Vous êtes un professionnel et vous avez besoin d'une formation ? Coder avec une
Intelligence Artificielle Voir le programme détaillé

Module « scipy.stats »

Fonction truncweibull_min - module scipy.stats

Signature de la fonction truncweibull_min

def truncweibull_min(*args, **kwds) 

Description

help(scipy.stats.truncweibull_min)

A doubly truncated Weibull minimum continuous random variable.

As an instance of the `rv_continuous` class, `truncweibull_min` 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(c, a, b, loc=0, scale=1, size=1, random_state=None)
    Random variates.
pdf(x, c, a, b, loc=0, scale=1)
    Probability density function.
logpdf(x, c, a, b, loc=0, scale=1)
    Log of the probability density function.
cdf(x, c, a, b, loc=0, scale=1)
    Cumulative distribution function.
logcdf(x, c, a, b, loc=0, scale=1)
    Log of the cumulative distribution function.
sf(x, c, a, b, loc=0, scale=1)
    Survival function  (also defined as ``1 - cdf``, but `sf` is sometimes more accurate).
logsf(x, c, a, b, loc=0, scale=1)
    Log of the survival function.
ppf(q, c, a, b, loc=0, scale=1)
    Percent point function (inverse of ``cdf`` --- percentiles).
isf(q, c, a, b, loc=0, scale=1)
    Inverse survival function (inverse of ``sf``).
moment(order, c, a, b, loc=0, scale=1)
    Non-central moment of the specified order.
stats(c, a, b, loc=0, scale=1, moments='mv')
    Mean('m'), variance('v'), skew('s'), and/or kurtosis('k').
entropy(c, a, b, loc=0, scale=1)
    (Differential) entropy of the RV.
fit(data)
    Parameter estimates for generic data.
    See `scipy.stats.rv_continuous.fit <https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.rv_continuous.fit.html#scipy.stats.rv_continuous.fit>`__ for detailed documentation of the
    keyword arguments.
expect(func, args=(c, a, b), loc=0, scale=1, lb=None, ub=None, conditional=False, **kwds)
    Expected value of a function (of one argument) with respect to the distribution.
median(c, a, b, loc=0, scale=1)
    Median of the distribution.
mean(c, a, b, loc=0, scale=1)
    Mean of the distribution.
var(c, a, b, loc=0, scale=1)
    Variance of the distribution.
std(c, a, b, loc=0, scale=1)
    Standard deviation of the distribution.
interval(confidence, c, a, b, loc=0, scale=1)
    Confidence interval with equal areas around the median.

See Also
--------
weibull_min, truncexpon

Notes
-----
The probability density function for `truncweibull_min` is:

.. math::

    f(x, a, b, c) = \frac{c x^{c-1} \exp(-x^c)}{\exp(-a^c) - \exp(-b^c)}

for :math:`a < x <= b`, :math:`0 \le a < b` and :math:`c > 0`.

`truncweibull_min` takes :math:`a`, :math:`b`, and :math:`c` as shape
parameters.

Notice that the truncation values, :math:`a` and :math:`b`, are defined in
standardized form:

.. math::

    a = (u_l - loc)/scale
    b = (u_r - loc)/scale

where :math:`u_l` and :math:`u_r` are the specific left and right
truncation values, respectively. In other words, the support of the
distribution becomes :math:`(a*scale + loc) < x <= (b*scale + loc)` when
:math:`loc` and/or :math:`scale` are provided.

The probability density above is defined in the "standardized" form. To shift
and/or scale the distribution use the ``loc`` and ``scale`` parameters.
Specifically, ``truncweibull_min.pdf(x, c, a, b, loc, scale)`` is identically
equivalent to ``truncweibull_min.pdf(y, c, a, b) / scale`` with
``y = (x - loc) / scale``. Note that shifting the location of a distribution
does not make it a "noncentral" distribution; noncentral generalizations of
some distributions are available in separate classes.

References
----------

.. [1] Rinne, H. "The Weibull Distribution: A Handbook". CRC Press (2009).

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

Calculate the first four moments:

>>> c, a, b = 2.5, 0.25, 1.75
>>> mean, var, skew, kurt = truncweibull_min.stats(c, a, b, moments='mvsk')

Display the probability density function (``pdf``):

>>> x = np.linspace(truncweibull_min.ppf(0.01, c, a, b),
...                 truncweibull_min.ppf(0.99, c, a, b), 100)
>>> ax.plot(x, truncweibull_min.pdf(x, c, a, b),
...        'r-', lw=5, alpha=0.6, label='truncweibull_min pdf')

Alternatively, the distribution object can be called (as a function)
to fix the shape, location and scale parameters. This returns a "frozen"
RV object holding the given parameters fixed.

Freeze the distribution and display the frozen ``pdf``:

>>> rv = truncweibull_min(c, a, b)
>>> ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf')

Check accuracy of ``cdf`` and ``ppf``:

>>> vals = truncweibull_min.ppf([0.001, 0.5, 0.999], c, a, b)
>>> np.allclose([0.001, 0.5, 0.999], truncweibull_min.cdf(vals, c, a, b))
True

Generate random numbers:

>>> r = truncweibull_min.rvs(c, a, b, size=1000)

And compare the histogram:

>>> ax.hist(r, density=True, bins='auto', histtype='stepfilled', alpha=0.2)
>>> ax.set_xlim([x[0], x[-1]])
>>> ax.legend(loc='best', frameon=False)
>>> plt.show()

Vous êtes un professionnel et vous avez besoin d'une formation ? Sensibilisation à
l'Intelligence Artificielle Voir le programme détaillé