Academic degreeAn academic degree is a qualification awarded to a student upon successful completion of a course of study in higher education, usually at a college or university. These institutions often offer degrees at various levels, usually divided into undergraduate and postgraduate degrees. The most common undergraduate degree is the bachelor's degree, although some educational systems offer lower level undergraduate degrees such as associate and foundation degrees. Common postgraduate degrees include master's degrees and doctorates.
Laplace distributionIn probability theory and statistics, the Laplace distribution is a continuous probability distribution named after Pierre-Simon Laplace. It is also sometimes called the double exponential distribution, because it can be thought of as two exponential distributions (with an additional location parameter) spliced together along the abscissa, although the term is also sometimes used to refer to the Gumbel distribution.
UnivariateIn mathematics, a univariate object is an expression, equation, function or polynomial involving only one variable. Objects involving more than one variable are multivariate. In some cases the distinction between the univariate and multivariate cases is fundamental; for example, the fundamental theorem of algebra and Euclid's algorithm for polynomials are fundamental properties of univariate polynomials that cannot be generalized to multivariate polynomials.
Almost surelyIn probability theory, an event is said to happen almost surely (sometimes abbreviated as a.s.) if it happens with probability 1 (or Lebesgue measure 1). In other words, the set of possible exceptions may be non-empty, but it has probability 0. The concept is analogous to the concept of "almost everywhere" in measure theory.
Mahalanobis distanceThe Mahalanobis distance is a measure of the distance between a point P and a distribution D, introduced by P. C. Mahalanobis in 1936. Mahalanobis's definition was prompted by the problem of identifying the similarities of skulls based on measurements in 1927. It is a multi-dimensional generalization of the idea of measuring how many standard deviations away P is from the mean of D. This distance is zero for P at the mean of D and grows as P moves away from the mean along each principal component axis.
Hellinger distanceIn probability and statistics, the Hellinger distance (closely related to, although different from, the Bhattacharyya distance) is used to quantify the similarity between two probability distributions. It is a type of f-divergence. The Hellinger distance is defined in terms of the Hellinger integral, which was introduced by Ernst Hellinger in 1909. It is sometimes called the Jeffreys distance. To define the Hellinger distance in terms of measure theory, let and denote two probability measures on a measure space that are absolutely continuous with respect to an auxiliary measure .
