File Name: geometric modeling in probability and statistics .zip
This book covers topics of Informational Geometry, a field which deals with the differential geometric study of the manifold probability density functions.
Documentation Help Center. The geometric distribution is a one-parameter family of curves that models the number of failures before one success in a series of independent trials, where each trial results in either success or failure, and the probability of success in any individual trial is constant. For example, if you toss a coin, the geometric distribution models the number of tails observed before the result is heads. The geometric distribution is discrete, existing only on the nonnegative integers.
The use of geometrical methods in statistics has a long and rich history highlighting many different aspects. These methods are usually based on a Riemannian structure defined on the space of parameters that characterize a family of probabilities. In this paper, we consider the finite dimensional case but the basic ideas can be extended similarly to the infinite-dimensional case. Our aim is to understand exponential families of probabilities on a finite set from an intrinsic geometrical point of view and not through the parameters that characterize some given family of probabilities. For that purpose, we consider a Riemannian geometry defined on the set of positive vectors in a finite-dimensional space. In this space, the probabilities on a finite set comprise a submanifold in which exponential families correspond to geodesic surfaces. Matrix Theory, 29 ,
It seems that you're in Germany. We have a dedicated site for Germany. Authors: Calin , Ovidiu, Udriste , Constantin. This book covers topics of Informational Geometry, a field which deals with the differential geometric study of the manifold probability density functions. This is a field that is increasingly attracting the interest of researchers from many different areas of science, including mathematics, statistics, geometry, computer science, signal processing, physics and neuroscience.
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Buy this book. eBook 50,28 €. price for Spain (gross). Buy eBook. ISBN ; Digitally watermarked, DRM-free; Included format: EPUB, PDF.Coralia O. 23.05.2021 at 00:53
Statistical manifolds are geometric abstractions used to model information, their field of study belonging to Information Geometry, a relatively recent branch of.Fectsilgeno 23.05.2021 at 09:21
Geometric modeling in probability and statistics, by O. Calin and C. Udriste, Spring- er, Cham, Switzerland, , ISBNVincent F. 26.05.2021 at 20:37
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Trials, n, must be a whole number greater than 0.