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variance | A Wisdom Archive on variance | | variance A selection of articles related to variance | |
| We recommend this article: variance - 1, and also this: variance - 2. |
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variance, Variance, Variance - Definition, Variance - Generalizations, Variance - History, Variance - Moment of inertia, Variance - Population variance and sample variance, Variance - Properties, Variance - An unbiased estimator, expected value, standard deviation, skewness, kurtosis, statistical dispersion, an inequality on location and scale parameters, law of total variance
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| ARTICLES RELATED TO variance | | | |  variance: Encyclopedia II - Estimation theory - Example: DC gain in white Gaussian noiseConsider a received discrete signal, x[n], of N independent samples that consists of a DC gain A with Additive white Gaussian noise w[n] with known variance σ2 (i.e., ). Since the variance is known then the only unknown parameter is A.
The model for the signal is then
Two possible (of ...
See also:Estimation theory, Estimation theory - Fields that use estimation theory, Estimation theory - Estimation process, Estimation theory - Basics, Estimation theory - Estimators, Estimation theory - Example: DC gain in white Gaussian noise, Estimation theory - Maximum likelihood, Estimation theory - Cramér-Rao lower bounds, Estimation theory - Books Read more here: » Estimation theory: Encyclopedia II - Estimation theory - Example: DC gain in white Gaussian noise |
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| | | | | variance: Encyclopedia II - Probability-generating function - Properties
Probability-generating function - Power series.
Probability-generating functions obey all the rules of power series with non-negative coefficients. In particular, G(1-) = 1, since the probabilities must sum to one, and where G(1-) = limz→1G(z), then the radius of convergence of any probability-generating function must be at least 1, by Abel's theorem for power series with non-negative coefficients.
Probability-generating function - Probabilities and expectations.
The following properties allow t ...
See also:Probability-generating function, Probability-generating function - Definition, Probability-generating function - Properties, Probability-generating function - Power series, Probability-generating function - Probabilities and expectations, Probability-generating function - Functions of independent random variables, Probability-generating function - Examples, Probability-generating function - Related concepts Read more here: » Probability-generating function: Encyclopedia II - Probability-generating function - Properties |
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| | | | | | | | | | variance: Encyclopedia II - Random variable - Definitions
Random variable - Random variables.
Some consider the expression random variable a misnomer, as a random variable is not a variable but rather a function that maps events to numbers. Let A be a σ-algebra and Ω the space of events relevant to the experiment being performed. In the die-rolling example, the space of events is just the possible outcomes of a roll, i.e. Ω = { 1, 2, 3, 4, 5, 6 }, and A would be the power set of Ω. In this case, an appropriate random variable might be the identi ...
See also:Random variable, Random variable - Definitions, Random variable - Random variables, Random variable - Distribution functions, Random variable - Functions of random variables, Random variable - Example, Random variable - Moments, Random variable - Equivalence of random variables, Random variable - Equality in distribution, Random variable - Equality in mean, Random variable - Almost sure equality, Random variable - Equality, Random variable - Convergence, Random variable - Literature Read more here: » Random variable: Encyclopedia II - Random variable - Definitions |
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| | | | | | | | variance: Encyclopedia II - Autoregressive moving average model - Autoregressive model The notation AR(p) refers to an autoregressive model of order p. An AR(p) model is written
where are the parameters of the model, c is a constant and εt is an error term (see below). The constant term is omitted by many authors for simplicity.
An autoregressive model is essentially an infini ...
See also:Autoregressive moving average model, Autoregressive moving average model - Autoregressive model, Autoregressive moving average model - Example: An AR1-Process, Autoregressive moving average model - Calculation of the AR parameters, Autoregressive moving average model - Moving average model, Autoregressive moving average model - Autoregressive moving average model, Autoregressive moving average model - Note about the error terms, Autoregressive moving average model - Specification in terms of lag operator, Autoregressive moving average model - Fitting models, Autoregressive moving average model - Generalizations, Autoregressive moving average model - Reference Read more here: » Autoregressive moving average model: Encyclopedia II - Autoregressive moving average model - Autoregressive model |
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| | | | | | variance: Encyclopedia II - Mean - Arithmetic mean The arithmetic mean is the "standard" average, often simply called the "mean".
