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Module « scipy.stats »

Fonction planck - module scipy.stats

Signature de la fonction planck

def planck(*args, **kwds) 

Description

help(scipy.stats.planck)

A Planck discrete exponential random variable.

As an instance of the `rv_discrete` class, `planck` 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.

Methods
-------
rvs(lambda_, loc=0, size=1, random_state=None)
    Random variates.
pmf(k, lambda_, loc=0)
    Probability mass function.
logpmf(k, lambda_, loc=0)
    Log of the probability mass function.
cdf(k, lambda_, loc=0)
    Cumulative distribution function.
logcdf(k, lambda_, loc=0)
    Log of the cumulative distribution function.
sf(k, lambda_, loc=0)
    Survival function  (also defined as ``1 - cdf``, but `sf` is sometimes more accurate).
logsf(k, lambda_, loc=0)
    Log of the survival function.
ppf(q, lambda_, loc=0)
    Percent point function (inverse of ``cdf`` --- percentiles).
isf(q, lambda_, loc=0)
    Inverse survival function (inverse of ``sf``).
stats(lambda_, loc=0, moments='mv')
    Mean('m'), variance('v'), skew('s'), and/or kurtosis('k').
entropy(lambda_, loc=0)
    (Differential) entropy of the RV.
expect(func, args=(lambda_,), loc=0, lb=None, ub=None, conditional=False)
    Expected value of a function (of one argument) with respect to the distribution.
median(lambda_, loc=0)
    Median of the distribution.
mean(lambda_, loc=0)
    Mean of the distribution.
var(lambda_, loc=0)
    Variance of the distribution.
std(lambda_, loc=0)
    Standard deviation of the distribution.
interval(confidence, lambda_, loc=0)
    Confidence interval with equal areas around the median.

Notes
-----
The probability mass function for `planck` is:

.. math::

    f(k) = (1-\exp(-\lambda)) \exp(-\lambda k)

for :math:`k \ge 0` and :math:`\lambda > 0`.

`planck` takes :math:`\lambda` as shape parameter. The Planck distribution
can be written as a geometric distribution (`geom`) with
:math:`p = 1 - \exp(-\lambda)` shifted by ``loc = -1``.

The probability mass function above is defined in the "standardized" form.
To shift distribution use the ``loc`` parameter.
Specifically, ``planck.pmf(k, lambda_, loc)`` is identically
equivalent to ``planck.pmf(k - loc, lambda_)``.

See Also
--------
geom

Examples
--------
>>> import numpy as np
>>> from scipy.stats import planck
>>> import matplotlib.pyplot as plt
>>> fig, ax = plt.subplots(1, 1)

Calculate the first four moments:

>>> lambda_ = 0.51
>>> mean, var, skew, kurt = planck.stats(lambda_, moments='mvsk')

Display the probability mass function (``pmf``):

>>> x = np.arange(planck.ppf(0.01, lambda_),
...               planck.ppf(0.99, lambda_))
>>> ax.plot(x, planck.pmf(x, lambda_), 'bo', ms=8, label='planck pmf')
>>> ax.vlines(x, 0, planck.pmf(x, lambda_), 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 = planck(lambda_)
>>> 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 = planck.cdf(x, lambda_)
>>> np.allclose(x, planck.ppf(prob, lambda_))
True

Generate random numbers:

>>> r = planck.rvs(lambda_, size=1000)

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