Approximate Percentage Points for Pearson Distributions

Abstract

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ASAS/IMLMacro for Computing Percentage Points of Pearson Distributions

“…The Pearson percentage points were approximated by Bowman and Shenton (1979) using the rational fraction approximation, i.e., the 19-point formula:…”

“…For a particular percentile of α = 1.0%, 2.5%, 5.0%, 10.0%, 25.0%, 50.0%, 75.0%, 90.0%, 95.0%, 97.5%, or 99.0%, 19 points are chosen from the "A" array to be plugged into the formula. The numerical error was assessed as less than 1.0% of the true value (Bowman and Shenton 1979;Davis and Stephens 1983).…”

Coverage estimation methods for stratified fault-injection

“…We observe that the random variable " that is so defined satisfies the requirement for an upper IHH percent confidence limit given by (5). So, for w I, "…”

“…the t distribution (type VII). Bowman and Shenton [5] introduced a rational fraction approximation for any percentile y (p y ) of a standardized distribution (" I HY " P I) of the Pearson system. This approximation uses a 19-point formula:…”

“…The values for a 99 percent level are presented in Fig. 3 (values for other levels are given in [5]). The approximation is valid for H I R. In the case of a 99 percent level, the numerical error due to the approximation is less than 0.4 percent.…”