An Explicit Solution for S_B, Parameters Using Four Percentile Points

Abstract

The S _B distributions were defined by Johnson (1949). Tables for fitting the four S _B parameters by the method of moments have been provided by Johnson and Kitchen (1971a, b). Bukač (1972) showed that a choice of four symmetrical and equidistant standard normal deviates simplified the solution to allow a direct solution of a quartic equation for the S _B parameters. This paper presents a method of reducing Bukač's quartic equations to a quadratic equation which leads to an explicit solution for the S _B parameters.

KEY WORDS:

• Percentile points
• Curve fittings
• S _B distribution