def outer(s, z):
return s**(nu - 1) * phi(sqrt(nu) * s) * inner(s, z)
def outer(s, z):
inner_int = inner(s, z)
return s**(nu - 1) * phi(np.sqrt(nu) * s) * inner_int
def inner(s, z):
return phi(z) * (Phi(z + q * s) - Phi(z))**(k - 1)
def outer(s):
def inner(z):
return phi(z) * (Phi(z + q * s) - Phi(z))**(k - 1)
inner_int = quad(inner, -np.inf, np.inf, epsabs=1e-12, limit=1000)[0]
return s**(nu - 1) * phi(np.sqrt(nu) * s) * inner_int
def integrand(z):
return phi(z) * (Phi(z + q) - Phi(z))**(k - 1)
def integral(q, s, z):
return k * (k - 1) * s * phi(z) * phi(s * q + z) \
* (Phi(s * q + z) - Phi(z)) ** (k - 2)
def outer(q, s, z):
return s ** nu * phi(sqrt(nu) * s) * inner(q, s, z)
def inner(q, s, z):
return phi(z + q * s) * phi(z) * (Phi(z + q * s) - Phi(z)) ** (k - 2)
