In [1]:

    

push!(LOAD_PATH, "$(pwd())/../src"); using PyPlot, StatsBase, Distributions, StochasticProcesses;


    

In [20]:

    

type Pearson
    a
end

Distributions.pdf(p::Pearson, t) = abs(p.a)*exp(-p.a^2/(2*t))*t^(-3/2)/sqrt(2*pi)


    

    




WARNING: Method definition (::Type{Main.Pearson})(Any) in module Main at In[18]:2 overwritten at In[20]:2.
WARNING: Method definition pdf(Main.Pearson, Any) in module Main at In[18]:5 overwritten at In[20]:5.

In [32]:

    

plt[:hist](sim(FirstTime(BrownianMotion(), (t, y) -> y > .5), linspace(0, 10, 10000), 10000), bins=50, normed=true);
let x=linspace(0,10,1000)
    plot(x, (x -> pdf(Pearson(.5), x)).(x), color="red");
end


    

    













    
Out[32]:





1-element Array{Any,1}:
 PyObject <matplotlib.lines.Line2D object at 0x7fb8293a4748>

In [33]:

    

sim(FirstTime(BrownianMotion(), (t, y) -> y > 1), linspace(0, 1, 10000), 5)


    

    
Out[33]:





3-element Array{Float64,1}:
 0.655266
 0.80458 
 0.825783

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