Test of bivariate independence based on angular probability integral transform with emphasis on circular-circular and circular-linear data
The probability integral transform of a continuous random variable with distribution function is a uniformly distributed random variable . We define the angular probability integral transform (APIT) as , which corresponds to a uniformly distributed angle on the unit circle. For circular (angular) ra...
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| Vydané v: | Dependence modeling Ročník 11; číslo 1; s. 547 - 556 |
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| Hlavní autori: | , |
| Médium: | Journal Article |
| Jazyk: | English |
| Vydavateľské údaje: |
De Gruyter
20.10.2023
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| Predmet: | |
| ISSN: | 2300-2298, 2300-2298 |
| On-line prístup: | Získať plný text |
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| Shrnutí: | The probability integral transform of a continuous random variable
with distribution function
is a uniformly distributed random variable
. We define the angular probability integral transform (APIT) as
, which corresponds to a uniformly distributed angle on the unit circle. For circular (angular) random variables, the sum modulus 2
of absolutely continuous independent circular uniform random variables is a circular uniform random variable, that is, the circular uniform distribution is closed under summation modulus 2
, and it is a stable continuous distribution on the unit circle. If we consider the sum (difference) of the APITs of two random variables,
and
, and test for the circular uniformity of their sum (difference) modulus 2
, this is equivalent to test of independence of the original variables. In this study, we used a flexible family of nonnegative trigonometric sums (NNTS) circular distributions, which include the uniform circular distribution as a member of the family, to evaluate the power of the proposed independence test by generating samples from NNTS alternative distributions that could be at a closer proximity with respect to the circular uniform null distribution. |
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| ISSN: | 2300-2298 2300-2298 |
| DOI: | 10.1515/demo-2023-0103 |