_order_statistic#

normtest.ryan_joiner._order_statistic(sample_size, cte_alpha='3/8')[source]#

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

Parameters:
sample_sizeint

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

cte_alphastr, optional

A str with the cte_alpha value that should be adopted (see details in the Notes section). The options are:

  • “0”;

  • “3/8” (default);

  • “1/2”;

Returns:
pinumpy array

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

See also

ryan_joiner

Notes

The cte_alpha (\(\alpha_{cte}\)) parameter corresponds to the values studied by [1], which adopts the following equation to estimate the statistical order:

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

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

Info

cte_alpha=”3/8” is adopted in the implementations of the Ryan-Joiner test in Minitab and Statext software. This option is also cited as an alternative by [2].

References

[1] (1,2)

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

[2]

RYAN, T. A., JOINER, B. L. Normal Probability Plots and Tests for Normality, Technical Report, Statistics Department, The Pennsylvania State University, 1976. Available at www.additive-net.de. Access on: 22 Jul. 2023.

Examples

>>> from normtest import ryan_joiner
>>> size = 10
>>> pi = ryan_joiner._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]