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Exponential Family Distributions
Exponential may refer to any of several mathematical topics related to exponentiation, including: * Exponential function, also: **Matrix exponential, the matrix analogue to the above *Exponential decay, decrease at a rate proportional to value * Exponential discounting, a specific form of the discount function, used in the analysis of choice over time *Exponential growth, where the growth rate of a mathematical function is proportional to the function's current value * Exponential map (Riemannian geometry), in Riemannian geometry *Exponential map (Lie theory), in Lie theory * Exponential notation, also known as scientific notation, or standard form *Exponential object, in category theory * Exponential time, in complexity theory *in probability and statistics: **Exponential distribution, a family of continuous probability distributions ** Exponentially modified Gaussian distribution, describes the sum of independent normal and exponential random variables ** Exponential family, a pa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Exponentiation
In mathematics, exponentiation, denoted , is an operation (mathematics), operation involving two numbers: the ''base'', , and the ''exponent'' or ''power'', . When is a positive integer, exponentiation corresponds to repeated multiplication of the base: that is, is the product (mathematics), product of multiplying bases: b^n = \underbrace_.In particular, b^1=b. The exponent is usually shown as a superscript to the right of the base as or in computer code as b^n. This binary operation is often read as " to the power "; it may also be referred to as " raised to the th power", "the th power of ", or, most briefly, " to the ". The above definition of b^n immediately implies several properties, in particular the multiplication rule:There are three common notations for multiplication: x\times y is most commonly used for explicit numbers and at a very elementary level; xy is most common when variable (mathematics), variables are used; x\cdot y is used for emphasizing that one ta ... [...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] |
Exponential Technology
Exponential Technology (originally Renaissance Microsystems) was a vendor of PowerPC microprocessors. The company was founded by George Taylor and Jim Blomgren in 1993. The company's plan was to use BiCMOS technology to produce very fast processors for the Apple Computer market. Logic used 3-level ECL circuits (single-ended for control logic, and differential for datapaths) while RAM structures used CMOS. Rick Shriner was the CEO. Their chips were manufactured by Hitachi. Their product, the Exponential X704, was advertised to run at 533 MHz, but the first version of the device only ran at about 400 MHz, still significantly faster than the 233 MHz PowerPC 604e used in Macintosh computers at the time. This lower frequency along with small level-one caches, produced systems which had good but not stellar performance. This allowed Motorola (Apple's traditional processor vendor), to convince the computer maker that Motorola's future roadmap would produce processors wi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
List Of Exponential Topics
{{Short description, none This is a list of exponential topics, by Wikipedia page. See also list of logarithm topics. * Accelerating change * Mental calculation, Approximating natural exponents (log base e) * Artin–Hasse exponential Talk:Artin–Hasse exponential, * Bacterial growth Talk:Bacterial growth, * Baker–Campbell–Hausdorff formula * Cell growth Talk:Cell growth, * Barometric formula Talk:Barometric formula, * Beer–Lambert law Talk:Beer–Lambert law, * Characterizations of the exponential function Talk:Characterizations of the exponential function, * Catenary Talk:Catenary, * Compound interest Talk:Compound interest, * De Moivre's formula Talk:de Moivre's formula, * Derivative of the exponential map Talk:Derivative of the exponential map, * Doléans-Dade exponential Talk:Doléans-Dade exponential, * Doubling time Talk:Doubling time, * e-folding, ''e''-folding Talk:e-folding, * Elimination half-life Talk:Elimination half-life, * Error expone ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Exponential Type
In complex analysis, a branch of mathematics, a holomorphic function is said to be of exponential type C if its growth is bounded by the exponential function e^ for some real-valued constant C as , z, \to\infty. When a function is bounded in this way, it is then possible to express it as certain kinds of convergent summations over a series of other complex functions, as well as understanding when it is possible to apply techniques such as Borel summation, or, for example, to apply the Mellin transform, or to perform approximations using the Euler–Maclaurin formula. The general case is handled by Nachbin's theorem, which defines the analogous notion of \Psi-type for a general function \Psi(z) as opposed to e^z. Basic idea A function f(z) defined on the complex plane is said to be of exponential type if there exist real-valued constants M and \tau such that :\left, f\left(re^\right)\ \le Me^ in the limit of r\to\infty. Here, the complex variable z was written as z=re^ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Function Type
In computer science and mathematical logic, a function type (or arrow type or exponential) is the type of a variable or parameter to which a function has or can be assigned, or an argument or result type of a higher-order function taking or returning a function. A function type depends on the type of the parameters and the result type of the function (it, or more accurately the unapplied type constructor , is a higher-kinded type). In theoretical settings and programming languages where functions are defined in curried form, such as the simply typed lambda calculus, a function type depends on exactly two types, the domain ''A'' and the range ''B''. Here a function type is often denoted , following mathematical convention, or , based on there existing exactly (exponentially many) set-theoretic functions mappings ''A'' to ''B'' in the category of sets. The class of such maps or functions is called the exponential object. The act of currying makes the function type adjoint to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Exponential Smoothing
Exponential smoothing or exponential moving average (EMA) is a rule of thumb technique for smoothing time series data using the exponential window function. Whereas in the simple moving average the past observations are weighted equally, exponential functions are used to assign exponentially decreasing weights over time. It is an easily learned and easily applied procedure for making some determination based on prior assumptions by the user, such as seasonality. Exponential smoothing is often used for analysis of time-series data. Exponential smoothing is one of many window functions commonly applied to smooth data in signal processing, acting as low-pass filters to remove high-frequency noise. This method is preceded by Poisson's use of recursive exponential window functions in convolutions from the 19th century, as well as Kolmogorov and Zurbenko's use of recursive moving averages from their studies of turbulence in the 1940s. The raw data sequence is often represented by \ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Exponential Family
In probability and statistics, an exponential family is a parametric set of probability distributions of a certain form, specified below. This special form is chosen for mathematical convenience, including the enabling of the user to calculate expectations, covariances using differentiation based on some useful algebraic properties, as well as for generality, as exponential families are in a sense very natural sets of distributions to consider. The term exponential class is sometimes used in place of "exponential family", or the older term Koopman–Darmois family. Sometimes loosely referred to as ''the'' exponential family, this class of distributions is distinct because they all possess a variety of desirable properties, most importantly the existence of a sufficient statistic. The concept of exponential families is credited to E. J. G. Pitman, G. Darmois, and B. O. Koopman in 1935–1936. Exponential families of distributions provide a general framework for selecting ... [...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] |
