Abstract: The Pearson manifold
(W.P.EldertonandN.L.Johnson,Systemsof Frequency Curves, Cambridge University Press, 1969) draws attention to
the differential equation for a probability functionnamely,Here, we study the Hansmann manifold
(Biometrika 26 (1934), 129-195),for
symmetric distributions. Hansmann noticed a set of recursive results such as for which a base for continued fraction
development. Hansmann derived sets of such equations but had little idea of the
relation to continued fractions. However, Hansmann did discover some new
symmetric distributions. A simple case occurs when the second moment is defined as with Other examples refer to a modified
Poisson distribution and a modified binomial distribution.
Keywords and phrases: central moments, continued fraction, symmetry.
