array_binom_manual = np.zeros(10**4)
array_binom_standard = np.zeros(10**4)
for i in range(10**4):
alpha = np.random.uniform()
r = 0
while alpha > 0:
alpha -= get_p(N, p, r)
r += 1
array_binom_manual[i] = r-1
array_binom_standard[i] = np.random.binomial(N, p)
D_m = np.var(array_binom_manual)
M_m = np.mean(array_binom_manual)
D_s = np.var(array_binom_standard)
M_s = np.mean(array_binom_standard)
print(tabulate([["M", M_m, M_s, get_expected_value(N, p)],
["D", D_m, D_s, get_variance(N, p)]],
headers=["Characteristics", "Manual", "Standard", "Theoretical"]))
plots_functions.draw_hist(array_binom_standard, "Binomial")
p = 0.5
array_geom_manual = run_first_alg(p, 10**5)
array_geom_direct = run_second_alg(p, 10**6)
array_geom_log = run_third_alg(p, 10**5)
D_m = np.var(array_geom_manual)
M_m = np.mean(array_geom_manual)
D_d = np.var(array_geom_direct)
M_d = np.mean(array_geom_direct)
D_l = np.var(array_geom_log)
M_l = np.mean(array_geom_log)
print(M_m, D_m)
print(M_d, D_d)
print(M_l, D_l)
plots_functions.draw_hist(array_geom_manual, "Geometric, manual")
plots_functions.draw_hist(array_geom_direct, "Geometric, direct")
plots_functions.draw_hist(array_geom_log, "Geometric, log")
print(
tabulate([["M", M_m, M_d, M_l, get_expected_value(p)],
["D", D_m, D_d, D_l, get_variance(p)]],
headers=[
"Characteristics", "Cumulative", "Direct", "Log",
"Theoretical"
]))
def get_num_BoxMuller():
return np.sqrt(-2 * np.log(np.random.uniform())) * np.cos(
2 * np.pi * np.random.uniform())
def run_bm_alg(num_loop):
variables = np.zeros(num_loop)
for i in range(num_loop):
variables[i] = get_num_BoxMuller()
return variables
variables_c = run_central_alg(10**5)
variables_bm = run_bm_alg(10**5)
plots_functions.draw_hist(variables_c)
plots_functions.draw_hist(variables_bm)
M_c = np.mean(variables_c)
D_c = np.var(variables_c)
M_bm = np.mean(variables_bm)
D_bm = np.var(variables_bm)
print(
tabulate(
[["M", M_c, M_bm, get_expected_value(0)],
["D", D_c, D_bm, get_variance(1)]],
headers=["Characteristics", "Central", "Box-Muller", "Theoretical"]))
def get_variance(r_low, r_up):
n = r_up - r_low + 1
return (n**2 - 1) / 12
r_low = 1
r_up = 100
array_uniform = np.zeros(10**6)
for i in range(10**6):
array_uniform[i] = get_number_uniform(r_low, r_up)
D = np.var(array_uniform)
M = np.mean(array_uniform)
plots_functions.draw_hist(array_uniform)
print(
tabulate([[
"M", M,
abs(M - get_expected_value(r_low, r_up)),
get_expected_value(r_low, r_up)
], ["D", D,
abs(D - get_variance(r_low, r_up)),
get_variance(r_low, r_up)]],
headers=["", "Experimental", "Inaccuracy", "Theoretical"]))
if r == 0:
return np.exp(-mu)
else:
return get_p(mu, r - 1) * mu / r
def run_alg1(mu, num_loop: int) -> np.array:
variables = np.zeros(num_loop)
for i in range(num_loop):
alpha = np.random.uniform()
r = 0
while alpha > 0:
alpha -= get_p(mu, r)
r += 1
variables[i] = r - 1
return variables
mu = 10
variables_1 = run_alg1(mu, 10**5)
variables_2 = run_alg2(mu, 10**5)
plots_functions.draw_hist(variables_1)
print(
tabulate([["M", mu, mu, "10.0"], ["D", mu, mu, "10.0"]],
headers=[
"Characteristics", "Cumulative", "Alternative", "Theoretical"
]))
r = 0
while alpha > 0:
alpha -= get_p(N, p, r)
r += 1
#print(get_p_binom(N, p, r))
array_binom_manual[i] = r - 1
array_binom_standard[i] = np.random.binomial(N, p)
D_m = np.var(array_binom_manual)
M_m = np.mean(array_binom_manual)
D_s = np.var(array_binom_standard)
