

In [1]:

    
using Plots, ApproxFun

Piecewise function sampling



In [2]:

    
f = abs(Fun(sin,[-5,5]))
r = ApproxFun.sample(f,10000)
plot(f/sum(f))               
histogram!(r;normed=true,nbins=100)









    



[Plots.jl] Initializing backend: gr






    Out[2]:

Jacobi singularity sampling



In [3]:

    
x=Fun(identity)
f = exp(x)*sqrt(1-x^2)
r = ApproxFun.sample(f,10000)
plot(f/sum(f))                     
histogram!(r;normed=true,nbins=100)









    Out[3]:



In [4]:

    
x=Fun(identity)
f = exp(x)/sqrt(1-x^2)
r = ApproxFun.sample(f,10000)
plot(f/sum(f);ylims=(0.,5.))    
histogram!(r;normed=true,nbins=100)









    Out[4]:



In [5]:

    
x=Fun(identity)
f = exp(x)*(1-x)^0.123*(1+x)^(-0.234)
r = ApproxFun.sample(f,10000)
plot(f/sum(f))                         
histogram!(r;normed=true,nbins=100)









    Out[5]:

Heavy-tail sampling



In [6]:

    
f=Fun(x->(1+sech(x))/(1+x^2),[-Inf,Inf])
r=ApproxFun.sample(f,10000)

plot(-15.:.01:15.,f/sum(f))
histogram!(filter!(r->abs(r)<15,r);normed=true,nbins=100)









    Out[6]:



In [7]:

    
f=Fun(x->(exp(-x)+1)/(1+x^2),[0,Inf])
r=ApproxFun.sample(f,10000)

plot(0:.05:15,f/sum(f))
histogram!(filter!(r->0<r<15,r);normed=true,nbins=100)









    Out[7]: