def F(y):
the_sum = 0
for i in range(1, 200):
def my_factorial(k):
return GammaFunc(k + 1)
c = GammaFunc((i * m - 3.0) / n) / my_factorial(i)
the_sum += c * y**i
return y**(3 / (n - m)) * (GammaFunc((n - 3.0) / n) - 3 / n * the_sum)
def dFdy(y):
the_sum, the_derivsum = 0, 0
for i in range(1, 200):
def my_factorial(k):
return GammaFunc(k + 1)
c = GammaFunc((i * m - 3.0) / n) / my_factorial(i)
the_sum += c * y**i
the_derivsum += i * c * y**(i - 1)
return y**(3 / (n - m)) * (-3 / n * the_derivsum) + (
3 / (n - m)) * y**(3 / (n - m) - 1) * (GammaFunc(
(n - 3.0) / n) - 3 / n * the_sum)
def t_negative_llh(params, p, q, r, gjr=False, out=None):
c, phi, theta = params[0], params[1:p + 1], params[p + 1:p + q + 1]
if gjr:
omega, alpha, gamma, beta, v = params[-5:]
else:
omega, alpha, beta, v = params[-4:]
gamma = None
eps = get_epsilon(c, phi, theta, r)
sigma2 = get_sigma2(omega, alpha, beta, gamma, r, eps, gjr)
llh = np.log(GammaFunc((v + 1) / 2) / (GammaFunc(v / 2) * np.sqrt(np.pi * (v - 2) * sigma2)) * \
(1 + eps ** 2 / ((v - 2) * sigma2)) ** (-(v + 1) / 2))
neg_llh = -llh # minimize negative log likelihood
total_llh = np.sum(neg_llh)
if out is None:
return total_llh
else:
return total_llh, llh, sigma2
def t_negative_loglikelihood(params, r):
c = params[0]
phi = params[1]
theta = params[2]
omega = params[3]
alpha = params[4]
beta = params[5]
v = params[6]
eps = get_epsilon(c, phi, theta, r)
sigma2 = get_sigma2(omega, alpha, beta, eps)
llh = np.log(GammaFunc((v + 1) / 2) / (GammaFunc(v / 2) * np.sqrt(np.pi * (v - 2) * sigma2)) * \
(1 + eps ** 2 / ((v - 2) * sigma2)) ** (-(v + 1) / 2))
neg_llh = -llh # minimize negative log likelihood
total_llh = np.sum(neg_llh)
return total_llh
def my_factorial(k):
return GammaFunc(k + 1)