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scipy.stats.

# jarque_bera

scipy.stats.jarque_bera(x, *, axis=None, nan_policy='propagate', keepdims=False)

  Perform the Jarque-Bera goodness of fit test on sample data.

  The Jarque-Bera test tests whether the sample data has the skewness and kurtosis matching a normal distribution.

  Note that this test only works for a large enough number of data samples (>2000) as the test statistic asymptotically has a Chi-squared distribution with 2 degrees of freedom.

  Parameters:
    x array_like

      Observations of a random variable.

    axis int or None, default: None

      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.

    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:
    result SignificanceResult

      An object with the following attributes:

      statisticfloat

        The test statistic.

      pvaluefloat

        The p-value for the hypothesis test.

  See also

  Jarque-Bera goodness of fit test

    Extended example

  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`.

  `jarque_bera` 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 | ⚠️ computes graph | n/a

  See Support for the array API standard for more information.

  References

  [1]

  Jarque, C. and Bera, A. (1980) “Efficient tests for normality, homoscedasticity and serial independence of regression residuals”, 6 Econometric Letters 255-259.

  Examples

      >>> import numpy as np
      >>> from scipy import stats
      >>> rng = np.random.default_rng()
      >>> x = rng.normal(0, 1, 100000)
      >>> jarque_bera_test = stats.jarque_bera(x)
      >>> jarque_bera_test
      Jarque_beraResult(statistic=3.3415184718131554, pvalue=0.18810419594996775)
      >>> jarque_bera_test.statistic
      3.3415184718131554
      >>> jarque_bera_test.pvalue
      0.18810419594996775

  For a more detailed example, see Jarque-Bera goodness of fit test.