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A metric on a set X is a function (called the distance function or simply distance) d : X × X → R + (where R + is the set of non-negative real numbers). For all x, y, z in X, this function is required to satisfy the following conditions: d(x, y) ≥ 0 (non-negativity) d(x, y) = 0 if and only if x = y (identity of indiscernibles.
In statistics, a location parameter of a probability distribution is a scalar- or vector-valued parameter, which determines the "location" or shift of the distribution.In the literature of location parameter estimation, the probability distributions with such parameter are found to be formally defined in one of the following equivalent ways:
An example of a one-sample location test would be a comparison of the location parameter for the blood pressure distribution of a population to a given reference value. In a one-sided test, it is stated before the analysis is carried out that it is only of interest if the location parameter is either larger than, or smaller than the given ...
Objects are detected out to a pre-determined maximum detection distance w. Not all objects within w will be detected, but a fundamental assumption is that all objects at zero distance (i.e., on the line itself) are detected. Overall detection probability is thus expected to be 1 on the line, and to decrease with increasing distance from the line.
The geometric-distance matrix is a different type of distance matrix that is based on the graph-theoretical distance matrix of a molecule to represent and graph the 3-D molecule structure. [8] The geometric-distance matrix of a molecular structure G is a real symmetric n x n matrix defined in the same way as a 2-D matrix.
Given a distance matrix with the distances between each pair of objects in a set, and a chosen number of dimensions, N, an MDS algorithm places each object into N-dimensional space (a lower-dimensional representation) such that the between-object distances are preserved as well as possible.
Total variation distance is half the absolute area between the two curves: Half the shaded area above. In probability theory, the total variation distance is a statistical distance between probability distributions, and is sometimes called the statistical distance, statistical difference or variational distance.
The algorithm is often presented as assigning objects to the nearest cluster by distance. Using a different distance function other than (squared) Euclidean distance may prevent the algorithm from converging. Various modifications of k-means such as spherical k-means and k-medoids have been proposed to allow using other distance measures ...