M_s = np.mean(array_binom_standard)
print(
tabulate([["M", M_m, M_s, get_expected_value(N, p)],
["D", D_m, D_s, get_variance(N, p)]],
headers=["Characteristics", "Manual", "Standard", "Theoretical"]))
plots_functions.draw_hist(array_binom_standard)
# test get_p_binom
array_test = np.zeros(N)
for i in range(N):
array_test[i] = get_p_binom(N, p, i)
print(array_test[i])
print("test sum = ", sum(array_test))
return np.sqrt(-2 * np.log(np.random.uniform())) * np.cos(
2 * np.pi * np.random.uniform())
def run_bm_alg(num_loop):
variables = np.zeros(num_loop)
for i in range(num_loop):
variables[i] = get_num_BoxMuller()
return variables
if __name__ == '__main__':
variables_c = run_central_alg(10**5)
variables_bm = run_bm_alg(10**5)
plots_functions.draw_hist(variables_c, "Normal, central")
plots_functions.draw_hist(variables_bm, "Normal, Box-Muller")
M_c = np.mean(variables_c)
D_c = np.var(variables_c)
M_bm = np.mean(variables_bm)
D_bm = np.var(variables_bm)
print(
tabulate([["M", M_c, M_bm, get_expected_value(0)],
["D", D_c, D_bm, get_variance(1)]],
headers=[
"Characteristics", "Central", "Box-Muller", "Theoretical"
]))
standard_deviation = np.zeros(len(testsTypes))
for k in range(len(testsTypes)):
n = testsTypes[k]
u = np.random.rand(n)
expected_value[k] = sum(u)/n
variance[k] = sum((u - expected_value[k])**2)/n
standard_deviation[k] = math.sqrt(variance[k])
correlation = np.zeros(n)
x_data = np.zeros(n)
for i in range(1, n):
correlation[i] = sum((u[:(n-i)] - expected_value[k])*(u[i:] - expected_value[k]))/sum((u - expected_value[k])**2)
x_data[i] = i
draw_plot(x_data, correlation, 1)
plt.show(block=True)
plots_functions.draw_hist(u, "Uniform")
header = ["n", "characteristics", "experimental data", "theoretical data", "difference"]
table = [[testsTypes[0], "M", expected_value[0], 0.5, abs(0.5-expected_value[0])],
[testsTypes[0], "D", variance[0], 0.08333, abs(0.08333-variance[0])]]
for i in range(1, len(testsTypes)):
table.append([testsTypes[i], "M", expected_value[i], 0.5, abs(0.5-expected_value[i])])
table.append([testsTypes[i], "D", variance[i], 0.08333, abs(0.08333-variance[i])])
print(tabulate(table, header, tablefmt="simple"))
return (r_low + r_up) / 2
def get_variance(r_low, r_up):
n = r_up - r_low + 1
return (n**2 - 1) / 12
r_low = 1
r_up = 100
array_uniform = np.zeros(10**6)
for i in range(10**6):
array_uniform[i] = get_number_uniform(r_low, r_up)
D = np.var(array_uniform)
M = np.mean(array_uniform)
plots_functions.draw_hist(array_uniform, "Uniform")
print(
tabulate([[
"M", M,
abs(M - get_expected_value(r_low, r_up)),
get_expected_value(r_low, r_up)
], ["D", D,
abs(D - get_variance(r_low, r_up)),
get_variance(r_low, r_up)]],
headers=["", "Experimental", "Inaccuracy", "Theoretical"]))
return np.exp(-mu)
else:
return get_p(mu, r - 1) * mu / r
def run_alg1(mu, num_loop: int) -> np.array:
variables = np.zeros(num_loop)
for i in range(num_loop):
alpha = np.random.uniform()
r = 0
while alpha > 0:
alpha -= get_p(mu, r)
r += 1
variables[i] = r - 1
return variables
mu = 10
variables_1 = run_alg1(mu, 10**5)
variables_2 = run_alg2(mu, 10**5)
plots_functions.draw_hist(variables_1, "Poisson, cumulative")
plots_functions.draw_hist(variables_2, "Poisson, alternative")
print(
tabulate([["M", mu, mu, "10.0"], ["D", mu, mu, "10.0"]],
headers=[
"Characteristics", "Cumulative", "Alternative", "Theoretical"
]))
def get_num(a, b):
return (b - a) * np.random.uniform() + a
