def make_hist(p, n, num_points):
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 make_hist(p, n, num_points):
data = [binomial(n, p) for _ in range(num_points)]
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))
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 Dist. vs. Normal Approximation")
plt.show()
def make_hist(p, n, num_points):
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, hi, mu=0, sigma=1):
return normal_cdf(hi, mu, sigma) - normal_cdf(lo, mu, sigma)
def normal_probability_above(lo, mu=0, sigma=1):
return 1 - normal_cdf(lo, mu, sigma)
"""
Graph plot for cumulative density function for normal distribution
"""
from matplotlib import pyplot as plt
from distributions 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) # bottom right
plt.title("Various Normal cdfs")
plt.show()
"""
Graph plot for cumulative density function for normal distribution
"""
from matplotlib import pyplot as plt
from distributions 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) # bottom right
plt.title("Various Normal cdfs")
plt.show()
def normal_probability_between(lo, hi, mu=0, sigma=1):
return normal_cdf(hi, mu, sigma) - normal_cdf(lo, mu, sigma)
def normal_probability_above(lo, mu=0, sigma=1):
return 1 - normal_cdf(lo, mu, sigma)