Statistics on uncertain values and collections

This package extends many of the statistical algorithms in StatsBase for uncertain values. The statistics are computed using a resampling approach.

To use these methods, you first have to run the following in your Julia console to bring the functions into scope:

using StatsBase

Exact vs. approximate error propagation

For exact error propagation of normally distributed uncertain values that are potentially correlated, you can use Measurements.jl. It is, however, not always the case that data points have normally distributed uncertainties.

This where the resampling approach becomes useful. In this package, the resampling approach allows you to approximate any statistic for any type of uncertain value. You may still use normal distributions to represent uncertain values, but the various statistics are approximated through resampling, rather than computed exactly.

List of statistics

Some statistics are implemented only for uncertain values, while other statistics are implemented only for collections of uncertain values. Some statistics also work on pairs of of uncertain values, or pairs of uncertain value collections. Here's an overview:

• Uncertain values, on single values
• Uncertain values, on pairs of values
• Uncertain collections, on single collections
• Uncertain collections, on pairs of collections

Accepted collection types

In the documentation for the statistical methods, you'll notice that the inputs are supposed to be of type UVAL_COLLECTION_TYPES. This is a type union representing all types of collections for which the statistical methods are defined. Currently, this includes UncertainValueDataset, UncertainIndexDataset and vectors of uncertain values (Vector{T} where T <: AbstractUncertainValue).

const UVAL_COLLECTION_TYPES = Union{UD, UV} where {
    UD <: AbstractUncertainValueDataset,
    UV <: AbstractVector{T} where {T <: AbstractUncertainValue}}