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Exponentially Modified Gaussian Distribution
In probability theory, an exponentially modified Gaussian distribution (EMG, also known as exGaussian distribution) describes the sum of independent Normal distribution, normal and Exponential distribution, exponential random variables. An exGaussian random variable ''Z'' may be expressed as , where ''X'' and ''Y'' are independent, ''X'' is Gaussian with mean ''μ'' and variance ''σ''2, and ''Y'' is exponential of rate ''λ''. It has a characteristic positive skew from the exponential component. It may also be regarded as a weighted function of a shifted exponential with the weight being a function of the normal distribution. Definition The probability density function (pdf) of the exponentially modified Gaussian distribution is :f(x;\mu,\sigma,\lambda) = \frac \exp \left[\frac (2 \mu + \lambda \sigma^2 - 2 x)\right] \operatorname \left(\frac\right), where erfc is the complementary error function defined as :\begin \operatorname(x) & = 1-\operatorn ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
EMG Distribution PDF
EMG may refer to: Medicine and science * Electromyography, a technique for evaluating and recording electrical activity produced by skeletal muscles * Exponentially modified Gaussian distribution, in probability theory * Ɱ, or emg, a symbol used to transcribe a specific sound in the International Phonetic Alphabet Organisations * East Mediterranean Gas Company, an Egyptian pipeline company * EMG, Inc., an American guitar pickup manufacturer * E.M.G. Hand-Made Gramophones, a British gramophone manufacturer * Escape Media Group, Inc., owner of Grooveshark * Essential Media Group, former name of EQ Media Group * Euclid Media Group, an American media company * Executive Music Group, an American record label Other * Eastern Mewahang language * European Masters Games {{disambiguation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Skewness
In probability theory and statistics, skewness is a measure of the asymmetry of the probability distribution of a real-valued random variable about its mean. The skewness value can be positive, zero, negative, or undefined. For a unimodal distribution (a distribution with a single peak), negative skew commonly indicates that the ''tail'' is on the left side of the distribution, and positive skew indicates that the tail is on the right. In cases where one tail is long but the other tail is fat, skewness does not obey a simple rule. For example, a zero value in skewness means that the tails on both sides of the mean balance out overall; this is the case for a symmetric distribution but can also be true for an asymmetric distribution where one tail is long and thin, and the other is short but fat. Thus, the judgement on the symmetry of a given distribution by using only its skewness is risky; the distribution shape must be taken into account. Introduction Consider the two d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Continuous Distributions
Continuity or continuous may refer to: Mathematics * Continuity (mathematics), the opposing concept to discreteness; common examples include ** Continuous probability distribution or random variable in probability and statistics ** Continuous game, a generalization of games used in game theory ** Law of continuity, a heuristic principle of Gottfried Leibniz * Continuous function, in particular: ** Continuity (topology), a generalization to functions between topological spaces ** Scott continuity, for functions between posets ** Continuity (set theory), for functions between ordinals ** Continuity (category theory), for functors ** Graph continuity, for payoff functions in game theory * Continuity theorem may refer to one of two results: ** Lévy's continuity theorem, on random variables ** Kolmogorov continuity theorem, on stochastic processes * In geometry: ** Parametric continuity, for parametrised curves ** Geometric continuity, a concept primarily applied to the conic section ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Exponential Distribution
In probability theory and statistics, the exponential distribution or negative exponential distribution is the probability distribution of the distance between events in a Poisson point process, i.e., a process in which events occur continuously and independently at a constant average rate; the distance parameter could be any meaningful mono-dimensional measure of the process, such as time between production errors, or length along a roll of fabric in the weaving manufacturing process. It is a particular case of the gamma distribution. It is the continuous analogue of the geometric distribution, and it has the key property of being memoryless. In addition to being used for the analysis of Poisson point processes it is found in various other contexts. The exponential distribution is not the same as the class of exponential families of distributions. This is a large class of probability distributions that includes the exponential distribution as one of its members, but also includ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Normal Distribution
In probability theory and statistics, a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued random variable. The general form of its probability density function is f(x) = \frac e^\,. The parameter is the mean or expectation of the distribution (and also its median and mode), while the parameter \sigma^2 is the variance. The standard deviation of the distribution is (sigma). A random variable with a Gaussian distribution is said to be normally distributed, and is called a normal deviate. Normal distributions are important in statistics and are often used in the natural and social sciences to represent real-valued random variables whose distributions are not known. Their importance is partly due to the central limit theorem. It states that, under some conditions, the average of many samples (observations) of a random variable with finite mean and variance is itself a random variable—whose distribution c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Compound Probability Distribution
