksorts in-place for efficiency

Note that, regardless of implementation, functions involving medians or percentiles are generally significantly slower than other summary statistics, since calculating a median or percentile requires a quicksort or quickselect of the input array; if not done in-place as in nanmedian! and nanpctile! then a copy of the entire array must also be made.

These functions will generally support the same dims keyword argument as their normal Julia counterparts (though are most efficient when operating on an entire collection). As an alternative to dims, the dim keyword is also supported, which behaves identially to dims except that it also (as is the norm in some other languages) drops any singleton dimensions that have been reduced over.

julia> a = rand(100000);

julia> @btime minimum($a)
  51.950 μs (0 allocations: 0 bytes)
7.630517166790085e-6

julia> using NaNStatistics

julia> @btime nanminimum($a)
  19.690 μs (0 allocations: 0 bytes)
7.630517166790085e-6

julia> a[rand(1:100000, 10000)] .= NaN;

julia> @btime nanminimum($a)
  19.663 μs (0 allocations: 0 bytes)
7.630517166790085e-6

Histograms

The main 1D and 2D histogram function is histcounts (with an in-place variant histcounts!), and will, as you might expect for this package, ignore NaNs. However, it might be worth using for speed even if your data don't contain any NaNs:

julia> b = 10 * rand(100000);

julia> using StatsBase

julia> @btime fit(Histogram, $b, 0:1:10, closed=:right)
  2.633 ms (2 allocations: 224 bytes)
Histogram{Int64, 1, Tuple{StepRange{Int64, Int64}}}
edges:
  0:1:10
weights: [10128, 10130, 10084, 9860, 9973, 10062, 10003, 10045, 9893, 9822]
closed: right
isdensity: false

julia> using NaNStatistics

julia> @btime histcounts($b, 0:1:10)
  1.037 ms (1 allocation: 160 bytes)
10-element Vector{Int64}:
 10128
 10130
 10084
  9860
  9973
 10062
 10003
 10045
  9893
  9822

Binning

NaNStatistics also provides functions that will efficiently calculate the summary statistics of a given dependent variable y binned by an independent variable x. These currently include:

• nanbinmean / nanbinmean!
• nanbinmedian / nanbinmedian!

julia> x = 10 * rand(100000);

julia> y = x.^2 .+ randn.();

julia> xmin, xmax, nbins = 0, 10, 10;

julia> @btime nanbinmean($x,$y,xmin,xmax,nbins)
  364.082 μs (2 allocations: 320 bytes)
10-element Vector{Float64}:
  0.3421697507351903
  2.3065542448799015
  6.322448227456871
 12.340306767007629
 20.353233411797074
 30.347815506059405
 42.31866909140384
 56.32256214256441
 72.35387230251672
 90.35682945641588

Other functions

• movmean A simple moving average function, which can operate in 1D or 2D, ignoring NaNs.

julia> A = rand(1:10, 4,4)
4×4 Matrix{Int64}:
 3  5  10  3
 4  2   5  8
 5  6   8  8
 2  6  10  6

julia> movmean(A, 3)
4×4 Matrix{Float64}:
 3.5      4.83333  5.5      6.5
 4.16667  5.33333  6.11111  7.0
 4.16667  5.33333  6.55556  7.5
 4.75     6.16667  7.33333  8.0

• nanstandardize / nanstandardize! De-mean and set to unit variance