Methodological study demonstrates a maximized likelihood ratio test for non-negative skewed distributions, providing critical values to distinguish between log-normal and Weibull models.
The log-normal and the Weibull are often considered for situations in which a skewed distribution for a non-negative random variable is needed. The ratio of maximized likelihoods provides a good test for selecting one of these. A table of the necesqary critical values is given. The table may also be used for discriminnting between the normal and the type 1 extreme value distributions.
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Dumonceaux et al. (1973) studied this question.
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