Titlebook: Geometric Modeling in Probability and Statistics; Ovidiu Calin,Constantin Udrişte Textbook 2014 Springer International Publishing Switzerl

Nucleate

Maximum Entropy Distributionsof mean, variance, or any . moments. The solution of these variational problems belongs to the exponential family. However, explicit solutions exist only in a few particular cases. A distinguished role is played by the study of the Maxwell–Boltzmann distribution.

不在灌木丛中

智力高

上腭

Proponent

Contrast Functions on Statistical Modelsative entropy, .-divergence, Hellinger distance, Chernoff information, Jefferey distance, Kagan divergence, and exponential contrast function. The relation with the skewness tensor and .-connection is made. The goal of this chapter is to produce hands-on examples for the theoretical concepts introduced in Chap. ..

critic

Statistical Submanifolds the first and second fundamental forms, curvatures, mean curvatures, and the relations among them..This material adapts the well-known theory of submanifolds to the statistical manifolds framework and consists mainly in the contributions of the authors.

庄严

向前变椭圆

Dystopische Welten in der ,-TrilogieEntropy is a notion taken form Thermodynamics, where it describes the uncertainty in the movement of gas particles. In this chapter the entropy will be considered as a measure of uncertainty of a random variable.

繁重

https://doi.org/10.1007/978-3-322-88458-9The informational energy is a concept inspired from the kinetic energy expressionof Classical Mechanics. From the information theory point of view, the . is a measure of uncertainty or randomness of a probability system, and was introduced and studied for the first time by Onicescu [67, 68] in the mid-1960s.

Dawdle

Explicit ExamplesThis chapter presents a few examples of usual statistical models (normal, lognormal, beta, gamma, Bernoulli, and geometric) for which we provide the Fisher metricexplicitly and, if possible, the geodesicsand .-autoparallelcurves. Some Fisher metrics will involve the use of non-elementary functions, such as the digamma and trigamma functions.