Skip to content

Quesenberry-Miller test for uniformity

Description

Performs the Quesenberry-Miller spacing test for the hypothesis of uniformity on the interval \([a, b]\). The statistic combines squared spacings and products of consecutive spacings.

Hypothesis of Uniformity The null hypothesis is that the sample comes from a uniform distribution on the interval \([a, b]\).

Usage

from pysatl_criterion.statistics.goodness_of_fit import (
    QuesenberryMillerUniformGofStatistic,
)


test_statistic = QuesenberryMillerUniformGofStatistic(a=0, b=1)
statistic_result = test_statistic.execute_statistic([0.12, 0.25, 0.41, 0.53, 0.77, 0.91])
print(statistic_result)

Arguments

a - left boundary of the uniform distribution. Default value is 0.

b - right boundary of the uniform distribution. Default value is 1.

rvs - array-like sample data passed to execute_statistic.

Details

The implementation adds the boundaries \(a\) and \(b\) to the sorted sample, computes spacings \(D_i\), and returns

\[ Q = \sum_i D_i^2 + \sum_i D_iD_{i+1}. \]

Large values indicate stronger deviation from the uniform spacing pattern.

Author(s)

Aleksandr Podmarev, Alexey Mironov

References

Quesenberry, C.P. and Miller, F.L. (1977): Power studies of some tests for uniformity. - Journal of Statistical Computation and Simulation, vol. 5, pp. 169-191.

Examples

from pysatl_criterion.statistics.goodness_of_fit import (
    QuesenberryMillerUniformGofStatistic,
)


test_statistic = QuesenberryMillerUniformGofStatistic(a=0, b=1)
statistic_result = test_statistic.execute_statistic([0.12, 0.25, 0.41, 0.53, 0.77, 0.91])
print(statistic_result)