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 ?
The simulations used in this paper clearly show that the thumb rule of 'n [greater than or equal to] 30' for the CLT to provide a good normal approximation to the probability distribution of the sample mean does not work in the case of a heavily skewed probability distribution such as a typical slot game, and that the normal approximation is valid even for moderate sample sizes when the game has a symmetric probability distribution of payouts (e.
Chatterjee [7] provides a rate of normal approximation for the statistic [[?
Here we consider another approach to establishing a rate of normal approximation.
For the Wilcoxon Signed-Rank test, the normal approximation formula is:
For the Sign test, the normal approximation formula is:
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).
On first acquaintance with the central limit theorem, it is not uncommon for undergraduates to ask how accurate the normal approximation is for a sum of (say) twenty random variables.
The general rule of thumb is that if five or more deaths are expected, then the normal approximation is reasonable to use.
We propose an analysis based on a normal approximation that can be used when the variance of number of admissions at the individual level is known and none of the counties is too small.