# Approximation

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Related to normal approximation: normal distribution, Central limit theorem

## approximation

[ə¦präk·sə¦mā·shən]
(mathematics)
A result that is not exact but is near enough to the correct result for some specified purpose.
A procedure for obtaining such a result.

## Approximation

replacement of certain mathematical objects by others which are in one sense or another close to the initial objects. Approximation makes it possible to study the numerical characteristics and qualitative properties of the object, reducing the problem to a study of simpler or more convenient objects—for example, objects whose characteristics are easily computed or whose properties are already known. The theory of numbers studies Diophantine approximations—in particular, approximations of irrational numbers by rational numbers. Approximations of curves, surfaces, spaces, and mappings are investigated in geometry and topology. Some branches of mathematics are wholly devoted to approximations, as, for example, the approximation and interpolation of functions and numerical methods of analysis. The role of approximation in mathematics is continually growing. Presently, approximation can be viewed as one of the basic concepts of mathematics.

S. B. STECHKIN

References in periodicals archive ?
Here we consider another approach to establishing a rate of normal approximation.
90, is of the proper magnitude demanded by the normal approximation, equation (2) ([[chi].
Therefore, we get sufficiently close answers with the normal approximation and we find the calculations are generally easier than with the binomial pdf to justify its use, especially when we want cumulative binomial probabilities.
Comparing the exact distribution of R with the normal approximation reveals that they are very similar if [-square root of m[Eta]/[[Sigma].
The first inadequacy can be partially remedied when the denominator is large by treating n as Poisson, and adjusting for the resulting skewness in the above normal approximation (Ury and Wiggins 1985).
For large values of TW, the central limit theorem can be used to obtain normal approximations to [Q.
Since both sample sizes are at least ten, the normal approximation to T can be used (Anderson, et.
We provide normal approximation error bounds for sums of the form [[summation].
Thus, with small samples (n < 30), we commonly use the t distribution as the basis for confidence intervals and tests on [mu], but for large samples, we employ the normal approximation.
Following Koehler and Larntz (1980), we use a normal approximation to [[Chi].
The control lines are calculated by means of the standard formulae which follow the normal approximation to the binomial distribution[16].

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