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scipy.stats.

# lmoment

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

  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

  `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`.

  Array API Standard Support

  `lmoment` has experimental support for Python Array API Standard compatible backends in addition to NumPy. Please consider testing these features by setting an environment variable `SCIPY_ARRAY_API=1` and providing CuPy, PyTorch, JAX, or Dask arrays as array arguments. The following combinations of backend and device (or other capability) are supported.

  Library | CPU | GPU
  --- | --- | ---
  NumPy | ✅ | n/a
  CuPy | n/a | ✅
  PyTorch | ✅ | ⛔
  JAX | ⚠️ no JIT | ⚠️ no JIT
  Dask | ⛔ | n/a

  > See Support for the array API standard for more information.

  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()
      >>> 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.