Abstract
The method of maximum likelihood (MLH), frequently used to study experimental findings in accordance with Weibull statistics, become more biased as the number of samples becomes smaller. Semi-empirical corrective coefficients that have been proposed to attempt to correct the deficiency are unsatisfactory from a theoretical standpoint. It is demonstrated that MLH contains an implicit hypothesis, the validity of which is discussed. Generalization of the basic MLH formulas enables other hypotheses to be chosen. In particular, if the hypothesis chosen is derived from the median rank function, the whole becomes coherent.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>
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