Skew Student T Distr? (Hansen or Fernandes Steel)

Alex1 · July 25, 2025, 4:50am

Hi, is there a Skew Student T implementation in Julia?

Hansen or Fernandes-Steel variants, with analytical pdf, cdf, quantile?

technocrat · July 25, 2025, 4:58am

You’ll have to track it down, since it appears not to be registered, but check [ANN] ARCHModels.jl and the JSTATS paper.

Alex1 · July 25, 2025, 5:16am

Indeed it has StdSkewT thank you!

Alex1 · July 25, 2025, 9:35am

Actually, it has PDF and Quantile but not the CDF function

github.com/s-broda/ARCHModels.jl

src/univariatestandardizeddistributions.jl

master


      
          end
          
          function quantile(dist::StdGED, q::Real)
              p = dist.coefs[1]
              ip = 1/p
              qq = 2*q-1
              return sign(qq) * (gammainvcdf(ip, 1., abs(qq)))^ip/kernelinvariants(StdGED, [p])[1]
          end
          
          ################################################################################
          #Hansen's SKT-Distribution
          
          """
              StdSkewT{T} <: StandardizedDistribution{T}
          
          Hansen's standardized (mean zero, variance one) Skewed Student's t distribution.
          """
          struct StdSkewT{T} <: StandardizedDistribution{T}
              coefs::Vector{T}
              function StdSkewT{T}(coefs::Vector) where {T}
                  length(coefs) == 2 || throw(NumParamError(2, length(coefs)))

technocrat · July 25, 2025, 10:03am

It has been claimed

Since Hansen’s skew T is just two half-T distributions squished together and appropriately normaluzed to be a density, it is pretty easy to directly compute the PPF and CDF by parts.

Haven’t tried it myself.

Alex1 · July 26, 2025, 8:45am

I implemented SkewT Hanson variant

It has analytical pdf, cdf, quantile and should be faster (some constants cached)

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Skew Student T Distr? (Hansen or Fernandes Steel)

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