The non-null limiting distribution of the generalized Baumgartner statistic based on the Fourier series approximation

Ryo Miyazaki and Hidetoshi Murakami ()
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Ryo Miyazaki: Chuo University
Hidetoshi Murakami: Tokyo University of Science

Statistical Papers, 2020, vol. 61, issue 5, No 6, 1893-1909

Abstract: Abstract The non-null limiting distribution of the generalized Baumgartner statistic is approximated by applying the Fourier series approximation. Due to the development of computational power, the Fourier series approximation is readily utilized to approximate its probability density function. The infinite product part for a non-central parameter in the characteristic function is re-formulated by using a formula of the trigonometric function. The non-central parameter of the generalized Baumgartner statistic is formulated by the first moment of the generalized Baumgartner statistic under the alternative hypothesis. The non-central parameter is used to calculate the power of the generalized Baumgartner statistic.

Keywords: Fourier series approximation; Generalized Baumgartner statistic; Non-central weighted $$\chi ^2$$ χ 2 distribution; 62G10 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s00362-018-1012-2

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