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Multivariate Stable Distribution
The multivariate stable distribution is a multivariate probability distribution that is a multivariate generalisation of the univariate stable distribution. The multivariate stable distribution defines linear relations between stable distribution marginals. In the same way as for the univariate case, the distribution is defined in terms of its characteristic function (probability theory), characteristic function. The multivariate stable distribution can also be thought as an extension of the multivariate normal distribution. It has parameter, ''α'', which is defined over the range 0 < ''α'' ≤ 2, and where the case ''α'' = 2 is equivalent to the multivariate normal distribution. It has an additional skew parameter that allows for non-symmetric distributions, where the multivariate normal distribution is symmetric. Definition Let be the unit sphere in |
Mv Stable
MV may refer to: Businesses and organizations In transportation * Motor vessel, a motorized ship; used as a prefix for ship names * MV Agusta, a motorcycle manufacturer based in Cascina Costa, Italy * Armenian International Airways (IATA code MV) * Metropolitan-Vickers, an electrical equipment and vehicle manufacturer * Midland Valley Railroad, United States (reporting mark MV) Other organizations * Mieterverband, a Swiss tenant organization * Millennium Volunteers, a former UK government initiative * Minnesota Vikings, an American football team * Miss Venezuela, a beauty pageant * Museum Victoria, an organization which operates three major state-owned museums in Melbourne, Victoria, Australia Places * Martha's Vineyard, an island located south of Cape Cod in Massachusetts * Maldives (ISO 3166-1 alpha-2 country code MV) * Mecklenburg-Vorpommern, a German state at the Baltic Sea * Mountain View, California, Mountain View, a city in California, US People * M. Visvesvaraya, Indian ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Exponent
Exponentiation is a mathematical operation, written as , involving two numbers, the '' base'' and the ''exponent'' or ''power'' , and pronounced as " (raised) to the (power of) ". When is a positive integer, exponentiation corresponds to repeated multiplication of the base: that is, is the product of multiplying bases: b^n = \underbrace_. The exponent is usually shown as a superscript to the right of the base. In that case, is called "''b'' raised to the ''n''th power", "''b'' (raised) to the power of ''n''", "the ''n''th power of ''b''", "''b'' to the ''n''th power", or most briefly as "''b'' to the ''n''th". Starting from the basic fact stated above that, for any positive integer n, b^n is n occurrences of b all multiplied by each other, several other properties of exponentiation directly follow. In particular: \begin b^ & = \underbrace_ \\ ex& = \underbrace_ \times \underbrace_ \\ ex& = b^n \times b^m \end In other words, when multiplying a base raised to one exp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Probability Distribution
In probability theory and statistics, a probability distribution is the mathematical function that gives the probabilities of occurrence of different possible outcomes for an experiment. It is a mathematical description of a random phenomenon in terms of its sample space and the probabilities of events (subsets of the sample space). For instance, if is used to denote the outcome of a coin toss ("the experiment"), then the probability distribution of would take the value 0.5 (1 in 2 or 1/2) for , and 0.5 for (assuming that the coin is fair). Examples of random phenomena include the weather conditions at some future date, the height of a randomly selected person, the fraction of male students in a school, the results of a survey to be conducted, etc. Introduction A probability distribution is a mathematical description of the probabilities of events, subsets of the sample space. The sample space, often denoted by \Omega, is the set of all possible outcomes of a random phe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stable Distribution
In probability theory, a distribution is said to be stable if a linear combination of two independent random variables with this distribution has the same distribution, up to location and scale parameters. A random variable is said to be stable if its distribution is stable. The stable distribution family is also sometimes referred to as the Lévy alpha-stable distribution, after Paul Lévy, the first mathematician to have studied it.B. Mandelbrot, The Pareto–Lévy Law and the Distribution of Income, International Economic Review 1960 https://www.jstor.org/stable/2525289 Of the four parameters defining the family, most attention has been focused on the stability parameter, \alpha (see panel). Stable distributions have 0 < \alpha \leq 2, with the upper bound corresponding to the , and to the [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Characteristic Function (probability Theory)
In probability theory and statistics, the characteristic function of any real-valued random variable completely defines its probability distribution. If a random variable admits a probability density function, then the characteristic function is the Fourier transform of the probability density function. Thus it provides an alternative route to analytical results compared with working directly with probability density functions or cumulative distribution functions. There are particularly simple results for the characteristic functions of distributions defined by the weighted sums of random variables. In addition to univariate distributions, characteristic functions can be defined for vector- or matrix-valued random variables, and can also be extended to more generic cases. The characteristic function always exists when treated as a function of a real-valued argument, unlike the moment-generating function. There are relations between the behavior of the characteristic function of a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Multivariate Normal Distribution
In probability theory and statistics, the multivariate normal distribution, multivariate Gaussian distribution, or joint normal distribution is a generalization of the one-dimensional (univariate) normal distribution to higher dimensions. One definition is that a random vector is said to be ''k''-variate normally distributed if every linear combination of its ''k'' components has a univariate normal distribution. Its importance derives mainly from the multivariate central limit theorem. The multivariate normal distribution is often used to describe, at least approximately, any set of (possibly) correlated real-valued random variables each of which clusters around a mean value. Definitions Notation and parameterization The multivariate normal distribution of a ''k''-dimensional random vector \mathbf = (X_1,\ldots,X_k)^ can be written in the following notation: : \mathbf\ \sim\ \mathcal(\boldsymbol\mu,\, \boldsymbol\Sigma), or to make it explicitly known that ''X'' i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Random Vector
