def selective_quadrant(samples):
n1, n2, n3, n4 = 0, 0, 0, 0
mx, my = nc.sample_mean(samples[0]), nc.sample_mean(samples[1])
for i in range(len(samples[0])):
if samples[0][i] > mx and samples[1][i] >= my:
n1 += 1
elif samples[0][i] <= mx and samples[1][i] > my:
n2 += 1
elif samples[0][i] < mx and samples[1][i] <= my:
n3 += 1
elif samples[0][i] >= mx and samples[1][i] < my:
n4 += 1
return ((n1 + n3) - (n2 + n4)) / len(samples[0])
def complex_dist_test(capacity):
def f(cap): return 0.9 * np.random.multivariate_normal((0, 0), [[1, 0.9], [0.9, 1]], cap).T + \
0.1 * np.random.multivariate_normal((0, 0), [[100, -0.9], [-0.9, 100]], cap).T
data = np.array([[
c_cor(f(capacity))
for c_cor in [scc.pearson, scc.spearman, scc.selective_quadrant]
] for _ in range(1000)]).T
cell_text = [
list(
map(lambda x: "%.4f" % x, [
nc.sample_mean(data[i]),
nc.sample_mean(list(map(lambda x: x**2, data[i]))),
nc.dispersion_exp(data[i])
])) for i in range(3)
]
draw_table("complex normal distribution n = %i" % capacity,
np.array(cell_text).T)
def simple_dist_test(capacity):
for cov in [0, 0.5, 0.9]:
data = []
for _ in range(1000):
sample = np.random.multivariate_normal(
(0, 0), [[1, cov], [cov, 1]], capacity).T
data += [[
c_cor(sample) for c_cor in
[scc.pearson, scc.spearman, scc.selective_quadrant]
]]
data = np.array(data).T
cell_text = [
list(
map(lambda x: "%.4f" % x, [
nc.sample_mean(data[i]),
nc.sample_mean(list(map(lambda x: x**2, data[i]))),
nc.dispersion_exp(data[i])
])) for i in range(3)
]
draw_table("normal distribution n = %i, p = %.2f" % (capacity, cov),
np.array(cell_text).T)
def ellipse_test(capacity):
from matplotlib.patches import Ellipse
_, sp = plt.subplots(1, 3, figsize=(16, 6))
for cor, subplot in zip([0, 0.5, 0.9], sp):
dots = np.random.multivariate_normal((0, 0), [[1, cor], [cor, 1]],
capacity).T
vx = nc.dispersion_exp(dots[0])
vy = nc.dispersion_exp(dots[1])
angle = np.arctan(2 * np.sqrt(vx) * np.sqrt(vy) * cor / (vx - vy)) / 2
w = 5 * np.sqrt(vx * (np.cos(angle))**2 + cor * np.sqrt(vx) *
np.sqrt(vy) * np.sin(2 * angle) + vy *
(np.sin(angle))**2)
h = 5 * np.sqrt(vx * (np.sin(angle))**2 - cor * np.sqrt(vx) *
np.sqrt(vy) * np.sin(2 * angle) + vy *
(np.cos(angle))**2)
ell = Ellipse(xy=(nc.sample_mean(dots[0]), nc.sample_mean(dots[1])),
width=w,
height=h,
angle=np.rad2deg(angle))
draw_ellipse("normal distribution %s = %.1f" % (r'$\rho$', cor), ell,
dots, subplot)
plt.show()
def pearson(samples):
ex = nc.sample_mean(samples[0])
ey = nc.sample_mean(samples[1])
sdx = np.sqrt(nc.dispersion_exp(samples[0]))
sdy = np.sqrt(nc.dispersion_exp(samples[1]))
return (nc.sample_mean(np.array(samples[0])*np.array(samples[1])) - ex * ey) / (sdx * sdy)
plt.plot(dots, pl, color='blue')
plt.plot(dots, nl, color='red')
plt.title("%s, capacity:%s" % ("normal distribution", sum(n_list)))
plt.ylabel("fx")
plt.xlabel("X")
plt.grid()
plt.legend(('теоретические частоты', 'реальные частоты'))
plt.show()
if __name__ == "__main__":
k = 7
delta = 0.5
for n in [10, 100]:
x_i = sorted(dist.normal(n))
m0 = nc.sample_mean(x_i)
d = nc.dispersion_exp(x_i)
print("%.2f %.2f" % (m0, d))
d_i = [[-np.inf,
m0 - delta * 2.5], [m0 - delta * 2.5, m0 - delta * 1.5],
[m0 - delta * 1.5, m0 - delta * 0.5],
[m0 - delta * 0.5, m0 + delta * 0.5],
[m0 + delta * 0.5, m0 + delta * 1.5],
[m0 + delta * 1.5, m0 + delta * 2.5],
[m0 + delta * 2.5, np.inf]]
n_i = [0] * k
for x in x_i:
for i in range(k):
if d_i[i][0] < x <= d_i[i][1]:
n_i[i] += 1
p_i = [integrate.quad(den.normal, i[0], i[1])[0] for i in d_i]
import scipy.stats as st
import numpy as np
from Lab1.distribution import distribution as d
from Lab2.num_char import numerical_characteristics as nc
if __name__ == "__main__":
alpha = 0.05
for n in [20, 100]:
print("=========%i==========" % n)
x = d.normal(n)
m = nc.sample_mean(x)
s = np.sqrt(nc.dispersion_exp(x))
print("m: %.2f, %.2f" %
(m - s *
(st.t.ppf(1 - alpha / 2, n - 1)) / np.sqrt(n - 1), m + s *
(st.t.ppf(1 - alpha / 2, n - 1)) / np.sqrt(n - 1)))
print("sigma: %.2f, %.2f" %
(s * np.sqrt(n) / np.sqrt(st.chi2.ppf(1 - alpha / 2, n - 1)),
s * np.sqrt(n) / np.sqrt(st.chi2.ppf(alpha / 2, n - 1))))
print("m asymptotic :%.2f, %.2f" %
(m - st.norm.ppf(1 - alpha / 2) / np.sqrt(n),
m + st.norm.ppf(1 - alpha / 2) / np.sqrt(n)))
e = (sum(list(map(lambda el: (el - m)**4, x))) / n) / s**4 - 3
print("sigma asymptotic: %.2f, %.2f" %
(s / np.sqrt(1 + st.norm.ppf(1 - alpha / 2) * np.sqrt(
(e + 2) / n)), s /
np.sqrt(1 - st.norm.ppf(1 - alpha / 2) * np.sqrt((e + 2) / n))))
from Lab1.distribution import distribution as d
from Lab2.num_char import numerical_characteristics as nc
if __name__ == "__main__":
for dist in [d.uniform, d.poisson, d.laplace, d.normal, d.cauchy]:
print(dist.__name__)
for capacity in [10, 100, 1000]:
for num_char in [
nc.sample_mean, nc.median, nc.halfsum_extreme,
nc.halfsum_quartile, nc.truncated_mean
]:
print(num_char.__name__ + " cap: " + str(capacity))
data = [num_char(sorted(dist(capacity))) for _ in range(1000)]
print("%.6f" % nc.sample_mean(data))
print("%.6f" % nc.dispersion_exp(data))
print('==================================')