Stream: helpdesk (published)

Topic: ✔ Inverse normal transformation


view this post on Zulip Kevin Bonham (Aug 03 2021 at 15:32):

Are there any packages that implement INT? This is defined as

image.png

where Φ1\Phi^{-1} is the probit function, rir_{i} is the rank of observation ii, and NN is the number of observations.

view this post on Zulip Kevin Bonham (Aug 03 2021 at 15:34):

I did a bit of googling for this or for probit, but all of the results are about probit link functions in the context of linear modeling for example

view this post on Zulip Júlio Hoffimann (Aug 03 2021 at 15:46):

StatsFuns.jl has normcdf and norminvcdf

view this post on Zulip Júlio Hoffimann (Aug 03 2021 at 15:52):

Alternatively, take a look at the erf functions from SpecialFunctions.jl:

https://specialfunctions.juliamath.org/stable/functions_overview/#Error-Functions,-Dawson%E2%80%99s-and-Fresnel-Integrals-1

view this post on Zulip Júlio Hoffimann (Aug 03 2021 at 15:52):

The Gaussian cdf can be expressed and properly implemented with the erf function

view this post on Zulip Chad Scherrer (Aug 03 2021 at 16:16):

There might be a better way to get the ranks (is there?), but this works:

julia> x = [3,5,2,7]
4-element Vector{Int64}:
 3
 5
 2
 7

julia> (1:4)[invperm(sortperm(x))]
4-element Vector{Int64}:
 2
 3
 1
 4

view this post on Zulip Kevin Bonham (Aug 03 2021 at 16:32):

@Chad Scherrer That's the way I'd do it :laughing:... well, skipping using the range

julia> sortperm(x) |> invperm
4-element Vector{Int64}:
 2
 3
 1
 4

view this post on Zulip Kevin Bonham (Aug 03 2021 at 16:52):

Cool.

using Distributions
using CairoMakie
using StatsFuns
using StatsBase

function invnormaltransform(v; c=3/8)
    (μ, σ) = mean_and_var(v)
    rank = invperm(sortperm(v))
    N = length(v)
    return [norminvcdf(μ, σ, (x - c) / (N - 2c + 1)) for x in rank]
end

x = rand(Beta(3, 1), 1000); y = invnormaltransform(x);

hist(x)
hist!(y)
current_figure()

image.png

view this post on Zulip Notification Bot (Aug 05 2021 at 17:16):

Kevin Bonham has marked this topic as resolved.


Last updated: Nov 22 2024 at 04:41 UTC