def normal_cdfs_visualization():
xs = [x / 10.0 for x in range(-50, 50)]
plt.plot(xs, [ds_probability.normal_cdf(x, sigma=1) for x in xs],
'-',
label='mu=0-sigma=1')
plt.plot(xs, [ds_probability.normal_cdf(x, sigma=2) for x in xs],
'--',
label='mu=0-sigma=2')
plt.plot(xs, [ds_probability.normal_cdf(x, sigma=0.5) for x in xs],
':',
label='mu=0-sigma=0.5')
plt.plot(xs, [ds_probability.normal_cdf(x, mu=-1) for x in xs],
'-.',
label='mu=-1-sigma=1')
plt.legend()
plt.title('Various Normals cdfs')
plt.show()
def compare_binomial_dist_to_normal_approx(p, n, nb_points):
data = [ds_probability.binomial(n, p) for _ in range(nb_points)]
#showing actual binomial samples on bar chart
histogram = Counter(data)
plt.bar([x - 0.4 for x in histogram.keys()],
[v / nb_points for v in histogram.values()],
0.8,
color='0.7')
mu_px = p * n
sigma_px = math.sqrt(n * p * (1 - p))
#line chart that shows the normal approximation of the binomial variable
xs = range(min(data), max(data) + 1)
ys = [
ds_probability.normal_cdf(i + 0.5, mu_px, sigma_px) -
ds_probability.normal_cdf(i - 0.5, mu_px, sigma_px) for i in xs
]
plt.plot(xs, ys)
plt.title('Binomial Dist vs Normal approximation')
plt.show()
def normal_probability_between(lo, hi, mu=0, sigma=1):
return ds_probability.normal_cdf(
hi, mu, sigma) - ds_probability.normal_cdf(lo, mu, sigma)
def normal_probability_above(lo, mu=0, sigma=1):
return 1 - ds_probability.normal_cdf(lo)
def normal_probability_below(x, mu=0, sigma=1):
return ds_probability.normal_cdf(x)