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Point-estimate statistics

These estimators operate on single uncertain values, which can be of any type, such as populations, theoretical distributions, KDE distributions or fitted distributions. They compute the statistic in question by drawing a length-n draw of the uncertain value, then computing the statistic on that draw.

Syntax

The syntax for computing the statistic f for single instances of an uncertain value x is

  • f(x::AbstractUncertainValue, n::Int, args...; kwargs...), which estimates the statistic f for a length-n draw of x.

Methods

Mean

Statistics.mean — Method
mean(uv::AbstractUncertainValue, n::Int)

Compute the mean of an uncertain value over an n-draw sample of it.

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Mode

StatsBase.mode — Method
mode(uv::AbstractUncertainValue, n::Int)

Compute the mode of an uncertain value over an n-draw sample of it.

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Quantile

Statistics.quantile — Method
quantile(uv::AbstractUncertainValue, q, n::Int)

Compute the quantile(s) q of an uncertain value over an n-draw sample of it.

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IQR

StatsBase.iqr — Method
iqr(uv::AbstractUncertainValue, n::Int)

Compute the interquartile range (IQR), i.e. the 75th percentile minus the 25th percentile, over an n-draw sample of an uncertain value.

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Median

Statistics.median — Method
median(uv::AbstractUncertainValue, n::Int)

Compute the median of an uncertain value over an n-draw sample of it.

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Middle

Statistics.middle — Method
middle(uv::AbstractUncertainValue, n::Int)

Compute the middle of an uncertain value over an n-draw sample of it.

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Standard deviation

Statistics.std — Method
std(uv::AbstractUncertainValue, n::Int)

Compute the standard deviation of an uncertain value over an n-draw sample of it.

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Variance

Statistics.var — Method
variance(uv::AbstractUncertainValue, n::Int)

Compute the variance of an uncertain value over an n-draw sample of it.

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Generalized/power mean

StatsBase.genmean — Method
genmean(uv::AbstractUncertainValue, p, n::Int)

Compute the generalized/power mean with exponent p of an uncertain value over an n-draw sample of it.

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Generalized variance

StatsBase.genvar — Method
genvar(uv::AbstractUncertainValue, n::Int)

Compute the generalized sample variance of an uncertain value over an n-draw sample of it.

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Harmonic mean

StatsBase.harmmean — Method
harmmean(uv::AbstractUncertainValue, n::Int)

Compute the harmonic mean of an uncertain value over an n-draw sample of it.

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Geometric mean

StatsBase.geomean — Method
geomean(uv::AbstractUncertainValue, n::Int)

Compute the geometric mean of an uncertain value over an n-draw sample of it.

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Kurtosis

StatsBase.kurtosis — Method
kurtosis(uv::AbstractUncertainValue, n::Int, m = mean(uv, n))

Compute the excess kurtosis of an uncertain value over an n-draw sample of it, optionally specifying a center m).

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k-th order moment

StatsBase.moment — Function
moment(x::AbstractUncertainValue, k, n::Int, m = mean(x, n))

Compute the k-th order central moment of an uncertain value over an n-draw sample of it, optionally specifying a center m.

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Percentile

StatsBase.percentile — Method
percentile(x::AbstractUncertainValue, p, n::Int)

Compute the percentile(s) p of an uncertain value over an n-draw sample of it.

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Renyi entropy

StatsBase.renyientropy — Method
renyientropy(uv::AbstractUncertainValue, α, n::Int)

Compute the Rényi (generalized) entropy of order α of an uncertain value over an n-draw sample of it.

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Run-length encoding

StatsBase.rle — Method
rle(x::AbstractUncertainValue, n::Int)

Compute the run-length encoding of an uncertain value over a n-draw sample of it as a tuple. The first element of the tuple is a vector of values of the input and the second is the number of consecutive occurrences of each element.

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Standard error of the mean

StatsBase.sem — Method
sem(x::AbstractUncertainValue, n::Int)

Compute the standard error of the mean of an uncertain value over a n-draw sample of it, optionally specifying a center m, i.e. sqrt(var(x_draw, corrected = true) / length(x_draw)).

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Skewness

StatsBase.skewness — Method
skewness(x::AbstractUncertainValue, n::Int, m = mean(x, n))

Compute the standardized skewness of an uncertain value over an n-draw sample of it, optionally specifying a center m.

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Span

StatsBase.span — Method
span(x::AbstractUncertainValue, n::Int)

Compute the span of a collection, i.e. the range minimum(x):maximum(x), of an uncertain value over an n-draw sample of it. The minimum and maximum of the draws of x are computed in one pass using extrema.

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Summary statistics

StatsBase.summarystats — Method
summarystats(uv::AbstractUncertainValue, n::Int)

Compute summary statistics of an uncertain value over an n-draw sample of it. Returns a SummaryStats object containing the mean, minimum, 25th percentile, median, 75th percentile, and maximum.

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Total variance

StatsBase.totalvar — Method
totalvar(uv::AbstractUncertainValue, n::Int)

Compute the total sample variance of an uncertain value over an n-draw sample of it. For a single uncertain value, this is equivalent to the sample variance.

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Theoretical and fitted distributions

For theoretical distributions, both with known and fitted parameters, some of the stats functions may be called without the n argument, because the underlying distributions are represented as actual distributons. For these, we can compute several of the statistics from the distributions directly.