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:\[f(k) = \exp(-\mu) \frac{\mu^k}{k!}\]for \(k \ge 0\).
poisson
takes \(\mu \geq 0\) as shape parameter. When \(\mu = 0\), thepmf
method returns1.0
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 topoisson.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
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(confidence, mu, loc=0)
Confidence interval with equal areas around the median.