Normal approximation to the chi-square and non-central <i>F</i> probability functions

“…reporting values of b l and b 2 to five significant figures for several significance levels,p. Severo and Zelen (1960) noted the following approximation of equation (10): 24) and we will find it convenient to set H = ch c ' In an analogous fashion we can approximate equation (12) by h~~(c/v)h~ (25) and let H' = ch~. We then define either K = H or K = H', depending on which provides the best X~approximation by the equation…”

Section: (16)mentioning

confidence: 99%

“…The Severo-Zelen approximation Severo and Zelen (1960) considered the approximation to the normal probability function P(x+h) as given by the Taylor expansion about x: ) and the following terms of the Gram-Charlier Type A series for the Wilson-Hilferty normal approximation:…”

Section: Introductionmentioning

confidence: 99%

Approximations for the Percentage Points of the Chi-Squared Distribution

Zar¹

1978

Applied Statistics

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Summary Sixteen formulae for approximating percentage points of X2 were examined at each of 15 significance levels. The formula of Wilson and Hilferty is fairly good at most significance levels, but the best approximations without resorting to computer capability are obtained using the Cornish‐Fisher expansion or an empirically derived improvement of the Severo‐Zelen modification of the Wilson‐Hilferty formula.

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“…For the cumulative chi-square distribution no approximation for use on a hand calculator is found. For its inverse, many approximations are suggested (Merrington, 1951;Aroian, 1943;Severo-Zelen, 1960;Zar, 1978). But their formulae are too complicated or they involve the use of the percentage points of the standard normal distribution, so they are inconvenient for use on a hand calculator.…”

Section: Introductionmentioning

confidence: 99%