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Module « scipy.stats »

Fonction anderson - module scipy.stats

Signature de la fonction anderson

def anderson(x, dist='norm') 

Description

help(scipy.stats.anderson)

Anderson-Darling test for data coming from a particular distribution.

The Anderson-Darling test tests the null hypothesis that a sample is
drawn from a population that follows a particular distribution.
For the Anderson-Darling test, the critical values depend on
which distribution is being tested against.  This function works
for normal, exponential, logistic, weibull_min, or Gumbel (Extreme Value
Type I) distributions.

Parameters
----------
x : array_like
    Array of sample data.
dist : {'norm', 'expon', 'logistic', 'gumbel', 'gumbel_l', 'gumbel_r', 'extreme1', 'weibull_min'}, optional
    The type of distribution to test against.  The default is 'norm'.
    The names 'extreme1', 'gumbel_l' and 'gumbel' are synonyms for the
    same distribution.

Returns
-------
result : AndersonResult
    An object with the following attributes:

    statistic : float
        The Anderson-Darling test statistic.
    critical_values : list
        The critical values for this distribution.
    significance_level : list
        The significance levels for the corresponding critical values
        in percents.  The function returns critical values for a
        differing set of significance levels depending on the
        distribution that is being tested against.
    fit_result : `~scipy.stats._result_classes.FitResult`
        An object containing the results of fitting the distribution to
        the data.

See Also
--------
kstest : The Kolmogorov-Smirnov test for goodness-of-fit.

Notes
-----
Critical values provided are for the following significance levels:

normal/exponential
    15%, 10%, 5%, 2.5%, 1%
logistic
    25%, 10%, 5%, 2.5%, 1%, 0.5%
gumbel_l / gumbel_r
    25%, 10%, 5%, 2.5%, 1%
weibull_min
    50%, 25%, 15%, 10%, 5%, 2.5%, 1%, 0.5%

If the returned statistic is larger than these critical values then
for the corresponding significance level, the null hypothesis that
the data come from the chosen distribution can be rejected.
The returned statistic is referred to as 'A2' in the references.

For `weibull_min`, maximum likelihood estimation is known to be
challenging. If the test returns successfully, then the first order
conditions for a maximum likelihood estimate have been verified and
the critical values correspond relatively well to the significance levels,
provided that the sample is sufficiently large (>10 observations [7]).
However, for some data - especially data with no left tail - `anderson`
is likely to result in an error message. In this case, consider
performing a custom goodness of fit test using
`scipy.stats.monte_carlo_test`.

References
----------
.. [1] https://www.itl.nist.gov/div898/handbook/prc/section2/prc213.htm
.. [2] Stephens, M. A. (1974). EDF Statistics for Goodness of Fit and
       Some Comparisons, Journal of the American Statistical Association,
       Vol. 69, pp. 730-737.
.. [3] Stephens, M. A. (1976). Asymptotic Results for Goodness-of-Fit
       Statistics with Unknown Parameters, Annals of Statistics, Vol. 4,
       pp. 357-369.
.. [4] Stephens, M. A. (1977). Goodness of Fit for the Extreme Value
       Distribution, Biometrika, Vol. 64, pp. 583-588.
.. [5] Stephens, M. A. (1977). Goodness of Fit with Special Reference
       to Tests for Exponentiality , Technical Report No. 262,
       Department of Statistics, Stanford University, Stanford, CA.
.. [6] Stephens, M. A. (1979). Tests of Fit for the Logistic Distribution
       Based on the Empirical Distribution Function, Biometrika, Vol. 66,
       pp. 591-595.
.. [7] Richard A. Lockhart and Michael A. Stephens "Estimation and Tests of
       Fit for the Three-Parameter Weibull Distribution"
       Journal of the Royal Statistical Society.Series B(Methodological)
       Vol. 56, No. 3 (1994), pp. 491-500, Table 0.

Examples
--------
Test the null hypothesis that a random sample was drawn from a normal
distribution (with unspecified mean and standard deviation).

>>> import numpy as np
>>> from scipy.stats import anderson
>>> rng = np.random.default_rng()
>>> data = rng.random(size=35)
>>> res = anderson(data)
>>> res.statistic
0.8398018749744764
>>> res.critical_values
array([0.527, 0.6  , 0.719, 0.839, 0.998])
>>> res.significance_level
array([15. , 10. ,  5. ,  2.5,  1. ])

The value of the statistic (barely) exceeds the critical value associated
with a significance level of 2.5%, so the null hypothesis may be rejected
at a significance level of 2.5%, but not at a significance level of 1%.

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