Diskussionspapiere, Friedrich-Alexander-Universität Erlangen-Nürnberg, Lehrstuhl für Statistik und Ökonometrie 89/2010
J.M. Keynes (1911) shows how distributions look like for which the arithmetic, the geometric and the harmonic mean are most probable values. We propose a general class of distributions for which the quasi-arithmetic means are ML-estimators such that these distributions can be transformed into an normal or a truncated normal distribution. As special cases we get for example the generalized logarithmic distributions introduced by Chen (1995).
ML-estimator quasi-arithmetic mean exponential family generalized logarithmic distribution inverse transformed normal distribution