GLOSSARY ENTRY (DERIVED FROM QUESTION BELOW) | ||||||
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20:34 Mar 5, 2004 |
Russian to English translations [PRO] Science - Science (general) / math | |||||||
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| Selected response from: Alexander Konosov Russian Federation Local time: 22:58 | ||||||
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Summary of answers provided | ||||
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4 +1 | one-to-one mapping |
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3 | one-to-one transformation |
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one-to-one mapping Explanation: . |
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„r„x„p„y„}„~„Ђ„Ђ„t„~„Ђ„x„~„p„‰„~„Ђ„u „Ђ„„„Ђ„q„‚„p„w„u„~„y„u one-to-one transformation Explanation: The implication of example 3 is that, if X has uniform distribution on (0,1), i.e. a U(0,1) distribution, then Y=F-1(X) has distribution function F. If we therefore have n independent random values x1,...,xn from a U(0,1) distribution, and if we calculate yj=F-1(xj) for j=1,...,n, then y1,...,yn are n independent random values from a distributiuon with distribution functiion F. All programming languages and packages provide a random number generator which gives a sequence of pseudorandom numbers. These have the properties of a sequence of independent random values from a U(0,1) distribution. We can use these pseudorandom numbers x1,...,xn, which may be considered to be n independent random values from a U(0,1) distribution, to generate independent samples from any continuous distribution. Using the formal definition, for a transformation T: X ЃЁ Y, onto means For any y Ѓё Y, there is x Ѓё X, such that (x, y) Ѓё T, and one-to-one means (x, y) and (x', y) Ѓё T implies x = x'. Reference: http://www.maths.qmw.ac.uk/~lr/stats00n3.pdf Reference: http://algebra.math.ust.hk/matrix_linear_trans/09_transforma... |
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