Probability distributions and statistical functions with scipy

TODO

Official documentation:

https://docs.scipy.org/doc/scipy/reference/stats.html



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%matplotlib inline



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import numpy as np
import matplotlib.pyplot as plt
import scipy.stats

Discrete distributions

Binomial distribution

See https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.binom.html#scipy.stats.binom



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n = 20
p = 0.25

dist = scipy.stats.binom(n, p)

Probability mass function



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xmin = 0
xmax = n

x = np.arange(xmin, xmax, 1)
y = dist.pmf(x)

plt.plot(x, y, 'k.');

Cumulative distribution function



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xmin = 0
xmax = n + 1

x = np.arange(xmin, xmax, 1)
xstart = x[:-1]
xend = x[1:]

y = dist.cdf(xstart)

plt.hlines(y, xstart, xend, colors='k')
plt.plot(xstart, y, 'k.');

Poisson distribution

See https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.poisson.html#scipy.stats.poisson



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k = 3

dist = scipy.stats.poisson(k)

Probability mass function



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xmin = 0
xmax = 14 + 1  # TODO

x = np.arange(xmin, xmax, 1)
y = dist.pmf(x)

plt.plot(x, y, 'k.');

Cumulative distribution function



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xmin = 0
xmax = 14 + 2 # TODO

x = np.arange(xmin, xmax, 1)
xstart = x[:-1]
xend = x[1:]

y = dist.cdf(xstart)

plt.hlines(y, xstart, xend, colors='k')
plt.plot(xstart, y, 'k.');

Continuous distributions

Normal distribution

See https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.norm.html#scipy.stats.norm



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mu = 0.
sigma = 1.

dist = scipy.stats.norm(mu, sigma)

Probability density function



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xmin = -5.
xmax = 5.

x = np.arange(xmin, xmax, 0.01)
y = dist.pdf(x)

plt.plot(x, y, 'k-');

Cumulative distribution function



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xmin = -5.
xmax = 5.

x = np.arange(xmin, xmax, 0.01)
y = dist.cdf(x)

plt.plot(x, y, 'k-');