Two Moments of the Logitnormal Distribution

We display the first two moment functions of the Logitnormal(μ, σ2) family of distributions, conveniently described in terms of the Normal mean, μ, and the Normal signal-to-noise ratio, μ/σ, parameters that generate the family. Long neglected on account of the numerical integrations required to compute them, awareness of these moment functions should aid the sensible interpretation of logistic regression statistics and the specification of "diffuse" prior distributions in hierarchical models, which can be deceiving. We also use numerical integration to compare the correlation between bivariate Logitnormal variables with the correlation between the bivariate Normal variables from which they are transformed. Keywords: Adherent massesExtendible exchangeabilityHierarchical modelsLogistic regressionNumerical integration S B distributionsMathematics Subject Classification: 60E9960-0462E15 Acknowledgments This research was conducted while Frank Lad was a visiting professor of Statistics at the Institute for Advanced Study, University of Bologna, Department of Statistics. Thanks especially to an unknown referee and to Wes Johnson and Val Johnson for helpful comments.