Approximating the Distribution of the Maximum Partial Sum of Normal Deviates
AbstractThe largest partial sum of deviations from the mean is a statistic of importance in several areas of application, including hydrology and in testing for a change-point. Approximations to its distribution for the simple normal case have appeared in the literature, based either on functionals of Brownian motion asymptotics or on a methodology developed for crossing problems in sequential analysis. The former approximation is inaccurate except for very large samples, while the latter is based on rather difficult theory. In this paper, we first review some early findings about exact moments and extend them somewhat. We then use moments to fit simple Chi-squared and Beta approximations and show that they work very well.
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Bibliographic InfoPaper provided by Economic and Social Research Institute (ESRI) in its series Papers with number WP102.
Length: 11 pages
Date of creation: Jan 1999
Date of revision:
Change point; Chi-squared; Beta approximations; Cusum; Hydrology;
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