Distributions Gallery: Add LogitNormal #560
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aloctavodia
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Oct 8, 2024
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| The logit-normal distribution, also known as the logistic normal distribution, is a continuous probability distribution of a random variable whose [logit](https://en.wikipedia.org/wiki/Logit) (or log-odds) is normally distributed. Thus, if a random variable $X$ follows a logit-normal distribution, then $ Y = \text{logit}(X) = \log\left(\frac{X}{1-X}\right)$ is normally distributed. It is defined for values of $x$ between 0 and 1. It is characterized by two parameters: $\mu$ and $\sigma$, which are the mean and standard deviation of the logit-transformed variable, respectively, not the original variable. | ||
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| The logit-normal distribution is useful in modeling proportions or ratios. In Bayesian modeling the logit-normal distribution is sometimes used as an alternative to Dirichlet priors for BART (Bayesian Additive Regression Trees), as it allows for a more flexible correlation structure between the predictors. |
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This distribution being an alternative to the Dirichlet only applies to the multivariate version not the unidimensional version.
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