Module « scipy.stats »
Signature de la fonction tukeylambda
def tukeylambda(*args, **kwds)
Description
tukeylambda.__doc__
A Tukey-Lamdba continuous random variable.
As an instance of the `rv_continuous` class, `tukeylambda` 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(lam, loc=0, scale=1, size=1, random_state=None)
Random variates.
pdf(x, lam, loc=0, scale=1)
Probability density function.
logpdf(x, lam, loc=0, scale=1)
Log of the probability density function.
cdf(x, lam, loc=0, scale=1)
Cumulative distribution function.
logcdf(x, lam, loc=0, scale=1)
Log of the cumulative distribution function.
sf(x, lam, loc=0, scale=1)
Survival function (also defined as ``1 - cdf``, but `sf` is sometimes more accurate).
logsf(x, lam, loc=0, scale=1)
Log of the survival function.
ppf(q, lam, loc=0, scale=1)
Percent point function (inverse of ``cdf`` --- percentiles).
isf(q, lam, loc=0, scale=1)
Inverse survival function (inverse of ``sf``).
moment(n, lam, loc=0, scale=1)
Non-central moment of order n
stats(lam, loc=0, scale=1, moments='mv')
Mean('m'), variance('v'), skew('s'), and/or kurtosis('k').
entropy(lam, 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=(lam,), 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(lam, loc=0, scale=1)
Median of the distribution.
mean(lam, loc=0, scale=1)
Mean of the distribution.
var(lam, loc=0, scale=1)
Variance of the distribution.
std(lam, loc=0, scale=1)
Standard deviation of the distribution.
interval(alpha, lam, loc=0, scale=1)
Endpoints of the range that contains fraction alpha [0, 1] of the
distribution
Notes
-----
A flexible distribution, able to represent and interpolate between the
following distributions:
- Cauchy (:math:`lambda = -1`)
- logistic (:math:`lambda = 0`)
- approx Normal (:math:`lambda = 0.14`)
- uniform from -1 to 1 (:math:`lambda = 1`)
`tukeylambda` takes a real number :math:`lambda` (denoted ``lam``
in the implementation) as a shape parameter.
The probability density above is defined in the "standardized" form. To shift
and/or scale the distribution use the ``loc`` and ``scale`` parameters.
Specifically, ``tukeylambda.pdf(x, lam, loc, scale)`` is identically
equivalent to ``tukeylambda.pdf(y, lam) / 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.
Examples
--------
>>> from scipy.stats import tukeylambda
>>> import matplotlib.pyplot as plt
>>> fig, ax = plt.subplots(1, 1)
Calculate the first four moments:
>>> lam = 3.13
>>> mean, var, skew, kurt = tukeylambda.stats(lam, moments='mvsk')
Display the probability density function (``pdf``):
>>> x = np.linspace(tukeylambda.ppf(0.01, lam),
... tukeylambda.ppf(0.99, lam), 100)
>>> ax.plot(x, tukeylambda.pdf(x, lam),
... 'r-', lw=5, alpha=0.6, label='tukeylambda 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 = tukeylambda(lam)
>>> ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf')
Check accuracy of ``cdf`` and ``ppf``:
>>> vals = tukeylambda.ppf([0.001, 0.5, 0.999], lam)
>>> np.allclose([0.001, 0.5, 0.999], tukeylambda.cdf(vals, lam))
True
Generate random numbers:
>>> r = tukeylambda.rvs(lam, size=1000)
And compare the histogram:
>>> ax.hist(r, density=True, histtype='stepfilled', alpha=0.2)
>>> ax.legend(loc='best', frameon=False)
>>> plt.show()
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