Comparisons of the percentage points of distributions with the same first four moments, chosen from eight different systems of frequency curves

Abstract

Probability integrals and percentage points of univariate distributions from up to eight different families, having common first four moments are compared. Among interesting observations is the remarkable consistency in the standardized upper and lower 5% points over considerable regions of the √β₁, β₂ plane; also the closeness of agreement between the log-normal and non-central t distributions and the Pearson Type VI and Type IV curves respectively.

Keywords:

• Pearson
• Johnson
• Burr
• Weibull
• lognormal
• noncentral x²
• log-x²
• noncentral t
• skewness
• kurtosis