# logistic distribution

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)?

• Where did you hear such claim?
– Tim
Jun 15 '20 at 7:08

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.