scipy.stats.poisson¶
-
scipy.stats.
poisson
= <scipy.stats._discrete_distns.poisson_gen object>[source]¶ 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:poisson.pmf(k) = exp(-mu) * mu**k / k!
for
k >= 0
.poisson
takesmu
as shape parameter.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 topoisson.pmf(k - loc, mu)
.Examples
>>> from scipy.stats import poisson >>> import matplotlib.pyplot as plt >>> fig, ax = plt.subplots(1, 1)
Calculate a few first 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
andppf
:>>> prob = poisson.cdf(x, mu) >>> np.allclose(x, poisson.ppf(prob, mu)) True
Generate random numbers:
>>> r = poisson.rvs(mu, size=1000)
Methods
rvs(mu, loc=0, size=1, random_state=None)
Random variates. pmf(k, mu, loc=0)
Probability mass function. logpmf(k, mu, loc=0)
Log of the probability mass function. cdf(k, mu, loc=0)
Cumulative distribution function. logcdf(k, mu, loc=0)
Log of the cumulative distribution function. sf(k, mu, loc=0)
Survival function (also defined as 1 - cdf
, but sf is sometimes more accurate).logsf(k, mu, loc=0)
Log of the survival function. ppf(q, mu, loc=0)
Percent point function (inverse of cdf
— percentiles).isf(q, mu, loc=0)
Inverse survival function (inverse of sf
).stats(mu, loc=0, moments='mv')
Mean(‘m’), variance(‘v’), skew(‘s’), and/or kurtosis(‘k’). entropy(mu, loc=0)
(Differential) entropy of the RV. expect(func, args=(mu,), loc=0, lb=None, ub=None, conditional=False)
Expected value of a function (of one argument) with respect to the distribution. median(mu, loc=0)
Median of the distribution. mean(mu, loc=0)
Mean of the distribution. var(mu, loc=0)
Variance of the distribution. std(mu, loc=0)
Standard deviation of the distribution. interval(alpha, mu, loc=0)
Endpoints of the range that contains alpha percent of the distribution