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Univariate Vs
In mathematics, a univariate object is an expression, equation, function or polynomial involving only one variable. Objects involving more than one variable are multivariate. In some cases the distinction between the univariate and multivariate cases is fundamental; for example, the fundamental theorem of algebra and Euclid's algorithm for polynomials are fundamental properties of univariate polynomials that cannot be generalized to multivariate polynomials. In statistics, a univariate distribution characterizes one variable, although it can be applied in other ways as well. For example, univariate data are composed of a single scalar component. In time series analysis, the whole time series is the "variable": a univariate time series is the series of values over time of a single quantity. Correspondingly, a "multivariate time series" characterizes the changing values over time of several quantities. In some cases, the terminology is ambiguous, since the values within a univariat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Expression (mathematics)
In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context. Mathematical symbols can designate numbers ( constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax. Many authors distinguish an expression from a '' formula'', the former denoting a mathematical object, and the latter denoting a statement about mathematical objects. For example, 8x-5 is an expression, while 8x-5 \geq 5x-8 is a formula. However, in modern mathematics, and in particular in computer algebra, formulas are viewed as expressions that can be evaluated to ''true'' or ''false'', depending on the values that are given to the variables occurring in the expressions. For example 8x-5 \geq 5x-8 takes the value ''false'' if is given a value less than –1, and the value ''true'' otherwise. Examples The use of e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Univariate Time Series
In mathematics, a time series is a series of data points indexed (or listed or graphed) in time order. Most commonly, a time series is a sequence taken at successive equally spaced points in time. Thus it is a sequence of discrete-time data. Examples of time series are heights of ocean tides, counts of sunspots, and the daily closing value of the Dow Jones Industrial Average. A time series is very frequently plotted via a run chart (which is a temporal line chart). Time series are used in statistics, signal processing, pattern recognition, econometrics, mathematical finance, weather forecasting, earthquake prediction, electroencephalography, control engineering, astronomy, communications engineering, and largely in any domain of applied science and engineering which involves temporal measurements. Time series ''analysis'' comprises methods for analyzing time series data in order to extract meaningful statistics and other characteristics of the data. Time series ''forecast ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Univariate Distribution
In statistics, a univariate distribution is a probability distribution of only one random variable. This is in contrast to a multivariate distribution, the probability distribution of a random vector (consisting of multiple random variables). Examples One of the simplest examples of a discrete univariate distribution is the discrete uniform distribution, where all elements of a finite set are equally likely. It is the probability model for the outcomes of tossing a fair coin, rolling a fair die, etc. The univariate continuous uniform distribution on an interval 'a'', ''b''has the property that all sub-intervals of the same length are equally likely. Other examples of discrete univariate distributions include the binomial, geometric, negative binomial, and Poisson distributions.Johnson, N.L., Kemp, A.W., and Kotz, S. (2005) Discrete Univariate Distributions, 3rd Edition, Wiley, . At least 750 univariate discrete distributions have been reported in the literature.Wimmer G, A ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Univariate Binary Model
The general linear model or general multivariate regression model is a compact way of simultaneously writing several multiple linear regression models. In that sense it is not a separate statistical linear model. The various multiple linear regression models may be compactly written as : \mathbf = \mathbf\mathbf + \mathbf, where Y is a matrix with series of multivariate measurements (each column being a set of measurements on one of the dependent variables), X is a matrix of observations on independent variables that might be a design matrix (each column being a set of observations on one of the independent variables), B is a matrix containing parameters that are usually to be estimated and U is a matrix containing errors (noise). The errors are usually assumed to be uncorrelated across measurements, and follow a multivariate normal distribution. If the errors do not follow a multivariate normal distribution, generalized linear models may be used to relax assumptions about Y and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Univariate Analysis
Univariate analysis is perhaps the simplest form of statistical analysis. Like other forms of statistics, it can be inferential or descriptive. The key fact is that only one variable is involved. Univariate analysis can yield misleading results in cases in which multivariate analysis is more appropriate. Descriptive methods Descriptive statistics describe a sample or population. They can be part of exploratory data analysis. The appropriate statistic depends on the level of measurement. For nominal variables, a frequency table and a listing of the mode(s) is sufficient. For ordinal variables the median can be calculated as a measure of central tendency and the range (and variations of it) as a measure of dispersion. For interval level variables, the arithmetic mean (average) and standard deviation are added to the toolbox and, for ratio level variables, we add the geometric mean and harmonic mean as measures of central tendency and the coefficient of variation as a measure of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Multivariate (other)
