_order_statistic

normtest.looney_gulledge._order_statistic(sample_size)

This function estimates the normal statistical order (\(p_{i}\)) using an approximation [1].

Parameters:

sample_sizeint

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

Returns:

pinumpy array

The estimated statistical order (\(p_{i}\))

See also

normtest.ryan_joiner._order_statistic

Notes

The statistical order (\(p_{i}\)) is estimated using the following aproximation:

\[p_{i} = \frac{i - \alpha_{cte}}{n - 2 \times \alpha_{cte} + 1}\]

where \(n\) is the sample size, \(i\) is the ith observation and \(\alpha_{cte}\) is a constant equal to 3/8, which is the value proposed by [2].

References

[1]

BLOM, G. Statistical Estimates and Transformed Beta-Variables. New York: John Wiley and Sons, Inc, p. 71-72, 1958.

[2]

LOONEY, S. W.; GULLEDGE, T. R. Use of the Correlation Coefficient with Normal Probability Plots. The American Statistician, v. 39, n. 1, p. 75-79, fev. 1985.

Examples

>>> from normtest import looney_gulledge
>>> size = 10
>>> pi = looney_gulledge._order_statistic(size)
>>> print(pi)
[0.06097561 0.15853659 0.25609756 0.35365854 0.45121951 0.54878049
0.64634146 0.74390244 0.84146341 0.93902439]