A Note on Computing Extreme Tail Probabilities of the Noncentral t -Distribution with Large Noncentrality Parameter

Viktor Witkovský

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica (2013)

  • Volume: 52, Issue: 2, page 131-143
  • ISSN: 0231-9721

Abstract

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The noncentral t -distribution is a generalization of the Student’s t -distribution. In this paper we suggest an alternative approach for computing the cumulative distribution function (CDF) of the noncentral t -distribution which is based on a direct numerical integration of a well behaved function. With a double-precision arithmetic, the algorithm provides highly precise and fast evaluation of the extreme tail probabilities of the noncentral t -distribution, even for large values of the noncentrality parameter δ and the degrees of freedom ν . The implementation of the algorithm is available at the MATLAB Central, File Exchange: www.mathworks.com/matlabcentral/fileexchange/41790-nctcdfvw.

How to cite

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Witkovský, Viktor. "A Note on Computing Extreme Tail Probabilities of the Noncentral $t$-Distribution with Large Noncentrality Parameter." Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica 52.2 (2013): 131-143. <http://eudml.org/doc/260777>.

@article{Witkovský2013,
abstract = {The noncentral $t$-distribution is a generalization of the Student’s$t$-distribution. In this paper we suggest an alternative approach for computing the cumulative distribution function (CDF) of the noncentral$t$-distribution which is based on a direct numerical integration of a well behaved function. With a double-precision arithmetic, the algorithm provides highly precise and fast evaluation of the extreme tail probabilities of the noncentral $t$-distribution, even for large values of the noncentrality parameter $\delta $ and the degrees of freedom $\nu $. The implementation of the algorithm is available at the MATLAB Central, File Exchange: www.mathworks.com/matlabcentral/fileexchange/41790-nctcdfvw.},
author = {Witkovský, Viktor},
journal = {Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica},
keywords = {noncentral $t$-distribution; cumulative distribution function (CDF); noncentrality parameter; extreme tail probability; MATLAB algorithm; noncentral -distribution; cumulative distribution function (CDF); noncentrality parameter; extreme tail probability; MATLAB algorithm},
language = {eng},
number = {2},
pages = {131-143},
publisher = {Palacký University Olomouc},
title = {A Note on Computing Extreme Tail Probabilities of the Noncentral $t$-Distribution with Large Noncentrality Parameter},
url = {http://eudml.org/doc/260777},
volume = {52},
year = {2013},
}

TY - JOUR
AU - Witkovský, Viktor
TI - A Note on Computing Extreme Tail Probabilities of the Noncentral $t$-Distribution with Large Noncentrality Parameter
JO - Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
PY - 2013
PB - Palacký University Olomouc
VL - 52
IS - 2
SP - 131
EP - 143
AB - The noncentral $t$-distribution is a generalization of the Student’s$t$-distribution. In this paper we suggest an alternative approach for computing the cumulative distribution function (CDF) of the noncentral$t$-distribution which is based on a direct numerical integration of a well behaved function. With a double-precision arithmetic, the algorithm provides highly precise and fast evaluation of the extreme tail probabilities of the noncentral $t$-distribution, even for large values of the noncentrality parameter $\delta $ and the degrees of freedom $\nu $. The implementation of the algorithm is available at the MATLAB Central, File Exchange: www.mathworks.com/matlabcentral/fileexchange/41790-nctcdfvw.
LA - eng
KW - noncentral $t$-distribution; cumulative distribution function (CDF); noncentrality parameter; extreme tail probability; MATLAB algorithm; noncentral -distribution; cumulative distribution function (CDF); noncentrality parameter; extreme tail probability; MATLAB algorithm
UR - http://eudml.org/doc/260777
ER -

References

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