def get_expected_value(a, b):
return (a+b)/2
def get_variance(a, b):
return (b-a)**2/12
a = 1
b = 100
array_uniform = np.zeros(10**6)
for i in range(10**6):
array_uniform[i] = get_num(a, b)
D = np.var(array_uniform)
M = np.mean(array_uniform)
print(tabulate([["M", M, abs(M - get_expected_value(a, b)), get_expected_value(a, b)],
["D", D, abs(D - get_variance(a, b)), get_variance(a, b)]],
headers=["", "Experimental", "Inaccuracy", "Theoretical"]))
plots_functions.draw_hist(array_uniform, "Unifrom continuous")
return 0
def get_variance(N):
return N / (N - 2)
def get_random_num(N):
return get_norm() / np.sqrt(get_chi(N) / N)
def run_alg(num_loop, N):
variables = np.zeros(num_loop)
for i in range(num_loop):
variables[i] = get_random_num(N)
return variables
N = 10
variables_ = run_alg(10**5, N)
plots_functions.draw_hist(variables_, "Student")
D = np.var(variables_)
M = np.mean(variables_)
print(
tabulate([["M", M, get_expected_value()], ["D", D, get_variance(N)]],
headers=["", "Experimental", "Theoretical"]))
D[k] = sum((u - M[k])**2) / n
S[k] = math.sqrt(D[k])
#print(M, D)
K = np.zeros(n)
x_data = np.zeros(n)
for i in range(1, n):
K[i] = sum((u[:(n - i)] - M[k]) * (u[i:] - M[k])) / sum((u - M[k])**2)
x_data[i] = i
draw_plot(x_data, K, 1)
plt.show(block=True)
plots_functions.draw_hist(u)
header = [
"n", "characteristics", "experimental data", "theoretical data",
"difference"
]
table = [[testsTypes[0], "M", M[0], 0.5,
abs(0.5 - M[0])],
[testsTypes[0], "D", D[0], 0.08333,
abs(0.08333 - D[0])]]
for i in range(1, len(testsTypes)):
table.append([testsTypes[i], "M", M[i], 0.5, abs(0.5 - M[i])])
table.append([testsTypes[i], "D", D[i], 0.08333, abs(0.08333 - D[i])])
print(tabulate(table, header, tablefmt="simple"))
import numpy as np
import plots_functions
from tabulate import tabulate
def get_random_num(beta):
return -beta*np.log(np.random.uniform())
def run_alg(num_loop, beta):
variables = np.zeros(num_loop)
for i in range(num_loop):
variables[i] = get_random_num(beta)
return variables
variables_ = run_alg(10**5, 1)
plots_functions.draw_hist(variables_, "Exponential")
D = np.var(variables_)
M = np.mean(variables_)
print(tabulate([["M", M, 1],
["D", D, 1]],
headers=["", "Experimental", "Theoretical"]))
def get_p(p, r):
alpha = 1 / np.log(p)
return -alpha*(1-p)**r/r
def run_alg(p, num_loop):
variables = np.zeros(num_loop)
for i in range(num_loop):
r = 1
uniform_rand = np.random.uniform()
while uniform_rand > 0:
uniform_rand -= get_p(p, r)
r += 1
variables[i] = r - 1
return variables
p = 0.5
variables_ = run_alg(p, 10**5)
plots_functions.draw_hist(variables_, "Logarithmic")
D_m = np.var(variables_)
M_m = np.mean(variables_)
print(tabulate([["M", M_m, M_m-get_expected_value(p), get_expected_value(p)],
["D", D_m, D_m - get_variance(p), get_variance(p)]],
headers=["Characteristics", "Manual", "Difference", "Theoretical"]))
def get_random_num(N):
variable = 0
for i in range(N):
variable += norm.get_num_CentralTh()**2
return variable
def run_alg(num_loop, N):
variables = np.zeros(num_loop)
for i in range(num_loop):
variables[i] = get_random_num(N)
return variables
if __name__ == '__main__':
N = 10
variables_ = run_alg(10**5, N)
plots_functions.draw_hist(variables_, "Chi")
D = np.var(variables_)
M = np.mean(variables_)
print(
tabulate(
[["M", M, get_expected_value(N)], ["D", D, get_variance(N)]],
headers=["", "Experimental", "Theoretical"]))
