def pearson_r(x, y):
assert len(x) == len(y)
x_bar = average(x)
y_bar = average(y)
s_x = sqrt(s_2(x))
s_y = sqrt(s_2(y))
tmp = 0.0
for i in range(0, len(x)):
tmp += ((x[i] - x_bar) * (y[i] - y_bar) / s_x / s_y)
return tmp / (len(x) - 1)
def min_2(x, y):
assert len(x) == len(y)
x_bar = average(x)
y_bar = average(y)
lxy_1 = 0.0
for i in range(0, len(x)):
lxy_1 += (x[i] * y[i])
lxy = lxy_1 - sum(x) * sum(y) / len(x)
l_xx = sum(a ** 2 for a in x) - sum(x) ** 2 / len(x)
b = lxy / l_xx
a = y_bar - b * x_bar
r = pearson_r.pearson_r(x, y)
print('{}: y = {} + {}*x'.format(r, a, b))
return [r, a, b]
def infer_by_t(l1, l2, alpha=0.01, sigma=0):
n1 = len(l1)
n2 = len(l2)
x_aver = average(l1)
y_aver = average(l2)
s_1sq = s_2(l1)
s_2sq = s_2(l2)
s_w2 = ((n1 - 1) * s_1sq + (n2 - 1) * s_2sq) / (n1 + n2 - 2)
tv = ((x_aver - y_aver) - sigma) / sqrt(s_w2 * (1 / n1 + 1 / n2))
t_a = t.ppf(alpha, n1 + n2 - 2)
print('tv {} t_a {}'.format(tv, t_a))
if tv < t_a:
print('mu1 < mu2')
else:
print('mu1 >= mu2')
def infer_by_t(l1, l2, alpha=0.01, sigma=0):
n1 = len(l1)
n2 = len(l2)
x_aver = average(l1)
y_aver = average(l2)
s_1sq = s_2(l1)
s_2sq = s_2(l2)
s_w2 = ((n1 - 1) * s_1sq + (n2 - 1) * s_2sq) / (n1 + n2 - 2)
tv = ((x_aver - y_aver) - sigma) / sqrt(s_w2 * (1 / n1 + 1 / n2))
t_a = t.ppf(alpha, n1 + n2 - 2)
print('tv {} t_a {}'.format(tv, t_a))
if tv < t_a:
print('mu1 < mu2')
else:
print('mu1 >= mu2')
def t_check(l, mu, alpha=0.05):
aver = average(l)
n = len(l)
ss = s_2(l)
tt = (aver - mu) * sqrt(n) / sqrt(ss)
l, r = t.interval(1 - alpha, n - 1)
if tt > r or tt < l:
print('reject')
else:
print('accept')
def infer_ks_test_goodness(l1):
# l = np.histogram(l1)
# n = len(l)
mean = average(l1)
sigma = std(l1)
res = kstest(l1, 'norm', [mean, sigma])
if res[1] < 0.01:
print('reject')
else:
print('accept')
print(res)
def infer_ks_test_goodness(l1):
# l = np.histogram(l1)
# n = len(l)
mean = average(l1)
sigma = std(l1)
res = kstest(l1, 'norm', [mean, sigma])
if res[1] < 0.01:
print('reject')
else:
print('accept')
print(res)
