99
Views
17
CrossRef citations to date
0
Altmetric
General

Obtaining Distribution Functions by Numerical Inversion of Characteristic Functions with Applications

, &
Pages 346-350 | Received 01 Oct 1993, Published online: 27 Feb 2012

References

  • Baglivo , J. , Olivier , D. and Pagano , M. 1992 . “Methods for Exact Goodness-of-Fit Tests” . Journal of the American Statistical Association , 87 : 464 – 469 .
  • Bohman , H. 1961 . “Approximate Fourier Analysis of Distribution Functions” . Arkiv for Matematik , 4 : 99 – 157 .
  • Bohman , H. 1970 . “A Method to Calculate the Distribution Function when the Characteristic Function is Known” . BIT , 10 : 237 – 242 .
  • Bohman , H. 1972 . “From Characteristic Function to Distribution Function via Fourier Analysis” . BIT , 12 : 279 – 283 .
  • Bohman , H. 1975 . “Numerical Inversions of Characteristic Functions” . Scandinavian Actuarial Journal , : 121 – 124 .
  • Bohman , H. 1980 . “Numerical Fourier Inversion” . In Computational Probability , Edited by: Kahn , P. M. New York : Academic Press .
  • Breslow , N. E. , Lubin , J. H. , Marek , P. and Langholz , B. 1983 . “Multiplicative Models and Cohort Analysis” . Journal of the American Statistical Association , 78 : 1 – 12 .
  • Casella , G. and George , E. I. 1992 . “Explaining the Gibbs Sampler” . The American Statistician , 46 : 167 – 174 .
  • Conerly , M. D. and Hardin , J. M. 1990 . “A Comparison of Biased Regression Estimators using a Pitman Nearness Criterion” . Journal of Statistical Computation and Simulation , 34 : 75 – 95 .
  • Cox , D. R. and Hinkley , D. V. 1974 . Theoretical Statistics , London : Chapman and Hall .
  • Cressie , N. A. C. 1991 . Statistics for Spatial Data , New York : John Wiley .
  • Davies , R. B. 1973 . “Numerical Inversion of a Characteristic Function” . Biometrika , 60 : 415 – 417 .
  • Davies , R. B. 1980 . “ASS 155: The Distribution of a Linear Combination of Chi-Squared Random Variables” . Applied Statistics , 29 : 323 – 333 .
  • Diggle , P. J. and Hall , P. 1993 . “A Fourier Approach to Nonparametric Deconvolution of a Density Estimate” . Journal of the Royal Statistical Society , 55 : 523 – 531 . Ser. B
  • Efron , B. and Gong , G. 1983 . “A Leisurely Look at the Bootstrap, the Jackknife and Cross-Validation” . The American Statistician , 37 : 36 – 48 .
  • Gil-Pelaez , J. 1951 . “Note on the Inversion Theorem” . Biometrika , 38 : 481 – 482 .
  • Good , I. J. 1987 . “A Survey of the Use of the Fast Fourier Transform for Computing Distributions” . Journal of Statistical Computation and Simulation , 28 : 87 – 93 .
  • Hamming , R. W. 1973 . Numerical Methods for Scientists and Engineers , New York : Dover Publications .
  • Heck , A. 1993 . Introduction to Maple , New York : Springer-Verlag .
  • Imhof , J. P. 1961 . “Computing the Distribution of Quadratic Forms in Normal Variables” . Biometrika , 48 : 419 – 426 .
  • Lawson , A. B. 1993 . “On the Analysis of Mortality Events Associated with a Prespecified Fixed Point” . Journal of the Royal Statistical Society , 156 : 363 – 377 . Ser. A
  • MathSoft, Inc. 1993 . MathCAD, Version 4.0 , Cambridge , MA : Author .
  • Pagano , M. and Tritchler , D. 1983 . “On Obtaining Permutation Distributions in Polynomial Time” . Journal of the American Statistical Association , 78 : 435 – 440 .
  • Robert , C. P. , Hwang , J. T. G. and Strawderman , W. E. 1993 . “Is Pitman Closeness a Reasonable Criterion?” . Journal of the American Statistical Association , 88 : 57 – 76 . (with discussion)
  • Schorr , B. 1975 . “Numerical Inversion of a Class of Characteristic Functions” . BIT , 15 : 94 – 102 .
  • Seal , H. L. 1977 . “Numerical Inversion of Characteristic Functions” . Scandinavian Actuarial Journal , : 48 – 53 .
  • Shephard , N. G. 1991 . “From Characteristic Function to Distribution Function: A Simple Framework for the Theory” . Econometric Theory , 7 : 519 – 529 .
  • Spino , C. and Pagano , M. 1991a . “Efficient Calculation of the Permutation Distribution of Trimmed Means” . Journal of the American Statistical Association , 86 : 729 – 737 .
  • Spino , C. and Pagano , M. 1991b . “Efficient Calculation of the Permutation Distribution of Robust Two-Sample Statistics” . Computational Statistics and Data Analysis , 12 : 349 – 365 .
  • Stuart , A. and Ord , J. K. 1987 . Kendall's Advanced Theory of Statistics, Volume 1, Distribution Theory, , 5th ed. , Oxford : Oxford University Press .
  • Tanner , M. A. 1991 . Tools for Statistical Inference , New York : Springer-Verlag .
  • Tritchler , D. 1984 . “On Inverting Permutation Tests” . Journal of the American Statistical Association , 79 : 200 – 207 .
  • Waller , L. A. , Turnbull , B. W. , Clark , L. C. and Nasca , P. 1992 . “Chronic Disease Surveillance and Testing of Clustering of Disease and Exposure: Application to Leukemia Incidence and TCE-Contaminated Dumpsites in Upstate New York” . Environmetrics , 3 : 281 – 300 .
  • Waller , L. A. , Turnbull , B. W. , Clark , L. C. and Nasca , P. 1994 . “Spatial Pattern Analyses to Detect Rare Disease Clusters” . In Case Studies in Biometry , Edited by: Lange , N. , Ryan , L. , Billard , L. , Brillinger , D. , Conquest , L. and Greenhouse , J. New York : John Wiley .
  • Wolfram , S. 1991 . Mathematica: A System for Doing Mathematics by Computer, , 2nd ed. , Redwood City , CA : Addison-Wesley .
  • Zhang , C. H. 1990 . “Fourier Methods for Estimating Mixing Densities and Distributions” . Annals of Statistics , 18 : 806 – 831 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.