In probability and statistics, a compound probability distribution (also known as a mixture distribution or contagious distribution) is the probability distribution that results from assuming that a random variable is distributed according to some parametrized distribution, with (some of) the parameters of that distribution themselves being random variables. If the parameter is a scale parameter, the resulting mixture is also called a scale mixture. The compound distribution ("unconditional distribution") is the result of marginalizing (integrating) over the ''latent'' random variable(s) representing the parameter(s) of the parametrized distribution ("conditional distribution"). Definition A compound probability distribution is the probability distribution that results from assuming that a random variable X is distributed according to some parametrized distribution F with an unknown parameter \theta that is again distributed according to some other distribution G. The resulting ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Skew Normal Distribution
In probability theory and statistics, the skew normal distribution is a continuous probability distribution that generalises the normal distribution to allow for non-zero skewness. Definition Let \phi(x) denote the Normal distribution, standard normal probability density function :\phi(x)=\frace^ with the cumulative distribution function given by :\Phi(x) = \int_^ \phi(t)\ \mathrm dt = \frac \left[ 1 + \operatorname \left(\frac\right)\right], where "erf" is the error function. Then the probability density function (pdf) of the skew-normal distribution with parameter \alpha is given by :f(x) = 2\phi(x)\Phi(\alpha x). \, This distribution was first introduced by O'Hagan and Leonard (1976). Alternative forms to this distribution, with the corresponding quantile function, have been given by Ashour and Abdel-Hamid and by Mudholkar and Hutson. A stochastic process that underpins the distribution was described by Andel, Netuka and Zvara (1984). Both the distribution and its stochas ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stochastic Frontier Analysis
Stochastic frontier analysis (SFA) is a method of economic modeling. It has its starting point in the stochastic production frontier models simultaneously introduced by Aigner, Lovell and Schmidt (1977) and Meeusen and Van den Broeck (1977). The ''production frontier model'' without random component can be written as: y_i = f(x_i ;\beta ) \cdot TE_i where ''yi'' is the observed scalar output of the producer ''i''; ''i=1,..I, xi'' is a vector of ''N'' inputs used by the producer ''i''; \beta is a vector of technology parameters to be estimated; and ''f(xi, β)'' is the production frontier function. ''TEi'' denotes the technical efficiency defined as the ratio of observed output to maximum feasible output. ''TEi = 1'' shows that the ''i-th'' firm obtains the maximum feasible output, while ''TEi < 1'' provides a measure of the shortfall of the observed output from maximum feasible output. A stochastic component that describes random shocks affecting the production process is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cell Cycle
The cell cycle, or cell-division cycle, is the sequential series of events that take place in a cell (biology), cell that causes it to divide into two daughter cells. These events include the growth of the cell, duplication of its DNA (DNA replication) and some of its organelles, and subsequently the partitioning of its cytoplasm, chromosomes and other components into two daughter cells in a process called cell division. In eukaryotic cells (having a cell nucleus) including animal, plant, fungal, and protist cells, the cell cycle is divided into two main stages: interphase, and the M phase that includes mitosis and cytokinesis. During interphase, the cell grows, accumulating nutrients needed for mitosis, and replicates its DNA and some of its organelles. During the M phase, the replicated Chromosome, chromosomes, organelles, and cytoplasm separate into two new daughter cells. To ensure the proper replication of cellular components and division, there are control mechanisms kno ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chromatography
In chemical analysis, chromatography is a laboratory technique for the Separation process, separation of a mixture into its components. The mixture is dissolved in a fluid solvent (gas or liquid) called the ''mobile phase'', which carries it through a system (a column, a capillary tube, a plate, or a sheet) on which a material called the ''stationary phase'' is fixed. Because the different constituents of the mixture tend to have different affinities for the stationary phase and are retained for different lengths of time depending on their interactions with its surface sites, the constituents travel at different apparent velocities in the mobile fluid, causing them to separate. The separation is based on the differential partitioning between the mobile and the stationary phases. Subtle differences in a compound's partition coefficient result in differential retention on the stationary phase and thus affect the separation. Chromatography may be ''preparative'' or ''analytical' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nonparametric Skew
In statistics and probability theory, the nonparametric skew is a statistic occasionally used with random variables that take real values.Arnold BC, Groeneveld RA (1995) Measuring skewness with respect to the mode. The American Statistician 49 (1) 34–38 DOI:10.1080/00031305.1995.10476109Rubio F.J.; Steel M.F.J. (2012) "On the Marshall–Olkin transformation as a skewing mechanism". ''Computational Statistics & Data Analysis''Preprint/ref> It is a measure of the skewness of a random variable's distribution—that is, the distribution's tendency to "lean" to one side or the other of the mean. Its calculation does not require any knowledge of the form of the underlying distribution—hence the name nonparametric. It has some desirable properties: it is zero for any symmetric distribution; it is unaffected by a scale shift; and it reveals either left- or right-skewness equally well. In some statistical samples it has been shown to be less powerfulTabor J (2010) Investi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
