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Normalization of the Kolmogorov–Smirnov and Shapiro–Wilk tests of normality

100%

Hanusz Z., Tarasińska J.

Biometrical Letters

2015

tom 52

nr 2

85-93

Two very well-known tests for normality, the Kolmogorov-Smirnov and the Shapiro- Wilk tests, are considered. Both of them may be normalized using Johnson’s (1949) SB distribution. In this paper, functions for normalizing constants, dependent on the sample size, are given. These functions eliminate the need to use non-standard statistical tables with normalizing constants, and make it easy to obtain p-values for testing normality.

Intersection topologies with respect to separable GO-spaces and the countable ordinals

75%

Jones M. R.

Fundamenta Mathematicae

1994-1995

tom 146

nr 2

153-158

Given two topologies, $T_1$ and $T_2$, on the same set X, the intersection topology} with respect to $T_1$ and $T_2$ is the topology with basis ${U_1 ∩ U_2 :U_1 ∈ T_1, U_2 ∈ T_2}$. Equivalently, T is the join of $T_1$ and $T_2$ in the lattice of topologies on the set X. Following the work of Reed concerning intersection topologies with respect to the real line and the countable ordinals, Kunen made an extensive investigation of normality, perfectness and $ω_1$-compactness in this class of topologies. We demonstrate that the majority of his results generalise to the intersection topology with respect to an arbitrary separable GO-space and $ω_1$, employing a well-behaved second countable subtopology of the separable GO-space.

Ograniczanie wyników

1 Biometrical Letters

1 Fundamenta Mathematicae

1 Hanusz Z.

1 Jones M. R.

1 Tarasińska J.

1 2015

1 1995

Wyniki wyszukiwania

Normalization of the Kolmogorov–Smirnov and Shapiro–Wilk tests of normality

Intersection topologies with respect to separable GO-spaces and the countable ordinals