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Normal Distribution
In 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 \mu is the mean or expectation of the distribution (and also its median and mode), while the parameter \sigma is its standard deviation. The variance of the distribution is \sigma^2. 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 converges to a normal dist ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Location Parameter
In geography, location or place are used to denote a region (point, line, or area) on Earth's surface or elsewhere. The term ''location'' generally implies a higher degree of certainty than ''place'', the latter often indicating an entity with an ambiguous boundary, relying more on human or social attributes of place identity and sense of place than on geometry. Types Locality A locality, settlement, or populated place is likely to have a well-defined name but a boundary that is not well defined varies by context. London, for instance, has a legal boundary, but this is unlikely to completely match with general usage. An area within a town, such as Covent Garden in London, also almost always has some ambiguity as to its extent. In geography, location is considered to be more precise than "place". Relative location A relative location, or situation, is described as a displacement from another site. An example is "3 miles northwest of Seattle". Absolute location An absolute lo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Measurement Error
Observational error (or measurement error) is the difference between a measured value of a quantity and its true value.Dodge, Y. (2003) ''The Oxford Dictionary of Statistical Terms'', OUP. In statistics, an error is not necessarily a "mistake". Variability is an inherent part of the results of measurements and of the measurement process. Measurement errors can be divided into two components: ''random'' and ''systematic''. Random errors are errors in measurement that lead to measurable values being inconsistent when repeated measurements of a constant attribute or quantity are taken. Systematic errors are errors that are not determined by chance but are introduced by repeatable processes inherent to the system. Systematic error may also refer to an error with a non-zero mean, the effect of which is not reduced when observations are averaged. Measurement errors can be summarized in terms of accuracy and precision. Measurement error should not be confused with measuremen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Phi (letter)
Phi (; uppercase Φ, lowercase φ or ϕ; grc, ϕεῖ ''pheî'' ; Modern Greek: ''fi'' ) is the 21st letter of the Greek alphabet. In Archaic and Classical Greek (c. 9th century BC to 4th century BC), it represented an aspirated voiceless bilabial plosive (), which was the origin of its usual romanization as . During the later part of Classical Antiquity, in Koine Greek (c. 4th century BC to 4th century AD), its pronunciation shifted to that of a voiceless bilabial fricative (), and by the Byzantine Greek period (c. 4th century AD to 15th century AD) it developed its modern pronunciation as a voiceless labiodental fricative (). The romanization of the Modern Greek phoneme is therefore usually . It may be that phi originated as the letter qoppa (Ϙ, ϙ), and initially represented the sound before shifting to Classical Greek . In traditional Greek numerals, phi has a value of 500 () or 500,000 (). The Cyrillic letter Ef (Ф, ф) descends from phi. As with other Gre ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Standard Normal Deviate
A standard normal deviate is a normally distributed deviate. It is a realization of a standard normal random variable, defined as a random variable with expected value 0 and variance 1.Dodge, Y. (2003) The Oxford Dictionary of Statistical Terms. OUP. Where collections of such random variables are used, there is often an associated (possibly unstated) assumption that members of such collections are statistically independent. Standard normal variables play a major role in theoretical statistics in the description of many types of models, particularly in regression analysis, the analysis of variance and time series analysis. When the term "deviate" is used, rather than "variable", there is a connotation that the value concerned is treated as the no-longer-random outcome of a standard normal random variable. The terminology here is the same as that for random variable and random variate. Standard normal deviates arise in practical statistics in two ways. :*Given a mod ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stephen Stigler
Stephen Mack Stigler (born August 10, 1941) is Ernest DeWitt Burton Distinguished Service Professor at the Department of Statistics of the University of Chicago. He has authored several books on the history of statistics; he is the son of the economist George Stigler. Stigler is also known for Stigler's law of eponymy which states that no scientific discovery is named after its original discoverer (whose first formulation he credits to sociologist Robert K. Merton). Biography Stigler was born in Minneapolis. He received his Ph.D. in 1967 from the University of California, Berkeley. His dissertation was on linear functions of order statistics, and his advisor was Lucien Le Cam. His research has focused on statistical theory of robust estimators and the history of statistics. Stigler taught at University of Wisconsin–Madison until 1979 when he joined the University of Chicago. In 2006, he was elected to membership of the American Philosophical Society, and is a past ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Carl Friedrich Gauss
