Turning point test: Difference between revisions
Content deleted Content added
Gareth Jones (talk | contribs) →Test statistic: add missing ref tag |
Gareth Jones (talk | contribs) →Test statistic: rm absolute values for quantity to be normally distributed |
||
| Line 17: | Line 17: | ||
Let ''T'' be the number of turning points then for large ''n'', ''T'' is approximately [[normal distribution|normally distributed]] with mean (2''n'' − 4)/3 and variance (16''n'' − 29)/90. The test statistic<ref>{{cite doi|10.1007/978-94-007-1861-6_4}}</ref> |
Let ''T'' be the number of turning points then for large ''n'', ''T'' is approximately [[normal distribution|normally distributed]] with mean (2''n'' − 4)/3 and variance (16''n'' − 29)/90. The test statistic<ref>{{cite doi|10.1007/978-94-007-1861-6_4}}</ref> |
||
:<math>z =\frac{ |
:<math>z =\frac{T - \frac{2n-4}{3}}{\sqrt{\frac{16n-29}{90}}}</math> |
||
has standard normal distribution. |
has standard normal distribution. |
||
Revision as of 11:43, 17 June 2013
In statistical hypothesis testing, a turning point test is a statistical test of the independence of a series of random variables.[1][2][3]
Statement of test
The turning point tests the null hypothesis[1]
- H0: X1, X2, ... Xn are independent and identically distributed random variables
against
- H1: X1, X2, ... Xn are not iid.
Test statistic
We say i is a turning point if the vector X1, X2, ..., Xi, ..., Xn is not monotonic at index i.
Let T be the number of turning points then for large n, T is approximately normally distributed with mean (2n − 4)/3 and variance (16n − 29)/90. The test statistic[4]
has standard normal distribution.
References
- ^ a b Le Boudec, Jean-Yves (2010). Performance Evaluation Of Computer And Communication Systems (PDF). EPFL Press. pp. 136–137. ISBN 978-2-940222-40-7.
- ^ Attention: This template ({{cite doi}}) is deprecated. To cite the publication identified by doi:10.1007/b97391, please use {{cite journal}} (if it was published in a bona fide academic journal, otherwise {{cite report}} with
|doi=10.1007/b97391instead. - ^ Kendall, Maurice George (1973). Time series. Griffin. ISBN 0852642202.
- ^ Attention: This template ({{cite doi}}) is deprecated. To cite the publication identified by doi:10.1007/978-94-007-1861-6_4, please use {{cite journal}} (if it was published in a bona fide academic journal, otherwise {{cite report}} with
|doi=10.1007/978-94-007-1861-6_4instead.
 | This statistics-related article is a stub. You can help Wikipedia by expanding it. |