Fit with constraints?

[henry2004y]

Hi,

Thanks for the package! I have a question about the possibility of constrained parameter fitting.

When I tried this package with my data, I found

Fitted Parameters for path_length_01 (mu=0.1):
α (stability): 0.9092045908319368
β (skewness):  1.0
σ (scale):     0.05121054252961137
μ (location):  -0.34840504748351264

The location parameter is negative. However, I may wish to enforce that μ is a nonnegative parameter. Is it possible, and how can I achieve that? Thanks!

[ymtoo]

@henry2004y The quantile-based estimator does not support parameter constraints like μ≥0 during fitting. If you are able to share an example of the stable-distributed data, I would be happy to take a closer look to better understand what is going wrong with the current implementation.

[henry2004y]

Hi @ymtoo, thanks for looking into this! My real data may contain errors that come from other sources, so for this constrained fitting purpose, probably a fake data would be enough:

using AlphaStableDistributions

d1 = AlphaStable(1.5, 0.0, 1.0, -1.0)
s = rand(d1, 2000);

# Helper function to fit the distribution and print the results
function fit_and_print(data::Vector{Float64}, label::String)
   println("Fitting distribution for: ", label)

   # Fit the AlphaStable distribution to the provided data
   fitted_dist = fit(AlphaStable, data)
   #fitted_dist = fit(Stable, data)

   println("-----------------------------")
   println("Fitted Parameters for ", label, ":")
   println("α (stability): ", fitted_dist.α)
   println("β (skewness):  ", fitted_dist.β)
   if any(m -> nameof(m) == :StableDistributions, Base.loaded_modules_array())
      println("σ (scale):     ", fitted_dist.σ)
      println("μ (location):  ", fitted_dist.μ)
   else
      println("σ (scale):     ", fitted_dist.scale)
      println("μ (location):  ", fitted_dist.location)
   end
   println("\n")
end

fit_and_print(s, "fake data")

Fitting distribution for: fake data
-----------------------------
Fitted Parameters for fake data:
α (stability): 1.4802833226639578
β (skewness):  0.10014984450120547
σ (scale):     1.0279927031384772
μ (location):  -0.9427093686161129

Note that in the code above I also tried StableDistributions.jl as an alternative.

[ymtoo]

@henry2004y The estimated parameters roughly matches the actual parameters of the stable distribution. Could there be a typo in your MWE?

julia> d1 = AlphaStable(1.5, 0.0, 1.0, -1.0)
AlphaStable{Float64}(α=1.5, β=0.0, scale=1.0, location=-1.0)

julia> s = rand(d1, 20000)
20000-element Vector{Float64}:
 -0.8669243733129077
 -2.3213483948497187
 -1.3793632046742628
  6.356796641961264
  ⋮
 -1.1124639051144452
 -0.9685055595177586
 -0.19492195041860372
 39.57375162756041

julia> fitted_dist = fit(AlphaStable, s)
AlphaStable{Float64}(α=1.486817628229075, β=0.00916113555303879, scale=1.0009108680655825, location=-1.0041688201533447)

[henry2004y]

@henry2004y The estimated parameters roughly matches the actual parameters of the stable distribution. Could there be a typo in your MWE?

It matches the actual parameters, but I think the point we want to make here is how to get a constrained fitting such that the location parameter is nonnegative even though the unconstrained fit gives a negative location?

[ymtoo]

@henry2004y You could try maximizing the log-likelihood instead, using either constrained optimizers or by transforming the parameter to enforce the constraint indirectly. A more relevant question might be whether the data is actually well-described by a stable distribution since the location parameter is a real value.

[henry2004y]

Actually this is what I've tried: https://discourse.julialang.org/t/ann-stabledistributions-jl-stable-distributions-in-julia/111711/12?u=henry2004y

Unfortunately it did not converge.