def checkFacts_pdf_Phi(
nu=0, tau=0, phi_grid=None, **kwargs):
pdf_grid, phi_grid = make_pdfgrid_phi(nu, tau, phi_grid, **kwargs)
mu_grid = phi2mu(phi_grid, **kwargs)
IntegralVal = np.trapz(pdf_grid, phi_grid)
E_phi_numeric = np.trapz(pdf_grid * phi_grid, phi_grid)
E_phi_formula = E_phi(nu=nu, tau=tau, **kwargs)
E_mu_numeric = np.trapz(pdf_grid * mu_grid, phi_grid)
E_mu_formula = tau/nu
mode_phi_numeric = phi_grid[np.argmax(pdf_grid)]
mode_phi_formula = mu2phi(tau/nu, **kwargs)
print "nu=%7.3f tau=%7.3f" % (nu, tau)
print " Integral=% 7.3f should be % 7.3f" % (IntegralVal, 1.0)
print " E[mu]=% 7.3f should be % 7.3f" % (E_mu_numeric, E_mu_formula)
print " E[phi]=% 7.3f should be % 7.3f" % (E_phi_numeric, E_phi_formula)
print " mode[phi]=% 7.3f should be % 7.3f" % (
mode_phi_numeric, mode_phi_formula)
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