Abstract
This chapter defines the volume elements associated with two dual connections and investigates their relationship. First, we define the Riemannian volume element and show that it is parallel with respect to the Levi–Civita connection. Since the converse is also true, this provides an alternate definition for the volume element used in defining volume elements associated with other connections. In particular, we define and study the volume element associated with an α-connection. The volume elements for the exponential model and mixture model are computed, as examples of distinguished importance in the theory.
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Calin, O., Udrişte, C. (2014). Dual Volume Elements. In: Geometric Modeling in Probability and Statistics. Springer, Cham. https://doi.org/10.1007/978-3-319-07779-6_9
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DOI: https://doi.org/10.1007/978-3-319-07779-6_9
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