# Computing the distribution of a linear combination of inverted gamma variables

Kybernetika (2001)

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

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topWitkovský, 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 -

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