Concepts inAutomatic sampling with the ratio-of-uniforms method
Sampling (statistics)
In statistics and survey methodology, sampling is concerned with the selection of a subset of individuals from within a population to estimate characteristics of the whole population. Researchers rarely survey the entire population because the cost of a census is too high. The three main advantages of sampling are that the cost is lower, data collection is faster, and since the data set is smaller it is possible to ensure homogeneity and to improve the accuracy and quality of the data.
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Logarithmically concave function
In convex analysis, a non-negative function f : R ¿ R+ is logarithmically concave (or log-concave for short) if its domain is a convex set, and if it satisfies the inequality for all x,y ¿ dom f and 0 < ¿ < 1. If f is strictly positive, this is equivalent to saying that the logarithm of the function, log ¿ f, is concave; that is, for all x,y ¿ dom f and 0 < ¿ < 1.
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Random variate
A random variate is a particular outcome of a random variable: the random variates which are other outcomes of the same random variable would have different values. Random variates are used when simulating processes driven by random influences.
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Efficiency (statistics)
In statistics, efficiency is a term used in the comparison of various statistical procedures and, in particular, it refers to a measure of the optimality of an estimator, of an experimental design or of an hypothesis testing procedure. Essentially, a more efficient estimator, experiment or test needs fewer samples than a less efficient one to achieve a given performance.
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Uniform distribution (continuous)
In probability theory and statistics, the continuous uniform distribution or rectangular distribution is a family of probability distributions such that for each member of the family, all intervals of the same length on the distribution's support are equally probable. The support is defined by the two parameters, a and b, which are its minimum and maximum values. The distribution is often abbreviated U(a,b).
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Expected value
In probability theory, the expected value (or expectation, or mathematical expectation, or mean, or the first moment) of a random variable is the weighted average of all possible values that this random variable can take on. The weights used in computing this average correspond to the probabilities in case of a discrete random variable, or densities in case of a continuous random variable.
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Closed-form expression
In mathematics, an expression is said to be a closed-form expression if it can be expressed analytically in terms of a finite number of certain "well-known" functions. Typically, these well-known functions are defined to be elementary functions¿constants, one variable x, elementary operations of arithmetic (+ ¿ × ÷), nth roots, exponent and logarithm (which thus also include trigonometric functions and inverse trigonometric functions).
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