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Biometrika 1968 55(1):29-41; doi:10.1093/biomet/55.1.29
© 1968 by Biometrika Trust
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Inverse cumulative approximation and applications

M. E. TARTER

Department of Biostatistics, University of Michigan

The following general problem is considered: fit the inverse cumulative distribution function F–1(y) by a polynomial expansion in terms of a more tractable function G–1(y).It is shown that the computation of the coefficients of this expansion need not depend upon the evaluation of F–1(y) for specific values of y, but instead can be based on the evaluation of the cumulative F(x). If G–1(y) is chosen to be - log (1 - y), the solution in this particular case is shown to be based upon the Laguerre polynomials. Applications of the above methods are briefly described for such problems, as: random number generation, order statistic moment and product moment calculation, as well as the smoothing of the sample cumulative.


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