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Keywords = Edgeworth–Sargan distribution

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18 pages, 1182 KiB  
Article
Contributions to Risk Assessment with Edgeworth–Sargan Density Expansions (I): Stability Testing
by Ignacio Mauleón
Mathematics 2022, 10(7), 1074; https://doi.org/10.3390/math10071074 - 27 Mar 2022
Viewed by 1529
Abstract
This paper analytically derives a stability test for the probability distribution of a random variable that follows the Edgeworth–Sargan density, also called Gram–Charlier. The distribution of the test is a weighted sum of Chi-squared densities of increasing degrees of freedom, starting with the [...] Read more.
This paper analytically derives a stability test for the probability distribution of a random variable that follows the Edgeworth–Sargan density, also called Gram–Charlier. The distribution of the test is a weighted sum of Chi-squared densities of increasing degrees of freedom, starting with the standard equivalent Chi-squared under the same conditions. The weights turn out to be linear combinations of the parameters of the distribution and the moments of a Gaussian density, and can be computed exactly. This is a convenient result, since then the probability intervals can be easily calculated from existing Chi-squared distribution tables. The test is applied to assess the weekly solar irradiance data stability for a twelve-year period. It shows that the density is acceptably stable overall, except for some eventual and localised dates. It is also shown that the usual probability intervals implemented in stability testing are larger than those of the equivalent Chi-squared distribution under comparable conditions. This implies that the common upper tail interval values for rejecting the null stability hypothesis are larger. Full article
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