_uniform_order_medians#

normtest.filliben._uniform_order_medians(sample_size)[source]#

This function estimates the uniform order statistic median (\(m_{i}\)) used in the Filliben normality test [1].

Parameters:

sample_sizeint: The sample size. Must be equal or greater than 4;

Returns:

minumpy array: The estimated the uniform order statistic median (\(m_{{i}}\))

See also

fi_test

Notes

The uniform order statistic median is estimated using:

\[\begin{split}m_{i} = \begin{cases}1-0.5^{1/n} & i = 1\\ \frac{i-0.3175}{n+0.365} & i = 2, 3, \ldots , n-1 \\ 0.5^{1/n}& i=n \end{cases}\end{split}\]

where \(n\) is the sample size and \(i\) is the ith observation.

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
>>> uniform_order = filliben._uniform_order_medians(7)
>>> print(uniform_order)
array([0.09427634, 0.22844535, 0.36422267, 0.5       , 0.63577733,
       0.77155465, 0.90572366])