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Module « scipy.stats »

Fonction lmoment - module scipy.stats

Signature de la fonction lmoment

def lmoment(sample, order=None, *, axis=0, sorted=False, standardize=True, nan_policy='propagate', keepdims=False) 

Description

help(scipy.stats.lmoment)

    


Compute L-moments of a sample from a continuous distribution

The L-moments of a probability distribution are summary statistics with
uses similar to those of conventional moments, but they are defined in
terms of the expected values of order statistics.
Sample L-moments are defined analogously to population L-moments, and
they can serve as estimators of population L-moments. They tend to be less
sensitive to extreme observations than conventional moments.

Parameters
----------
sample : array_like
    The real-valued sample whose L-moments are desired.
order : array_like, optional
    The (positive integer) orders of the desired L-moments.
    Must be a scalar or non-empty 1D array. Default is [1, 2, 3, 4].
axis : int or None, default: 0
    If an int, the axis of the input along which to compute the statistic.
    The statistic of each axis-slice (e.g. row) of the input will appear in a
    corresponding element of the output.
    If ``None``, the input will be raveled before computing the statistic.
sorted : bool, default=False
    Whether `sample` is already sorted in increasing order along `axis`.
    If False (default), `sample` will be sorted.
standardize : bool, default=True
    Whether to return L-moment ratios for orders 3 and higher.
    L-moment ratios are analogous to standardized conventional
    moments: they are the non-standardized L-moments divided
    by the L-moment of order 2.
nan_policy : {'propagate', 'omit', 'raise'}
    Defines how to handle input NaNs.
    
    - ``propagate``: if a NaN is present in the axis slice (e.g. row) along
      which the  statistic is computed, the corresponding entry of the output
      will be NaN.
    - ``omit``: NaNs will be omitted when performing the calculation.
      If insufficient data remains in the axis slice along which the
      statistic is computed, the corresponding entry of the output will be
      NaN.
    - ``raise``: if a NaN is present, a ``ValueError`` will be raised.
keepdims : bool, default: False
    If this is set to True, the axes which are reduced are left
    in the result as dimensions with size one. With this option,
    the result will broadcast correctly against the input array.

Returns
-------
lmoments : ndarray
    The sample L-moments of order `order`.

See Also
--------

:func:`moment`
    ..

Notes
-----

Beginning in SciPy 1.9, ``np.matrix`` inputs (not recommended for new
code) are converted to ``np.ndarray`` before the calculation is performed. In
this case, the output will be a scalar or ``np.ndarray`` of appropriate shape
rather than a 2D ``np.matrix``. Similarly, while masked elements of masked
arrays are ignored, the output will be a scalar or ``np.ndarray`` rather than a
masked array with ``mask=False``.

References
----------
.. [1] D. Bilkova. "L-Moments and TL-Moments as an Alternative Tool of
       Statistical Data Analysis". Journal of Applied Mathematics and
       Physics. 2014. :doi:`10.4236/jamp.2014.210104`
.. [2] J. R. M. Hosking. "L-Moments: Analysis and Estimation of Distributions
       Using Linear Combinations of Order Statistics". Journal of the Royal
       Statistical Society. 1990. :doi:`10.1111/j.2517-6161.1990.tb01775.x`
.. [3] "L-moment". *Wikipedia*. https://en.wikipedia.org/wiki/L-moment.

Examples
--------
>>> import numpy as np
>>> from scipy import stats
>>> rng = np.random.default_rng(328458568356392)
>>> sample = rng.exponential(size=100000)
>>> stats.lmoment(sample)
array([1.00124272, 0.50111437, 0.3340092 , 0.16755338])

Note that the first four standardized population L-moments of the standard
exponential distribution are 1, 1/2, 1/3, and 1/6; the sample L-moments
provide reasonable estimates.

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