The mean may often be confused with the median or mode. The mean is the arithmetic average of a set of values, or distribution; however, for skewed distributions, the mean is not the same as the middle value (median), or most likely (mode). For example, mean income is skewed upwards by a small number of people with very large incomes, so that the majority have an income lower than the mean. By contrast, the median income is the l ...
See also:Mean, Mean - Arithmetic mean, Mean - An example, Mean - Geometric mean, Mean - An example, Mean - Harmonic mean, Mean - An example, Mean - Generalized mean, Mean - Weighted mean, Mean - Truncated mean, Mean - Interquartile mean, Mean - Mean of a function, Mean - Other means Read more here: » Mean: Encyclopedia II - Mean - Arithmetic mean |
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| | | | | | variance: Encyclopedia II - True variance - Conventional language of computation In statistics, the term true variance is often used to refer to the unobservable variance of a whole population, as distinguished from an observable statistic based on a sample. Suppose a number, such as a person's height or income or age or cholesterol level, is assigned to every member of a population of n individuals. Let xi be the number assigned to the ith individual, for i = 1, ..., n. Then ...
See also:True variance, True variance - Computation of the true and unbiased variance, True variance - Changing true variance to unbiased variance and vice versa, True variance - Degrees of freedom, True variance - Degrees of freedom: Monte Carlo simulation, True variance - True variance and all possible differences between values of a variable, True variance - Matrices of differences, True variance - Differences between data elements and their mean, True variance - Variance and Information, True variance - Retrospect, True variance - Conventional language of computation Read more here: » True variance: Encyclopedia II - True variance - Conventional language of computation |
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| | | | | variance: Encyclopedia II - Chebyshev's inequality - Proof
Chebyshev's inequality - Measure-theoretic proof.
Let At be defined as At = {x ∈ X | f(x) ≥ t}, and let
be the indicator function of the set At. Then, it is easy to check that
and therefore,
The desired inequality follows from dividing the above inequality by g(t).
Cheb ...
See also:Chebyshev's inequality, Chebyshev's inequality - General statement, Chebyshev's inequality - Measure-theoretic statement, Chebyshev's inequality - Probabilistic statement, Chebyshev's inequality - Example application, Chebyshev's inequality - Variants, Chebyshev's inequality - Proof, Chebyshev's inequality - Measure-theoretic proof, Chebyshev's inequality - Probabilistic proof Read more here: » Chebyshev's inequality: Encyclopedia II - Chebyshev's inequality - Proof |
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| | | | | variance: Encyclopedia II - True variance - Variance and Information Binarization of the vector x into its adjacent implicational matrix, shown below
and subtraction of the transpose of this binarized implicational matrix from itself (cf., matrix subtraction)
results in the same skew symmetric matrix as that of the major difference of the vector x. This matrix can be triangularized,
into a skew asymmetrix matrix. The above matrix can provide information about the number of bits contained by the data, ...
See also:True variance, True variance - Computation of the true and unbiased variance, True variance - Changing true variance to unbiased variance and vice versa, True variance - Degrees of freedom, True variance - Degrees of freedom: Monte Carlo simulation, True variance - True variance and all possible differences between values of a variable, True variance - Matrices of differences, True variance - Differences between data elements and their mean, True variance - Variance and Information, True variance - Retrospect, True variance - Conventional language of computation Read more here: » True variance: Encyclopedia II - True variance - Variance and Information |
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| | | | | variance: Encyclopedia II - Pareto distribution - Parameter estimation The likelihood function for the Pareto distribution parameters k and xm, given a sample x = (x1,x2,...,xn), is
Therefore, the logarithmic likelihood function is
It can be seen that is monotonically increasing with xm, that is, the greater the value of xm, the greater the value of the likelihood fu ...
See also:Pareto distribution, Pareto distribution - Properties, Pareto distribution - Pareto Lorenz and Gini, Pareto distribution - Parameter estimation Read more here: » Pareto distribution: Encyclopedia II - Pareto distribution - Parameter estimation |
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