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from __future__ import division
%qtconsole
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import sympy as S
import sympy.stats as st
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u=S.symbols('u')
p=st.LogNormal('u',0,0.5)
pu=st.density(p)(u)
fx=S.lambdify(u,pu,'numpy')
x = linspace(0.001,4,100)
hist([st.sample(p) for i in range(1000)],bins=50,normed=1);
plot(x,fx(x),'r-',lw=3.)
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pw=[i*(S.Heaviside(u-j/2)-S.Heaviside(u-j/2-1/2)) for i,j in zip(S.symbols('a:8'),range(8))]
pwf = lambda i: sum(pw).subs(u,i)
Rectangle Wedge Tail Decomposition¶
$$ f(x) = \exp\left(-\frac{(x-1)^2}{2x} \right)(x+1)/12 $$
where $x>0$
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x = linspace(0.001,10,100)
f= lambda x: (sqrt(1/x) + sqrt(x))/ (2.*pow(exp(1),pow(-sqrt(1/x) + sqrt(x),2)/ 2.)*sqrt(2*pi)*x)
fx = f(x)
plot(x,fx)
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u=S.symbols('u')
p=S.Piecewise(*[(f(j),(i<u<=j)) for i,j in zip(range(10),range(1,11))]+[(0,True)])
plot(x,[p.subs(u,i) for i in x],x,fx)
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