Some statistical properties of a family of continuous univariate distributions. (English) Zbl 0676.62015

Summary: A new two-parameter family of continuous univariate distributions on the interval (-1,1) is introduced, and some properties are given. It is shown that parameters \(\theta\) and \(\nu\) are globally orthogonal in the Fisher information sense and that, to some extent, they have the properties of a location parameter and a precision parameter, respectively. A pivotal statistic is constructed whose distribution is independent of the location parameter. Finally, the connection with ultraspherical functions and Brownian motion is described.


62E15 Exact distribution theory in statistics
62E10 Characterization and structure theory of statistical distributions
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