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The characteristic of stereographic circular beta model. (English) Zbl 1458.62063

Summary: Beta is one of the extreme continuous distributions limited to \((0,1)\) with two positive parameters both in real domains. This paper proposed a new model of Beta in the circular domain by using the projection methods. The methods start with a distribution on real line, and then apply a stereographic projection on the circumference of the circle. From the stereographic circular model, we determine the characteristic of the distribution through the trigonometric moment of the function, the mean direction and variance circular from the population of the random variable.

MSC:

62E15 Exact distribution theory in statistics
62E10 Characterization and structure theory of statistical distributions
60E05 Probability distributions: general theory
62R30 Statistics on manifolds
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