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Is it true that almost every discrete data set containing positive values follow logistic distribution if the data set is log-transformed and standardised(subtracting mean and dividing by standard deviation)?

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    $\begingroup$ Where did you hear such claim? $\endgroup$
    – Tim
    Jun 15 '20 at 7:08
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No, it is not true. One could give unlimited number of counterexamples, e.g. if distribution $X$ non-negative and bimodal, then after log-transformation the two modes would not collapse, while logistic distribution is not bimodal. If $Y$ follows standard log-normal distribution, then taking log of it would make the transformed variable follow normal distribution. Another example, basic way of sampling from logistic distribution is to take standard uniform variable $U$ and then $\log(U) - \log(1-U)$ is a standard logistic distribution, so it is not $\log$ alone.

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