Error contours for Student's t under nonnormality [electronic resource].
- Oak Ridge, Tenn. : Distributed by the Office of Scientific and Technical Information, U.S. Dept. of Energy, 1977.
- Physical Description:
- Pages: 10 : digital, PDF file
- Additional Creators:
- United States. Department of Energy. Office of Scientific and Technical Information
- Geary (Biometrika 34, 1947) has introduced a differential series for the density function of Student's t under nonnormality where the sample population is assumed to have finite moments up to a certain order. If (K/sub r/) and (K'/sub r/) are the cumulants of t under the two regimes (normality and nonnormality), then the discrepancies (K/sub r/--K'/sub r/) can be ordered with respect to sample size, in an ordering in powers of 1/..sqrt..n(n = sample size) of the modified density and cumulative distribution function of t. Geary carried this out to order n/sup -2/. Relative error contours comparing Geary's n/sup -1/ and n/sup -2/ approximations of the upper and lower modified probability levels for ..cap alpha.. = 0.05 and n = 15, 20, and 25 are given for sets of mixtures of normal distributions, and Pearson distributions, in the (..sqrt beta../sub 1/,..beta../sub 2/) plane. Additional comparisons are given comparing these approximations from the results of a Monte Carlo simulation for a wide range of mixtures of normal distributions. 2 figures, 2 tables. (RWR)
- Published through SciTech Connect.
Proceedings of the statistical computing section-American Statistical Association, Chicago, IL, USA, 15 Aug 1977.
Beauchamp, J. J.; Bowman, K. O.; Shenton, L. R.
Union Carbide Corp., Oak Ridge, Tenn. (USA). Computer Sciences Div.
Georgia Univ., Athens (USA)
- Funding Information:
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