A Technical Note on the Logitnormal Distribution
Patrizio Frederic and Frank Lad
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Abstract
We present the technical details of the logitnormal distribution of a variable supported on the open unit-interval. Although this distribution has been used widely in a variety of statistical applications under a transformation, its direct analysis has not been exposited. The density function can be expressed algebraically, and the moments can be computed easily by numerical integration as functions of the parameters of the transformed normal distribution. The family of densities has characteristics different from the Beta family especially near 0 and 1, although some members of each family resemble each other. Limiting members of the family provide examples of distributions with adherent masses at 0 and 1. We also examine the bivariate exchangeable logitnormal distribution.
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