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Approximating the Distribution of the Maximum Partial Sum of Normal Deviates

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Author Info

  • Denis Conniffe

    (Economic and Social Research Institute (ESRI))

  • John E. Spencer

    (The Queen's University of Belfast)

Abstract

The 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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File URL: http://www.esri.ie/UserFiles/publications/20071004161501/WP102.pdf
File Function: First version, 1999
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Bibliographic Info

Paper provided by Economic and Social Research Institute (ESRI) in its series Papers with number WP102.

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Length: 11 pages
Date of creation: Jan 1999
Date of revision:
Handle: RePEc:esr:wpaper:wp102

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Related research

Keywords: Change point; Chi-squared; Beta approximations; Cusum; Hydrology;

References

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  1. Andrews, Donald W K, 1993. "Tests for Parameter Instability and Structural Change with Unknown Change Point," Econometrica, Econometric Society, vol. 61(4), pages 821-56, July.
  2. Ploberger, Werner & Kramer, Walter, 1992. "The CUSUM Test with OLS Residuals," Econometrica, Econometric Society, vol. 60(2), pages 271-85, March.
  3. B. Mandelbrot, 1972. "Statistical Methodology For Nonperiodic Cycles: From The Covariance To Rs Analysis," NBER Chapters, in: Annals of Economic and Social Measurement, Volume 1, number 3, pages 259-290 National Bureau of Economic Research, Inc.
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Cited by:
  1. Denis Conniffe & John E. Spencer, 1999. "Approximating the Distribution of the R/s Statistic," Papers WP104, Economic and Social Research Institute (ESRI).
  2. Conniffe, Denis & Kelly, Robert, 2011. "Structural Breaks - An Instrumental Variable Approach," Research Technical Papers 4/RT/11, Central Bank of Ireland.

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