| Title:
|
A Note on Computing Extreme Tail Probabilities of the Noncentral $t$-Distribution with Large Noncentrality Parameter (English) |
| Author:
|
Witkovský, Viktor |
| Language:
|
English |
| Journal:
|
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica |
| ISSN:
|
0231-9721 |
| Volume:
|
52 |
| Issue:
|
2 |
| Year:
|
2013 |
| Pages:
|
131-143 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
noncentral $t$-distribution |
| Keyword:
|
cumulative distribution function (CDF) |
| Keyword:
|
noncentrality parameter |
| Keyword:
|
extreme tail probability |
| Keyword:
|
MATLAB algorithm |
| MSC:
|
62-04 |
| MSC:
|
62E15 |
| idZBL:
|
Zbl 06296021 |
| idMR:
|
MR3202386 |
| . |
| Date available:
|
2013-12-18T15:27:43Z |
| Last updated:
|
2014-07-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143545 |
| . |
| Reference:
|
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