Premium
Comparison and Evaluation of Three Methods of Estimation of the Johnson S b Distribution
Author(s) -
Siekierski Krzysztof
Publication year - 1992
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/bimj.4710340714
Subject(s) - mathematics , skewness , statistics , maximum likelihood , method of moments (probability theory) , percentile , distribution (mathematics) , sample size determination , sample (material) , mathematical analysis , chemistry , chromatography , estimator
Abstract Thre methods of estimating the parameters of the Johnson S 6 distribution were tested by simulation. The maximum likelihood method, the method based on percentiles of a sample and the method based on moments of a transformed random variable were taken into consideration. Many sets of samples were generated differing in sizes and in the actual values of parameters, whereupon the parameters were estimated by the three methods. It was proved that if the sample is small or the skewness of the distribution is considerable, the maximum likelihood estimates can assume preposterous values. The method based on moments is recommended due to its simplicity and to the fact that the estimates, though usually biased, never assume absurd values.