Simple extension of Distributions.jl providing support for interpolated pdfs. Currently only one type is implemented
LinearInterpolatedPDF{T,1,ITP,IT} <: ContinuousUnivariateDistributionA continuous univariate linearly interpolated distribution. The pdf, cdf, and inverse cdf are interpolated using Interpolations.jl.
The easiest way to create a distribution is to use fit_pdf
julia> x = range(0,pi/2,length=10)
0.0:0.17453292519943295:1.5707963267948966
julia> s = acos.(rand(1000));
julia> d = fit_pdf(x,s)
LinearInterpolatedPDF{Float64,1,Interpolations.ScaledInterpolation{Float64,1,Interpolations.BSplineInterpolation{Float64,1,Array{Float64,1},Interpolations.BSpline{Interpolations.Linear},Tuple{Base.OneTo{Int64}}},Interpolations.BSpline{Interpolations.Linear},Tuple{StepRangeLen{Float64,Base.TwicePrecision{Float64},Base.TwicePrecision{Float64}}}},Interpolations.BSpline{Interpolations.Linear}}(
pdf_itp: 10-element extrapolate(scale(interpolate(::Array{Float64,1}, BSpline(Interpolations.Linear())), (0.0:0.17453292519943295:1.5707963267948966,)), Throw()) with element type Float64:
0.02655632680672288
0.18866696639956113
0.37005881440239063
0.45112960446603656
0.6649161652243859
0.8050441586869701
0.7890753253462918
0.89708286054468
1.042727491447746
1.0151968027736178
cdf_itp: 10-element extrapolate(scale(interpolate(::Array{Float64,1}, BSpline(Interpolations.Linear())), (0.0:0.17453292519943295:1.5707963267948966,)), Throw()) with element type Float64:
0.0
0.018781775467173994
0.06753979792102491
0.1392020063635268
0.23659537278378787
0.36487361041346533
0.5039867787463332
0.6511318390125935
0.8204122265452835
1.0
invcdf_itp: 10-element extrapolate(interpolate((::Array{Float64,1},), ::Array{Float64,1}, Gridded(Interpolations.Linear())), Throw()) with element type Float64:
0.0
0.17453292519943295
0.3490658503988659
0.5235987755982988
0.6981317007977318
0.8726646259971648
1.0471975511965976
1.2217304763960306
1.3962634015954636
1.5707963267948966
)After fitting the distribution you can do useful things like
julia> pdf(d,1)
0.7933936499734955
julia> cdf(d,0.5)
0.12951248575312788
julia> quantile(d,0.9)
1.4736110218924767
julia> rand(d,10)
10-element Array{Float64,1}:
0.27565417806686643
1.074337923663701
1.237530643864552
0.4744230962935516
1.18776692814955
0.8436400094154567
1.0835325983972564
1.1413257453616537
0.8701141622223004
1.1702951450424084