Fitting distributions to data has a long history and many different procedures have been advocated. Although models like normal, log-normal and gamma lead to a wide variety of distribution shapes, they do not provide the degree of generality that is frequently desirable (Hahn & Shapiro, 1967). To formally represent a set of data by an empirical distribution, Johnson (1949) derived a system of curves with the flexibility to cover a wide variety of shapes. Methods available to estimate the parameters of the Johnson distribution are discussed, and a new approach to estimate the four parameters of the Johnson family is proposed. The estimate makes use of both the maximum likelihood procedure and least square theory. The new MLE-Least Square approach is compared with other two commonly used methods. A simulation study shows that the MLE-Least square approach provides better results for SB , S>U and SL families.
George, Florence and Ramachandran, K. M.
"Estimation of Parameters of Johnson’s System of Distributions,"
Journal of Modern Applied Statistical Methods:
2, Article 9.
Available at: http://digitalcommons.wayne.edu/jmasm/vol10/iss2/9