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Regular Parametric Model
In statistics, a parametric model or parametric family or finite-dimensional model is a particular class of statistical models. Specifically, a parametric model is a family of probability distributions that has a finite number of parameters. Definition A statistical model is a collection of probability distributions on some sample space. We assume that the collection, , is indexed by some set . The set is called the parameter set or, more commonly, the parameter space. For each , let denote the corresponding member of the collection; so is a cumulative distribution function. Then a statistical model can be written as : \mathcal = \big\. The model is a parametric model if for some positive integer . When the model consists of absolutely continuous distributions, it is often specified in terms of corresponding probability density functions: : \mathcal = \big\. Examples * The Poisson family of distributions is parametrized by a single number : : \mat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistics
Statistics (from German: '' Statistik'', "description of a state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a scientific, industrial, or social problem, it is conventional to begin with a statistical population or a statistical model to be studied. Populations can be diverse groups of people or objects such as "all people living in a country" or "every atom composing a crystal". Statistics deals with every aspect of data, including the planning of data collection in terms of the design of surveys and experiments.Dodge, Y. (2006) ''The Oxford Dictionary of Statistical Terms'', Oxford University Press. When census data cannot be collected, statisticians collect data by developing specific experiment designs and survey samples. Representative sampling assures that inferences and conclusions can reasonably extend from the sample to the population as a whole. An ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Parametric Statistics
Parametric statistics is a branch of statistics which assumes that sample data comes from a population that can be adequately modeled by a probability distribution that has a fixed set of parameters. Conversely a non-parametric model does not assume an explicit (finite-parametric) mathematical form for the distribution when modeling the data. However, it may make some assumptions about that distribution, such as continuity or symmetry. Most well-known statistical methods are parametric. Regarding nonparametric (and semiparametric) models, Sir David Cox has said, "These typically involve fewer assumptions of structure and distributional form but usually contain strong assumptions about independencies". Example The normal family of distributions all have the same general shape and are ''parameterized'' by mean and standard deviation. That means that if the mean and standard deviation are known and if the distribution is normal, the probability of any future observation lying in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cambridge University Press
Cambridge University Press is the university press of the University of Cambridge. Granted letters patent by King Henry VIII in 1534, it is the oldest university press in the world. It is also the King's Printer. Cambridge University Press is a department of the University of Cambridge and is both an academic and educational publisher. It became part of Cambridge University Press & Assessment, following a merger with Cambridge Assessment in 2021. With a global sales presence, publishing hubs, and offices in more than 40 countries, it publishes over 50,000 titles by authors from over 100 countries. Its publishing includes more than 380 academic journals, monographs, reference works, school and university textbooks, and English language teaching and learning publications. It also publishes Bibles, runs a bookshop in Cambridge, sells through Amazon, and has a conference venues business in Cambridge at the Pitt Building and the Sir Geoffrey Cass Sports and Social Centre. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Prentice-Hall
Prentice Hall was an American major educational publisher owned by Savvas Learning Company. Prentice Hall publishes print and digital content for the 6–12 and higher-education market, and distributes its technical titles through the Safari Books Online e-reference service. History On October 13, 1913, law professor Charles Gerstenberg and his student Richard Ettinger founded Prentice Hall. Gerstenberg and Ettinger took their mothers' maiden names, Prentice and Hall, to name their new company. Prentice Hall became known as a publisher of trade books by authors such as Norman Vincent Peale; elementary, secondary, and college textbooks; loose-leaf information services; and professional books. Prentice Hall acquired the training provider Deltak in 1979. Prentice Hall was acquired by Gulf+Western in 1984, and became part of that company's publishing division Simon & Schuster. S&S sold several Prentice Hall subsidiaries: Deltak and Resource Systems were sold to National Educatio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistical Model Specification
In statistics, model specification is part of the process of building a statistical model: specification consists of selecting an appropriate functional form for the model and choosing which variables to include. For example, given personal income y together with years of schooling s and on-the-job experience x, we might specify a functional relationship y = f(s,x) as follows: : \ln y = \ln y_0 + \rho s + \beta_1 x + \beta_2 x^2 + \varepsilon where \varepsilon is the unexplained error term that is supposed to comprise independent and identically distributed Gaussian variables. The statistician Sir David Cox has said, "How hetranslation from subject-matter problem to statistical model is done is often the most critical part of an analysis". Specification error and bias Specification error occurs when the functional form or the choice of independent variables poorly represent relevant aspects of the true data-generating process. In particular, bias (the expected value of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistical Model
