Search results
Results from the WOW.Com Content Network
Elliptical distributions are defined in terms of the characteristic function of probability theory. A random vector on a Euclidean space has an elliptical distribution if its characteristic function satisfies the following functional equation (for every column-vector )
1 October 2010 () No Proprietary: CLI, GUI: ROOT: ROOT Analysis Framework 6.24.00 (15 April 2021) Yes GNU GPL: GUI: C++ C++, Python SageMath >100 developers worldwide 9.5 (30 January 2022; 2 years ago (10] Yes GNU GPL: CLI & GUI: Python, Cython Python Salstat: Alan J. Salmoni, Mark Livingstone 16 May 2014 () Yes GNU GPL
An arbitrary function φ : R n → C is the characteristic function of some random variable if and only if φ is positive definite, continuous at the origin, and if φ(0) = 1. Khinchine’s criterion. A complex-valued, absolutely continuous function φ, with φ(0) = 1, is a characteristic function if and only if it admits the representation
Further, a foundation can be used to explain statistical paradoxes, provide descriptions of statistical laws, [1] and guide the application of statistics to real-world problems. Different statistical foundations may provide different, contrasting perspectives on the analysis and interpretation of data, and some of these contrasts have been ...
The Rademacher complexity is typically applied on a function class of models that are used for classification, with the goal of measuring their ability to classify points drawn from a probability space under arbitrary labellings.
In statistics, especially in Bayesian statistics, the kernel of a probability density function (pdf) or probability mass function (pmf) is the form of the pdf or pmf in which any factors that are not functions of any of the variables in the domain are omitted. [1] Note that such factors may well be functions of the parameters of the
JAX is a machine learning framework for transforming numerical functions. [2] [3] [4] It is described as bringing together a modified version of autograd (automatic obtaining of the gradient function through differentiation of a function) and OpenXLA's XLA (Accelerated Linear Algebra).
In probability theory and statistics, the Lévy distribution, named after Paul Lévy, is a continuous probability distribution for a non-negative random variable.In spectroscopy, this distribution, with frequency as the dependent variable, is known as a van der Waals profile.