Logistic-normal distributions:Some properties and uses

The logistic transformation applied to a d -dimensional normal distribution produces a distribution over the d -dimensional simplex which can sensibly be termed a logistic-normal distribution. Such distributions, implicitly used in a number of recent applications, are here given a formal identity and some useful properties are recorded. A main aim is to extend the area of application from the restricted role as a substitute for the Dirichlet conjugate prior class in the analysis of multinomial and contingency table data to the direct statistical description and analysis of compositional and probabilistic data.