A statistical model is a mathematical model that embodies a set of statistical assumptions concerning the generation of sample data (and similar data from a larger population). A statistical model represents, often in considerably idealized form, the data-generating process. A statistical model is usually specified as a mathematical relationship between one or more random variables and other non-random variables. As such, a statistical model is "a formal representation of a theory" ( Herman Adèr quoting Kenneth Bollen). All statistical hypothesis tests and all statistical estimators are derived via statistical models. More generally, statistical models are part of the foundation of statistical inference. Introduction Informally, a statistical model can be thought of as a statistical assumption (or set of statistical assumptions) with a certain property: that the assumption allows us to calculate the probability of any event. As an example, consider a pair of ordinary six ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Parametric Family
In mathematics and its applications, a parametric family or a parameterized family is a family of objects (a set of related objects) whose differences depend only on the chosen values for a set of parameters. Common examples are parametrized (families of) functions, probability distributions, curves, shapes, etc. In probability and its applications For example, the probability density function of a random variable may depend on a parameter . In that case, the function may be denoted f_X( \cdot \, ; \theta) to indicate the dependence on the parameter . is not a formal argument of the function as it is considered to be fixed. However, each different value of the parameter gives a different probability density function. Then the ''parametric family'' of densities is the set of functions \ , where denotes the parameter space, the set of all possible values that the parameter can take. As an example, the normal distribution is a family of similarly-shaped distributions par ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Continuum (set Theory)
In the mathematical field of set theory, the continuum means the real numbers, or the corresponding (infinite) cardinal number, denoted by \mathfrak. Georg Cantor proved that the cardinality \mathfrak is larger than the smallest infinity, namely, \aleph_0. He also proved that \mathfrak is equal to 2^\!, the cardinality of the power set of the natural numbers. The ''cardinality of the continuum'' is the size of the set of real numbers. The continuum hypothesis is sometimes stated by saying that no cardinality lies between that of the continuum and that of the natural numbers, \aleph_0, or alternatively, that \mathfrak = \aleph_1. Linear continuum According to Raymond Wilder (1965), there are four axioms that make a set ''C'' and the relation < into a linear continuum: * ''C'' is simply ordered with respect to <. * If [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cardinality
In mathematics, the cardinality of a set is a measure of the number of elements of the set. For example, the set A = \ contains 3 elements, and therefore A has a cardinality of 3. Beginning in the late 19th century, this concept was generalized to infinite sets, which allows one to distinguish between different types of infinity, and to perform arithmetic on them. There are two approaches to cardinality: one which compares sets directly using bijections and injections, and another which uses cardinal numbers. The cardinality of a set is also called its size, when no confusion with other notions of size is possible. The cardinality of a set A is usually denoted , A, , with a vertical bar on each side; this is the same notation as absolute value, and the meaning depends on context. The cardinality of a set A may alternatively be denoted by n(A), , \operatorname(A), or \#A. History A crude sense of cardinality, an awareness that groups of things or events compare with other grou ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nuisance Parameter
Nuisance (from archaic ''nocence'', through Fr. ''noisance'', ''nuisance'', from Lat. ''nocere'', "to hurt") is a common law tort. It means that which causes offence, annoyance, trouble or injury. A nuisance can be either public (also "common") or private. A public nuisance was defined by English scholar Sir James Fitzjames Stephen as, "an act not warranted by law, or an omission to discharge a legal duty, which act or omission obstructs or causes inconvenience or damage to the public in the exercise of rights common to all Her Majesty's subjects". ''Private nuisance'' is the interference with the right of specific people. Nuisance is one of the oldest causes of action known to the common law, with cases framed in nuisance going back almost to the beginning of recorded case law. Nuisance signifies that the "right of quiet enjoyment" is being disrupted to such a degree that a tort is being committed. Definition Under the common law, persons in possession of real property ( ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nonparametric Statistics
Nonparametric statistics is the branch of statistics that is not based solely on parametrized families of probability distributions (common examples of parameters are the mean and variance). Nonparametric statistics is based on either being distribution-free or having a specified distribution but with the distribution's parameters unspecified. Nonparametric statistics includes both descriptive statistics and statistical inference. Nonparametric tests are often used when the assumptions of parametric tests are violated. Definitions The term "nonparametric statistics" has been imprecisely defined in the following two ways, among others: Applications and purpose Non-parametric methods are widely used for studying populations that take on a ranked order (such as movie reviews receiving one to four stars). The use of non-parametric methods may be necessary when data have a ranking but no clear numerical interpretation, such as when assessing preferences. In terms of levels of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Non-parametric Model
Nonparametric statistics is the branch of statistics that is not based solely on parametrized families of probability distributions (common examples of parameters are the mean and variance). Nonparametric statistics is based on either being distribution-free or having a specified distribution but with the distribution's parameters unspecified. Nonparametric statistics includes both descriptive statistics and statistical inference. Nonparametric tests are often used when the assumptions of parametric tests are violated. Definitions The term "nonparametric statistics" has been imprecisely defined in the following two ways, among others: Applications and purpose Non-parametric methods are widely used for studying populations that take on a ranked order (such as movie reviews receiving one to four stars). The use of non-parametric methods may be necessary when data have a ranking but no clear numerical interpretation, such as when assessing preferences. In terms of levels of meas ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
