Hướng dẫn poisson distribution python scipy

A Poisson discrete random variable.

As an instance of the rv_discrete class, poisson object inherits from it a collection of generic methods [see below for the full list], and completes them with details specific for this particular distribution.

Notes

The probability mass function for poisson is:

\[f[k] = \exp[-\mu] \frac{\mu^k}{k!}\]

for \[k \ge 0\].

poisson takes \[\mu \geq 0\] as shape parameter. When \[\mu = 0\], the pmf method returns 1.0 at quantile \[k = 0\].

The probability mass function above is defined in the “standardized” form. To shift distribution use the loc parameter. Specifically, poisson.pmf[k, mu, loc] is identically equivalent to poisson.pmf[k - loc, mu].

Examples

>>> from scipy.stats import poisson
>>> import matplotlib.pyplot as plt
>>> fig, ax = plt.subplots[1, 1]

Calculate the first four moments:

>>> mu = 0.6
>>> mean, var, skew, kurt = poisson.stats[mu, moments='mvsk']

Display the probability mass function [pmf]:

>>> x = np.arange[poisson.ppf[0.01, mu],
...               poisson.ppf[0.99, mu]]
>>> ax.plot[x, poisson.pmf[x, mu], 'bo', ms=8, label='poisson pmf']
>>> ax.vlines[x, 0, poisson.pmf[x, mu], colors='b', lw=5, alpha=0.5]

Alternatively, the distribution object can be called [as a function] to fix the shape and location. This returns a “frozen” RV object holding the given parameters fixed.

Freeze the distribution and display the frozen pmf:

>>> rv = poisson[mu]
>>> ax.vlines[x, 0, rv.pmf[x], colors='k', linestyles='-', lw=1,
...         label='frozen pmf']
>>> ax.legend[loc='best', frameon=False]
>>> plt.show[]

Check accuracy of cdf and ppf:

>>> prob = poisson.cdf[x, mu]
>>> np.allclose[x, poisson.ppf[prob, mu]]
True

Generate random numbers:

>>> r = poisson.rvs[mu, size=1000]

Methods