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A Maximum Likelihood Estimator for Shape Parameters of S‐Distributions
Author(s) -
Voit Eberhard O.
Publication year - 2000
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 - 10.1002/1521-4036(200008)42:4<471::aid-bimj471>3.0.co;2-z
Subject(s) - mathematics , maximum likelihood , statistics , estimator , maximum likelihood sequence estimation , shape parameter , distribution (mathematics) , estimation theory , mathematical analysis
The S‐distribution is a four‐parameter distribution that is defined in terms of a differential equation, in which the cumulative is represented as the dependent variable:$$f = {{{\rm d} F} \over {{\rm d} X}} = \alpha F^g \cdot (1 - F^k) \qquad F(X_0) = 0.5 \,.$$The article proposes a maximum likelihood estimator for the shape parameters of this distribution.