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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.

MSC:
 6.2e+16 Exact distribution theory in statistics 6.2e+11 Characterization and structure theory of statistical distributions
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