Computing the distribution of a linear combination of inverted gamma variables

Viktor Witkovský

Kybernetika (2001)

  • Volume: 37, Issue: 1, page [79]-90
  • ISSN: 0023-5954

Abstract

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A formula for evaluation of the distribution of a linear combination of independent inverted gamma random variables by one-dimensional numerical integration is presented. The formula is direct application of the inversion formula given by Gil–Pelaez [gil-pelaez]. This method is applied to computation of the generalized p -values used for exact significance testing and interval estimation of the parameter of interest in the Behrens–Fisher problem and for variance components in balanced mixed linear model.

How to cite

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Witkovský, Viktor. "Computing the distribution of a linear combination of inverted gamma variables." Kybernetika 37.1 (2001): [79]-90. <http://eudml.org/doc/33518>.

@article{Witkovský2001,
abstract = {A formula for evaluation of the distribution of a linear combination of independent inverted gamma random variables by one-dimensional numerical integration is presented. The formula is direct application of the inversion formula given by Gil–Pelaez [gil-pelaez]. This method is applied to computation of the generalized $p$-values used for exact significance testing and interval estimation of the parameter of interest in the Behrens–Fisher problem and for variance components in balanced mixed linear model.},
author = {Witkovský, Viktor},
journal = {Kybernetika},
keywords = {generalized $p$-value; inversion formula; Behrens-Fisher problem; generalized -value; inversion formula; Behrens-Fisher problem},
language = {eng},
number = {1},
pages = {[79]-90},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Computing the distribution of a linear combination of inverted gamma variables},
url = {http://eudml.org/doc/33518},
volume = {37},
year = {2001},
}

TY - JOUR
AU - Witkovský, Viktor
TI - Computing the distribution of a linear combination of inverted gamma variables
JO - Kybernetika
PY - 2001
PB - Institute of Information Theory and Automation AS CR
VL - 37
IS - 1
SP - [79]
EP - 90
AB - A formula for evaluation of the distribution of a linear combination of independent inverted gamma random variables by one-dimensional numerical integration is presented. The formula is direct application of the inversion formula given by Gil–Pelaez [gil-pelaez]. This method is applied to computation of the generalized $p$-values used for exact significance testing and interval estimation of the parameter of interest in the Behrens–Fisher problem and for variance components in balanced mixed linear model.
LA - eng
KW - generalized $p$-value; inversion formula; Behrens-Fisher problem; generalized -value; inversion formula; Behrens-Fisher problem
UR - http://eudml.org/doc/33518
ER -

References

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  4. Gil–Pelaez J., 10.1093/biomet/38.3-4.481, Biometrika 38 (1951), 481–482 (1951) Zbl0045.07204MR0045992DOI10.1093/biomet/38.3-4.481
  5. Imhof J. P., 10.1093/biomet/48.3-4.419, Biometrika 48 (1961), 419–426 (1961) Zbl0136.41103MR0137199DOI10.1093/biomet/48.3-4.419
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  7. Prudnikov A. P., Brychkov Y. A., Marichev O. I., Integraly i Rjady, (Integrals and Series). Nauka, Moscow 1981 MR0635931
  8. Tsui K. W., Weerahandi S., Generalized p values in significance testing of hypotheses in the presence of nuisance parameters, J. Amer. Statist. Assoc. 84 (1989), 602–607 (1989) MR1010352
  9. Waller L. A., Turnbull B. W., Hardin J. M., Obtaining distribution functions by numerical inversion of characteristic functions with applications, Amer. Statist. 49 (1995), 4, 346–350 (1995) 
  10. Weerahandi S., Testing variance components in mixed models with generalized p values, J. Amer. Statist. Assoc. 86 (1991), 151–153 (1991) 
  11. Weerahandi S., Exact Statistical Methods for Data Analysis, Springer–Verlag, New York 1995 Zbl1050.62003MR1316663
  12. Witkovský V., 10.1016/S0378-3758(00)00208-1, J. Statist. Plann. Inference 94 (2001), 1, 1–13 Zbl0971.62012MR1820167DOI10.1016/S0378-3758(00)00208-1
  13. Zhou L., Mathew T., Some tests for variance components using generalized P -values, Technometrics 36 (1994), 394–402 (1994) Zbl0825.62603MR1304900

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