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The statistical treatment of such data is in the realm of directional statistics. [ 1 ] 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 ...
Concentration of measure. In mathematics, concentration of measure (about a median) is a principle that is applied in measure theory, probability and combinatorics, and has consequences for other fields such as Banach space theory. Informally, it states that "A random variable that depends in a Lipschitz way on many independent variables (but ...
The sphere has the smallest total mean curvature among all convex solids with a given surface area. The mean curvature is the average of the two principal curvatures, which is constant because the two principal curvatures are constant at all points of the sphere. The sphere has constant mean curvature.
The sphere is an example of a surface. The unit sphere of implicit equation. x 2 + y 2 + z 2 – 1 = 0. may be covered by an atlas of six charts: the plane z = 0 divides the sphere into two half spheres (z > 0 and z < 0), which may both be mapped on the disc x 2 + y 2 < 1 by the projection on the xy plane of coordinates. This provides two ...
Ball (mathematics) In Euclidean space, a ball is the volume bounded by a sphere. In mathematics, a ball is the solid figure bounded by a sphere; it is also called a solid sphere. [1] It may be a closed ball (including the boundary points that constitute the sphere) or an open ball (excluding them). These concepts are defined not only in three ...
In probability theory, a probability density function (PDF), density function, or density of an absolutely continuous random variable, is a function whose value at any given sample (or point) in the sample space (the set of possible values taken by the random variable) can be interpreted as providing a relative likelihood that the value of the ...
Spherical mean. The spherical mean of a function (shown in red) is the average of the values (top, in blue) with on a "sphere" of given radius around a given point (bottom, in blue). In mathematics, the spherical mean of a function around a point is the average of all values of that function on a sphere of given radius centered at that point.
t. e. Mathematical statistics is the application of probability theory, a branch of mathematics, to statistics, as opposed to techniques for collecting statistical data. Specific mathematical techniques which are used for this include mathematical analysis, linear algebra, stochastic analysis, differential equations, and measure theory. [1][2]