# Landau distribution or something similar
**URL:** https://discourse.julialang.org/t/landau-distribution-or-something-similar/66063
**Category:** Statistics
**Created:** [August 9, 2021, 7:47am UTC](https://discourse.julialang.org/t/landau-distribution-or-something-similar/66063 "2021-08-09T07:47:18Z")
**Posts on this page:** 4
**Page:** 2
### Author:  [@misha\_mikhasenko](https://discourse.julialang.org/u/misha_mikhasenko)
#### Post date: [August 12, 2021, 2:03pm UTC](https://discourse.julialang.org/t/landau-distribution-or-something-similar/66063/21 "2021-08-12T14:03:46Z")
Hey,
I see. What I meant, that assuming that `t/c` is a typo in wiki, the arbitrary Landau function is `L0((x-mu)/c)`, where mu an c are the parameters. L0 can be calculated once and use Interpolation for all instances.
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### Author:  [@jling](https://discourse.julialang.org/u/jling)
#### Post date: [August 12, 2021, 2:24pm UTC](https://discourse.julialang.org/t/landau-distribution-or-something-similar/66063/22 "2021-08-12T14:24:41Z")
assume I remember it correctly, I checked it against ROOT last time
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### Author:  [@misha\_mikhasenko](https://discourse.julialang.org/u/misha_mikhasenko)
#### Post date: [August 12, 2021, 4:43pm UTC](https://discourse.julialang.org/t/landau-distribution-or-something-similar/66063/23 "2021-08-12T16:43:23Z")
Out of curiosity, i cooked up a fitter of you functions
(I think ChiSq should become part of the AlgebraPDF, I just never fit chi2 before)
```julia
using QuadGK
using AlgebraPDF
using Plots
using Interpolations
theme(:wong2, frame=:box, grid=false, minorticks=true,
guidefontvalign=:top, guidefonthalign=:right)
integrand(t,x) = exp(-t)*cos(t*x+2*t/π*log(t))
landau(x) = quadgk(t->integrand(t,x), 0, Inf)[1]
@time landau(0)
@time plot(x->landau(x), -2:0.5:15)
const xv = range(-3,30, length=300)
const yv = landau.(xv)
const itr = interpolate((xv,), yv, Gridded(Linear()))
dlandau(x) = itr.knots[1][1] d->fixpars(d,(:μ1,:c1))
d2 = Landau(Ext(μ2= 10.5,c2=1.2)) |> d->fixpars(d,(:μ2,:c2))
d3 = Landau(Ext(μ3=-2.5,c3=1.5)) |> d->fixpars(d,(:μ3,:c3))
dsum = d1*(α1=1.1,) + d2*(α2=1.0,) + d3*(α3=1.1,)
plot(dsum, -5, 15)
pars(dsum) #
# (α1 = 1.1, α2 = 1.0, α3 = 1.1, μ1 = 2.0, c1 = 1.0, μ2 = 10.5, c2 = 1.2, μ3 = -2.5, c3 = 1.5)
data = generate(Normalized(dsum, (-5,15)), 10000)
h = Plots.StatsBase.fit(
Plots.StatsBase.Histogram,
data, nbins=100)
const xdata = Plots._bin_centers(h.edges[1])
const ydata = h.weights
plot(h, c=1, lab="data")
import AlgebraPDF: func, pars, updatevalueorflag
struct ChiSq{M,T<:NumberOrTuple,V<:Number} <: AbstractFunctionWithParameters
f::M
xdata::Vector{T}
ydata::Vector{V}
end
function func(d::ChiSq, x::NumberOrTuple; p=pars(d))
sum((ydata - dsum(xdata; p)).^2) # ./ ydata
end
pars(d::ChiSq, isfree::Bool) = pars(d.f, isfree)
updatevalueorflag(d::ChiSq, s::Symbol, isfree::Bool, v=getproperty(pars(d),s)) =
ChiSq(updatevalueorflag(d.f,s,isfree,v), d.xdata, d.ydata)
#
χ² = ChiSq(dsum, collect(xdata), ydata)
χ²(0,p2v(χ²))
fit_result = AlgebraPDF.minimize(x->χ²(0,x), p2v(χ²), MigradAndHesse())
fs = AlgebraPDF.fit_summary(fit_result, χ²)
fs.parameters
plot!(updatepars(dsum, fs.parameters), xdata[1], xdata[end], l=(2,:red), lab="fit")
```
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### Author:  [@tamasgal](https://discourse.julialang.org/u/tamasgal)
#### Post date: [August 12, 2021, 4:45pm UTC](https://discourse.julialang.org/t/landau-distribution-or-something-similar/66063/24 "2021-08-12T16:45:46Z")
Nice, thanks! `:)` Now I have another recipe to cook with `;)`
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