Directional Symmetry (time Series)

	Directional Symmetry (time Series) Directional symmetry may refer to: * Isotropy * Directional statistics Directional statistics (also circular statistics or spherical statistics) is the subdiscipline of statistics that deals with directions (unit vectors in Euclidean space, R''n''), axes ( lines through the origin in R''n'') or rotations in R''n''. M ... * Directional symmetry (time series) {{Disambiguation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
	Isotropy Isotropy is uniformity in all orientations; it is derived . Precise definitions depend on the subject area. Exceptions, or inequalities, are frequently indicated by the prefix ' or ', hence ''anisotropy''. ''Anisotropy'' is also used to describe situations where properties vary systematically, dependent on direction. Isotropic radiation has the same intensity regardless of the direction of measurement, and an isotropic field exerts the same action regardless of how the test particle is oriented. Mathematics Within mathematics, ''isotropy'' has a few different meanings: ; Isotropic manifolds: A manifold is isotropic if the geometry on the manifold is the same regardless of direction. A similar concept is homogeneity. ; Isotropic quadratic form: A quadratic form In mathematics, a quadratic form is a polynomial with terms all of degree two ("form" is another name for a homogeneous polynomial). For example, :4x^2 + 2xy - 3y^2 is a quadratic form in the variables and . Th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
picture info	Directional Statistics Directional statistics (also circular statistics or spherical statistics) is the subdiscipline of statistics that deals with directions (unit vectors in Euclidean space, R''n''), axes ( lines through the origin in R''n'') or rotations in R''n''. More generally, directional statistics deals with observations on compact Riemannian manifolds including the Stiefel manifold. The fact that 0 degrees and 360 degrees are identical angles, so that for example 180 degrees is not a sensible mean of 2 degrees and 358 degrees, provides one illustration that special statistical methods are required for the analysis of some types of data (in this case, angular data). Other examples of data that may be regarded as directional include statistics involving temporal periods (e.g. time of day, week, month, year, etc.), compass directions, dihedral angles in molecules, orientations, rotations and so on. Circular distributions Any probability density function (pdf) \ p(x) on the line can be "wra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]