import math
import matplotlib.pyplot as plt
import numpy as np
def odds(p):
"""성공확률 / 실패확률"""
return p / (1 - p)
def log_odds(p):
"""odds에 log를 취한 값"""
return math.log(odds(p))
def sigmoid(t):
"""logistic:
log_odds(odds에 log를 취한 값)을 알고 있을 때, 성공 확률 p를 계산"""
return 1 / (1 + math.exp(-t))
p = 0.8
print(f'p = {p}, odds(p) = {odds(p)}, log_odds(p) = {log_odds(p)}')
p = 0.8, odds(p) = 4.000000000000001, log_odds(p) = 1.3862943611198908
t = 1.386294361198908
probability = sigmoid(t)
print(f'probability={probability}')
probability=0.8000000000126428
# odds 함수 그래프
xs = np.linspace(0.01, 0.99, 100)
# print(xs)
ys = [odds(x) for x in xs]
plt.plot(xs, ys)
plt.ylim(bottom=0.0, top=10.0)
plt.title('odds')
for i in range(1, 5):
plt.axhline(y=2 * i, color='0.5')
plt.axvline(x=0.2 * i, color='0.5')
plt.title('odds')
plt.show()
# log_odds 그래프
ys = [log_odds(x) for x in xs]
plt.plot(xs, ys)
plt.axhline(color='0.5')
plt.axvline(color='0.5')
plt.axvline(x=0.5, color='0.5')
plt.axvline(x=1, color='0.5')
plt.title('log_odds')
plt.show()
# logistic ( sigmoid) 함수 그래프
xs = np.linspace(-10, 10, 100)
ys = [sigmoid(x) for x in xs]
plt.plot(xs, ys)
plt.axvline(color='0.5')
plt.axhline( color='0.5')
plt.axhline(y=0.5, color='0.5')
plt.axhline(y=1.0, color='0.5')
plt.title('Logistic(sigmoid)함수')
plt.show()
