def p_value(beta_hat_j: float, sigma_hat_j: float) -> float:
if beta_hat_j > 0:
# if the coefficient is positive, we need to compute twice the
# probability of seeing an even *larger* value
return 2 * (1 - normal_cdf(beta_hat_j / sigma_hat_j))
else:
# otherwise twice the probability of seeing a *smaller* value
return 2 * normal_cdf(beta_hat_j / sigma_hat_j)
def p_value(beta_hat_j: float, sigma_hat_j: float) -> float:
if beta_hat_j > 0:
# Jeżeli współczynnik ma wartość dodatnią, musimy obliczyć dwukrotność
# prawdopodobieństwa spotkania „większej” wartości.
return 2 * (1 - normal_cdf(beta_hat_j / sigma_hat_j))
else:
# W przeciwnym wypadku obliczamy dwukrotność prawdopodobieństwa spotkania „mniejszej” wartości.
return 2 * normal_cdf(beta_hat_j / sigma_hat_j)
def normal_probability_between(lo: float,
hi: float,
mu: float = 0,
sigma: float = 1) -> float:
return normal_cdf(hi, mu, sigma) - normal_cdf(lo, mu, sigma)
def normal_probability_above(lo: float,
mu: float = 0,
sigma: float = 1) -> float:
return 1 - normal_cdf(lo, mu, sigma)
def binomial_histogram(p: float, n: int, num_points: int) -> None:
"""Picks points from a Binomial(n, p) and plots their histogram"""
data = [binomial(n, p) for _ in range(num_points)]
# use a bar chart to show the actual binomial samples
histogram = Counter(data)
plt.bar([x - 0.4 for x in histogram.keys()],
[v / num_points for v in histogram.values()],
0.8,
color='0.75')
mu = p * n
sigma = math.sqrt(n * p * (1 - p))
# use a line chart to show the normal approximation
xs = range(min(data), max(data) + 1)
ys = [
normal_cdf(i + 0.5, mu, sigma) - normal_cdf(i - 0.5, mu, sigma)
for i in xs
]
plt.plot(xs, ys)
plt.title("Binomial Distribution vs Normal Approximation")
plt.show()
def normal_probability_between(lo: float,
hi: float,
mu: float = 0,
sigma: float = 1) -> float:
"""The probability that a N(mu, sigma) is between lo and hi."""
return normal_cdf(hi, mu, sigma) - normal_cdf(lo, mu, sigma)
def normal_probability_above(lo: float,
mu: float = 0,
sigma: float = 1) -> float:
"""The probability that a N(mu, sigma) is greater than lo."""
return 1 - normal_cdf(lo, mu, sigma)
def normal_probability_above(lo: float,
mu: float = 0,
sigma: float = 1) -> float:
"""N(mu, sigma)를 따르는 정규 분포가 lo보다 클 확률을 나타내준다."""
return 1 - normal_cdf(lo, mu, sigma)
from matplotlib import pyplot as plt
from scratch.probability import normal_cdf
xs = [x / 10.0 for x in range(-50, 50)]
plt.plot(xs, [normal_cdf(x, sigma=1) for x in xs], '-', label='mu=0,sigma=1')
plt.plot(xs, [normal_cdf(x, sigma=2) for x in xs], '-', label='mu=0,sigma=2')
plt.plot(xs, [normal_cdf(x, sigma=0.5) for x in xs],
'-',
label='mu=0,sigma=0.5')
plt.plot(xs, [normal_cdf(x, mu=-1) for x in xs], '-', label='mu=-1,sigma=1')
plt.legend(loc=4)
plt.title("Various Normal cdfs")
plt.show()
def normal_probability_between(lo: float,
hi: float,
mu: float = 0,
sigma: float = 1) -> float:
"""Prawdopodobieństwo tego, że N(mi, sigma) jest pomiędzy lo i hi."""
return normal_cdf(hi, mu, sigma) - normal_cdf(lo, mu, sigma)
def normal_probability_above(lo: float,
mu: float = 0,
sigma: float = 1) -> float:
"""Prawdopodobieństwo tego, że N(mi, sigma) jest większe niż lo."""
return 1 - normal_cdf(lo, mu, sigma)
def normal_probability_between(lo: float,
hi: float,
mu: float = 0,
sigma: float = 1):
"""mu(평균)와 sigma(표준편차)를 따르는 정규분포가 lo와 hi 사이에 있을 확률"""
return normal_cdf(hi, mu, sigma) - normal_cdf(lo, mu, sigma)
def normal_probability_above(lo: float, mu: float = 0, sigma: float = 1):
"""mu(평균)와 sigma(표준편차)를 따르는 정규분포가 lo보다 클 확률"""
return 1 - normal_cdf(lo, mu, sigma)
def normal_probability_between(lo: float,
hi: float,
mu: float = 0,
sigma: float = 1) -> float:
"""The probability that a N(mu, sigma) is between lo and hi."""
return normal_cdf(hi, mu, sigma) - normal_cdf(lo, mu, sigma)
def normal_probability_above(lo: float,
mu: float = 0,
sigma: float = 1) -> float:
"""The probability that a N(mu, sigma) is greater than lo."""
return 1 - normal_cdf(lo, mu, sigma)
def p_value(beta_hat_j: float, sigma_hat_j: float) -> float:
if beta_hat_j > 0:
return 2 * (1 - normal_cdf(beta_hat_j / sigma_hat_j))
else:
return 2 * normal_cdf(beta_hat_j / sigma_hat_j)
