Quantile estimators of Johnson curve parameters

Fitting human exposure data with the Johnson SB distribution

“…The quantile estimation procedure described by Wheeler (1980) provides estimates for gamma and delta. The sample median is used along with four additional percentile values at 7z and 7z/2, where z is determined as a function of the sample size N by…”

“…An example illustrating the use of the code to fit the S B distribution was not given. Wheeler (1980) presented quantile estimators for gamma and delta, similar to the percentile methods but including the sample median in the estimation process. A specific procedure for estimating the extremes was not included.…”

“…Unlike (Hill et al, 1976) this requires only the first four moments, which are calculated according to the analytic series formulas presented in Flynn (2005). This method of estimation is compared with the percentile methods of Slifker and Shapiro (1980), Mage (1980), and the quantile method of Wheeler (1980). The quantile method produces estimates of gamma and delta, epsilon and lambda are then estimated using equations (4) and (5) with the first two moments calculated by explicit formulas given in the Appendix A.…”

Coastal waters monitoring data: frequency distributions of the principal water quality variables

“…For log-normal distributions, only the δ is important in determining the shape of the function g(), (Wheeler 1980). By setting γ = 0, the transformation function to achieve normality will be:…”

Temporal Changes in the Parameters of Statistical Distribution of Journal Impact Factor

“…There are three well known methods of estimation of the parameters of Johnson S U (as well as SL and SB) distribution: (1) the moments matching method (Draper, 1952), (2) the percentile matching method (Slifker and Shapiro, 1980), and (3) the quantile estimation method (Wheeler, 1980). Another method, namely the MLE-least squares, suggested by George (2007), also performs very well.…”