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Transforming a random variable to a prescribed distribution: an application to school-based assessment

Part of: Numerical approximation and computational geometry

Published online by Cambridge University Press:  14 July 2016

Timothy C. Brown
Timothy C. Brown*
Affiliation:
Faculty of Science, Frank Fenner Building, Australian National University, Canberra ACT 0200, Australia. Email address: [email protected]
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Abstract

When can one find a smooth transformation of a random variable so that the transformed random variable has a specified distribution? If the random variable is continuous, the solution is elementary; if it is discrete, it may be impossible. In this paper, a simple method is given of transforming a random variable in a smooth way to match a specified number of quantiles of an arbitrary distribution. The problem arose from a request for a simple way of transforming marks given in school assessment so that the distribution of transformed marks matches the distribution of external assessment.

Keywords

Transformationsmatching quantilesinterpolationmatching meansschool assessmentexaminations

MSC classification

Primary: 65D05: Interpolation
Secondary: 65D32: Quadrature and cubature formulas
Type
Part 5. Properties of random variables
Information
Journal of Applied Probability , Volume 41 , Issue A: Stochastic Methods and their Applications , 2004 , pp. 239 - 252
Copyright
Copyright © Applied Probability Trust 2004 

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References

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