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Multivariate may refer to: In mathematics * Multivariable calculus * Multivariate function * Multivariate polynomial In computing * Multivariate cryptography * Multivariate division algorithm * Multivariate interpolation * Multivariate optical computing * Multivariate optimization, used for the design of heat exchangers, see In statistics * Multivariate analysis * Multivariate random variable * Multivariate statistics See also * Univariate * Bivariate (other) Bivariate may refer to: Mathematics * Bivariate function, a function of two variables * Bivariate polynomial, a polynomial of two indeterminates Statistics * Bivariate data, that shows the relationship between two variables * Bivariate analysi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bivariate (other)
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Bivariate may refer to: Mathematics * Bivariate function, a function of two variables * Bivariate polynomial, a polynomial of two indeterminates Statistics * Bivariate data, that shows the relationship between two variables * Bivariate analysis, statistical analysis of two variables * Bivariate distribution, a joint probability distribution for two variables Other * Bivariate map, a single map that displays two variables See also * Two-dimensional curve * Multivariate (other) Multivariate may refer to: In mathematics * Multivariable calculus * Multivariate function * Multivariate polynomial In computing * Multivariate cryptography * Multivariate division algorithm * Multivariate interpolation * Multivariate optical c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Arity
Arity () is the number of arguments or operands taken by a function, operation or relation in logic, mathematics, and computer science. In mathematics, arity may also be named ''rank'', but this word can have many other meanings in mathematics. In logic and philosophy, it is also called adicity and degree. In linguistics, it is usually named valency. Examples The term "arity" is rarely employed in everyday usage. For example, rather than saying "the arity of the addition operation is 2" or "addition is an operation of arity 2" one usually says "addition is a binary operation". In general, the naming of functions or operators with a given arity follows a convention similar to the one used for ''n''-based numeral systems such as binary and hexadecimal. One combines a Latin prefix with the -ary ending; for example: * A nullary function takes no arguments. ** Example: f()=2 * A unary function takes one argument. ** Example: f(x)=2x * A binary function takes two arguments. ** Examp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Joint Distributions
Given two random variables that are defined on the same probability space, the joint probability distribution is the corresponding probability distribution on all possible pairs of outputs. The joint distribution can just as well be considered for any given number of random variables. The joint distribution encodes the marginal distributions, i.e. the distributions of each of the individual random variables. It also encodes the conditional probability distributions, which deal with how the outputs of one random variable are distributed when given information on the outputs of the other random variable(s). In the formal mathematical setup of measure theory, the joint distribution is given by the pushforward measure, by the map obtained by pairing together the given random variables, of the sample space's probability measure. In the case of real-valued random variables, the joint distribution, as a particular multivariate distribution, may be expressed by a multivariate cumulativ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Multivariate Statistics
Multivariate statistics is a subdivision of statistics encompassing the simultaneous observation and analysis of more than one outcome variable. Multivariate statistics concerns understanding the different aims and background of each of the different forms of multivariate analysis, and how they relate to each other. The practical application of multivariate statistics to a particular problem may involve several types of univariate and multivariate analyses in order to understand the relationships between variables and their relevance to the problem being studied. In addition, multivariate statistics is concerned with multivariate probability distributions, in terms of both :*how these can be used to represent the distributions of observed data; :*how they can be used as part of statistical inference, particularly where several different quantities are of interest to the same analysis. Certain types of problems involving multivariate data, for example simple linear regression an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Time Series Analysis
In mathematics, a time series is a series of data points indexed (or listed or graphed) in time order. Most commonly, a time series is a sequence taken at successive equally spaced points in time. Thus it is a sequence of discrete-time data. Examples of time series are heights of ocean tides, counts of sunspots, and the daily closing value of the Dow Jones Industrial Average. A time series is very frequently plotted via a run chart (which is a temporal line chart). Time series are used in statistics, signal processing, pattern recognition, econometrics, mathematical finance, weather forecasting, earthquake prediction, electroencephalography, control engineering, astronomy, communications engineering, and largely in any domain of applied science and engineering which involves temporal measurements. Time series ''analysis'' comprises methods for analyzing time series data in order to extract meaningful statistics and other characteristics of the data. Time series ''forecasting'' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Equation
In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign . The word ''equation'' and its cognates in other languages may have subtly different meanings; for example, in French an ''équation'' is defined as containing one or more variables, while in English, any well-formed formula consisting of two expressions related with an equals sign is an equation. ''Solving'' an equation containing variables consists of determining which values of the variables make the equality true. The variables for which the equation has to be solved are also called unknowns, and the values of the unknowns that satisfy the equality are called solutions of the equation. There are two kinds of equations: identities and conditional equations. An identity is true for all values of the variables. A conditional equation is only true for particular values of the variables. An equation is written as two expressions, connected by a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
