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On a new transformation to normality. (English) Zbl 0564.62012
A Gaussian approximation to the distribution of the non-negative random variable Y is developed using the E. B. Wilson and M. M. Hilferty [Proc. Natl. Acad. Sci. USA 17, 684-688 (1931; Zbl 0004.36005)] approach. This approximation uses the symmetrizing transformation \(((Y+b)/k_ 1)^ h\) where \(k_ 1\) is the first moment of Y and h and b are determined from the first three cumulants of Y.
The approximation is illustrated in the case in which Y is a non-central chi-square, where numerical evaluations indicate that the new transformation is an improvement over existing ones especially for small values of \(k_ 1\).

MSC:
62E20 Asymptotic distribution theory in statistics
62E99 Statistical distribution theory
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References:
[1] Abdel-Aty S.H., Biometrika 41 pp 538– (1954)
[2] Fisher R.A., JRSS, Ser A 85 pp 87– (1922)
[3] Jensen D.R., JASA 67 pp 898– (1972)
[4] Johnson N.L., Continuoiis Univariate Distributions-1
[5] Moschopoulos P.G., Comm. Stat. 12 (1983)
[6] Mudholkar G.S., JASA 76 (374) pp 479– (1981) · doi:10.1080/01621459.1981.10477673
[7] Patnaik P.B., Biometrika 36 (374) pp 202– (1949)
[8] Pearson E.S., Biometrika 46 (374) pp 364– (1959) · Zbl 0101.35806 · doi:10.2307/2333533
[9] Wilson E.P., Proceedings of the National Academy of Science 17 (374) pp 684– (1931) · Zbl 0004.36005 · doi:10.1073/pnas.17.12.684
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