1408.sagews

# Complete gamma distribution, (Eq. 2.18)
var('mu, s, nu, x, alpha')
assume(mu > 0)
assume(nu > 0)
assume(mu, 'integer')
assume(nu, 'integer')
#assume(alpha > 0)
f(x) = (mu/s)*x**(nu*mu-1)*exp(-alpha*x**mu)
s = integrate(f(x),(x,0,infinity))
print s


# Compute the PDF for f(D)
var('D, Dn')
f(D) = f(x) / Dn
x = D/Dn
print f(D)
p = integrate(f(D),((D/Dn),0,infinity))
print p

(mu, s, nu, x, alpha) mu*integrate(x^(mu*nu - 1)*e^(-alpha*x^mu), x, 0, +Infinity)/s (D, Dn) mu*x^(mu*nu - 1)*e^(-alpha*x^mu)/(Dn*s) integrate(mu*x^(mu*nu - 1)*e^(-alpha*x^mu)/(Dn*s), D/Dn, 0, +Infinity)