Johann Carl Friedrich Gauss (; german: Gauß ; la, Carolus Fridericus Gauss; 30 April 177723 February 1855) was a German mathematician and physicist who made significant contributions to many fields in mathematics and science. Sometimes referred to as the ''Princeps mathematicorum'' () and "the greatest mathematician since antiquity", Gauss had an exceptional influence in many fields of mathematics and science, and he is ranked among history's most influential mathematicians. Also available at Retrieved 23 February 2014. Comprehensive biographical article. Biography Early years Johann Carl Friedrich Gauss was born on 30 April 1777 in Brunswick (Braunschweig), in the Duchy of Brunswick-Wolfenbüttel (now part of Lower Saxony, Germany), to poor, working-class parents. His mother was illiterate and never recorded the date of his birth, remembering only that he had been born on a Wednesday, eight days before the Feast of the Ascension (which occurs 39 days after Easter). ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Inflection Point
In differential calculus and differential geometry, an inflection point, point of inflection, flex, or inflection (British English: inflexion) is a point on a smooth plane curve at which the curvature changes sign. In particular, in the case of the graph of a function, it is a point where the function changes from being concave (concave downward) to convex (concave upward), or vice versa. For the graph of a function of differentiability class (''f'', its first derivative ''f, and its second derivative ''f'''', exist and are continuous), the condition ''f'' = 0'' can also be used to find an inflection point since a point of ''f'' = 0'' must be passed to change ''f'''' from a positive value (concave upward) to a negative value (concave downward) or vice versa as ''f'''' is continuous; an inflection point of the curve is where ''f'' = 0'' and changes its sign at the point (from positive to negative or from negative to positive). A point where the second derivative vanishes b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Matrix Normal Distribution
In statistics, the matrix normal distribution or matrix Gaussian distribution is a probability distribution that is a generalization of the multivariate normal distribution to matrix-valued random variables. Definition The probability density function for the random matrix X (''n'' × ''p'') that follows the matrix normal distribution \mathcal_(\mathbf, \mathbf, \mathbf) has the form: : p(\mathbf\mid\mathbf, \mathbf, \mathbf) = \frac where \mathrm denotes trace and M is ''n'' × ''p'', U is ''n'' × ''n'' and V is ''p'' × ''p'', and the density is understood as the probability density function with respect to the standard Lebesgue measure in \mathbb^, i.e.: the measure corresponding to integration with respect to dx_ dx_\dots dx_ dx_\dots dx_\dots dx_. The matrix normal is related to the multivariate normal distribution in the following way: :\mathbf \sim \mathcal_(\mathbf, \mathbf, \mathbf), if and only if :\m ... [...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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Naming
Naming is assigning a name to something. Naming may refer to: * Naming (parliamentary procedure), a procedure in certain parliamentary bodies * Naming ceremony, an event at which an infant is named * Product naming, the discipline of deciding what a product will be called See also * Nomenclature * Name (other) {{disambig ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Logistic Distribution
Logistic may refer to: Mathematics * Logistic function, a sigmoid function used in many fields ** Logistic map, a recurrence relation that sometimes exhibits chaos ** Logistic regression, a statistical model using the logistic function ** Logit, the inverse of the logistic function ** Logistic distribution, the derivative of the logistic function, a continuous probability distribution, used in probability theory and statistics * Mathematical logic, subfield of mathematics exploring the applications of formal logic to mathematics Other uses * Logistics, the management of resources and their distributions ** Logistic engineering, the scientific study of logistics ** Military logistics, the study of logistics at the service of military units and operations See also *Logic (other) Logic is the study of the principles and criteria of valid inference and demonstration Logic may also refer to: *Mathematical logic, a branch of mathematics that grew out of symbolic log ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Student's T-distribution
In probability and statistics, Student's ''t''-distribution (or simply the ''t''-distribution) is any member of a family of continuous probability distributions that arise when estimating the mean of a normally distributed population in situations where the sample size is small and the population's standard deviation is unknown. It was developed by English statistician William Sealy Gosset under the pseudonym "Student". The ''t''-distribution plays a role in a number of widely used statistical analyses, including Student's ''t''-test for assessing the statistical significance of the difference between two sample means, the construction of confidence intervals for the difference between two population means, and in linear regression analysis. Student's ''t''-distribution also arises in the Bayesian analysis of data from a normal family. If we take a sample of n observations from a normal distribution, then the ''t''-distribution with \nu=n-1 degrees of freedom can be d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