In probability, and statistics, a multivariate random variable or random vector is a list of mathematical variables each of whose value is unknown, either because the value has not yet occurred or because there is imperfect knowledge of its value. The individual variables in a random vector are grouped together because they are all part of a single mathematical system — often they represent different properties of an individual statistical unit. For example, while a given person has a specific age, height and weight, the representation of these features of ''an unspecified person'' from within a group would be a random vector. Normally each element of a random vector is a real number. Random vectors are often used as the underlying implementation of various types of aggregate random variables, e.g. a random matrix, random tree, random sequence, stochastic process, etc. More formally, a multivariate random variable is a column vector \mathbf = (X_1,\dots,X_n)^\mathsf (or its ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Elliptical Distribution
In probability and statistics, an elliptical distribution is any member of a broad family of probability distributions that generalize the multivariate normal distribution. Intuitively, in the simplified two and three dimensional case, the joint distribution forms an ellipse and an ellipsoid, respectively, in iso-density plots. In statistics, the normal distribution is used in ''classical'' multivariate analysis, while elliptical distributions are used in ''generalized'' multivariate analysis, for the study of symmetric distributions with tails that are heavy, like the multivariate t-distribution, or light (in comparison with the normal distribution). Some statistical methods that were originally motivated by the study of the normal distribution have good performance for general elliptical distributions (with finite variance), particularly for spherical distributions (which are defined below). Elliptical distributions are also used in robust statistics to evaluate proposed multivari ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mv Indp
MV may refer to: Businesses and organizations In transportation * Motor vessel, a motorized ship; used as a prefix for ship names * MV Agusta, a motorcycle manufacturer based in Cascina Costa, Italy * Armenian International Airways (IATA code MV) * Metropolitan-Vickers, an electrical equipment and vehicle manufacturer * Midland Valley Railroad, United States (reporting mark MV) Other organizations * Mieterverband, a Swiss tenant organization * Millennium Volunteers, a former UK government initiative * Minnesota Vikings, an American football team * Miss Venezuela, a beauty pageant * Museum Victoria, an organization which operates three major state-owned museums in Melbourne, Victoria, Australia Places * Martha's Vineyard, an island located south of Cape Cod in Massachusetts * Maldives (ISO 3166-1 alpha-2 country code MV) * Mecklenburg-Vorpommern, a German state at the Baltic Sea * Mountain View, a city in California, US People * M. Visvesvaraya, Indian engineer and statesman com ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mv Indp2
MV may refer to: Businesses and organizations In transportation * Motor vessel, a motorized ship; used as a prefix for ship names * MV Agusta, a motorcycle manufacturer based in Cascina Costa, Italy * Armenian International Airways (IATA code MV) * Metropolitan-Vickers, an electrical equipment and vehicle manufacturer * Midland Valley Railroad, United States (reporting mark MV) Other organizations * Mieterverband, a Swiss tenant organization * Millennium Volunteers, a former UK government initiative * Minnesota Vikings, an American football team * Miss Venezuela, a beauty pageant * Museum Victoria, an organization which operates three major state-owned museums in Melbourne, Victoria, Australia Places * Martha's Vineyard, an island located south of Cape Cod in Massachusetts * Maldives (ISO 3166-1 alpha-2 country code MV) * Mecklenburg-Vorpommern, a German state at the Baltic Sea * Mountain View, a city in California, US People * M. Visvesvaraya, Indian engineer and statesman com ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Factor Analysis
Factor analysis is a statistical method used to describe variability among observed, correlated variables in terms of a potentially lower number of unobserved variables called factors. For example, it is possible that variations in six observed variables mainly reflect the variations in two unobserved (underlying) variables. Factor analysis searches for such joint variations in response to unobserved latent variables. The observed variables are modelled as linear combinations of the potential factors plus "error" terms, hence factor analysis can be thought of as a special case of errors-in-variables models. Simply put, the factor loading of a variable quantifies the extent to which the variable is related to a given factor. A common rationale behind factor analytic methods is that the information gained about the interdependencies between observed variables can be used later to reduce the set of variables in a dataset. Factor analysis is commonly used in psychometrics, persona ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Multiuser Detection
Multiuser detection deals with demodulation of the mutually interfering digital streams of information that occur in areas such as wireless communications, high-speed data transmission, DSL, satellite communication, digital television, and magnetic recording. It is also being currently investigated for demodulation in low-power inter-chip and intra-chip communication. Multiuser detection encompasses both receiver technologies devoted to joint detection of all the interfering signals or to single-user receivers which are interested in recovering only one user but are robustified against multiuser interference and not just background noise. Mutual interference is unavoidable in modern spectrally efficient wireless systems: even when using orthogonal multiplexing systems such as TDMA, synchronous CDMA or OFDMA, multiuser interference originates from channel distortion and from out-of-cell interference. In addition, in multi-antenna (MIMO) systems, the digitally modulated streams eman ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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