_statistic#

normtest.filliben._statistic(x_data, zi)[source]#

This function estimates the statistic of the Filliben normality test [1]

Parameters:

x_datanumpy array: One dimension numpy array with at least 4 observations.
zinumpy array: The statistical order in the standard Normal distribution scale.

Returns:

statistic: The test statistic;

See also

fi_test

Notes

The test statistic (\(F_{p}\)) is estimated through the correlation between the ordered data and the Normal statistical order:

\[F_p = \frac{\sum_{i=1}^n \left(x_i - \overline{x}\right) \left(z_i - \overline{z}\right)}{\sqrt{\sum_{i=1}^n \left( x_i - \overline{x}\right)^2 \sum_{i=1}^n \left( z_i - \overline{z}\right)^2}}\]

where \(z_{i}\) values are the z-score values of the corresponding experimental data (\(x_{{i}}\)) value, and \(n\) is the sample size.

The correlation is estimated using scipy.stats.pearsonr().

References

[1]

FILLIBEN, J. J. The Probability Plot Correlation Coefficient Test for Normality. Technometrics, v. 17, n. 1, p. 111-117, 1975.

Examples

>>> from normtest import filliben
>>> import numpy as np
>>> x_data = np.array([6, 1, -4, 8, -2, 5, 0])
>>> uniform_order = filliben._uniform_order_medians(x_data.size)
>>> normal_order = filliben._normal_order_medians(uniform_order)
>>> x_data = np.sort(x_data)
>>> statistic = filliben._statistic(x_data, normal_order)
>>> print(statistic)
0.9854095718708367