Лабораторная 3 / Вариант_Экспоненциальное распределение / Lab3

import math
import matplotlib.pyplot as plt
import numpy as np


class MyRand:
    def __init__(self, r, M, seed=1):
        self.r = r
        self.M = M
        self.mod = 2 ** r
        self.A = seed % self.mod

    def next(self):
        self.A = (self.A * self.M) % self.mod

        return self.A / self.mod


N = 10000
X = []

# Exponential
print("Exponential")
r = MyRand(32, 3**12)
lambda_exp = 4
X.clear()
for i in range(N):
    z = r.next()
    X.append(-1 / lambda_exp * math.log(z))

M_expected = 1 / lambda_exp
D_expected = 1 / (lambda_exp ** 2)
M = sum(X) / N
D = sum([x ** 2 for x in X]) / N - M ** 2
M_delta = abs((M - M_expected) / M_expected) * 100
D_delta = abs((D - D_expected) / D_expected) * 100
print(f"Эмпирические: {M = :.3f}, {D = :.3f}")
print(f"Теоретические: M = {M_expected:.3f}, D = {D_expected:.3f}")
print(f"Относительные погрешности: δM = {M_delta:.2f} %, δD = {D_delta:.2f} %")

plt.hist(X, bins=30, weights=np.ones_like(X) / len(X))
plt.savefig("ms3.exponential.svg")
plt.show()


# Uniform
print("\nUniform")

A_uni = -10
B_uni = 5
X.clear()
for i in range(N):
    z = r.next()
    X.append(A_uni + (B_uni - A_uni) * z)

M_expected = A_uni + (B_uni - A_uni) / 2
D_expected = (B_uni - A_uni) ** 2 / 12
M = sum(X) / N
D = sum([x ** 2 for x in X]) / N - M ** 2
M_delta = abs((M - M_expected) / M_expected) * 100
D_delta = abs((D - D_expected) / D_expected) * 100
print(f"Эмпирические: {M = :.3f}, {D = :.3f}")
print(f"Теоретические: M = {M_expected:.3f}, D = {D_expected:.3f}")
print(f"Относительные погрешности: δM = {M_delta:.2f} %, δD = {D_delta:.2f} %")

plt.hist(X, bins=B_uni*8, weights=np.ones_like(X) / len(X))
plt.savefig("ms3.uniform.svg")
plt.show()


# Erlang
print("\nErlang")

k_erl = 4
lambda_erl = 4
X.clear()
for i in range(N):
    X.append(-1 / lambda_erl * math.log(math.prod(r.next()
                                                  for j in range(k_erl))))

M_expected = k_erl / lambda_erl
D_expected = k_erl / (lambda_erl ** 2)
M = sum(X) / N
D = sum([x ** 2 for x in X]) / N - M ** 2
M_delta = abs((M - M_expected) / M_expected) * 100
D_delta = abs((D - D_expected) / D_expected) * 100
print(f"Эмпирические: {M = :.3f}, {D = :.3f}")
print(f"Теоретические: M = {M_expected:.3f}, D = {D_expected:.3f}")
print(f"Относительные погрешности: δM = {M_delta:.2f} %, δD = {D_delta:.2f} %")

plt.hist(X, bins=30, weights=np.ones_like(X) / len(X))
plt.savefig("ms3.erlang.svg")
plt.show()


# Standard Normal
print("\nStandard Normal")

X.clear()
for i in range(N // 2):
    z1 = r.next()
    z2 = r.next()
    X.append(math.sqrt(-2 * math.log(z1)) * math.cos(2 * math.pi * z2))
    X.append(math.sqrt(-2 * math.log(z1)) * math.sin(2 * math.pi * z2))

M_expected = 0
D_expected = 1
M = sum(X) / N
D = sum([x ** 2 for x in X]) / N - M ** 2
D_delta = abs((D - D_expected) / D_expected) * 100
print(f"Эмпирические: {M = :.3f}, {D = :.3f}")
print(f"Теоретические: M = {M_expected:.3f}, D = {D_expected:.3f}")
print(f"Относительные погрешности: δD = {D_delta:.2f} %")

plt.hist(X, bins=40, weights=np.ones_like(X) / len(X))
plt.savefig("ms3.normal.svg")
plt.show()