Le Cam maximin tests for symmetry of circular data based on the characteristic function

2019 ◽  
Author(s):  
Simos Meintanis ◽  
Thomas Verdebout
Keyword(s):  
Characteristic Function ◽  
Circular Data ◽  
Tests For Symmetry

scholarly journals Computing the Sound of the Sea in a Seashell

2021 ◽  
Author(s):  
Jonathan Ben-Artzi ◽  
Marco Marletta ◽  
Frank Rösler
Keyword(s):  
Characteristic Function ◽  
Helmholtz Resonator ◽  
Positive Answer ◽  
Approximation Procedure ◽  
Universal Algorithm

AbstractThe question of whether there exists an approximation procedure to compute the resonances of any Helmholtz resonator, regardless of its particular shape, is addressed. A positive answer is given, and it is shown that all that one has to assume is that the resonator chamber is bounded and that its boundary is $${{\mathcal {C}}}^2$$ C 2 . The proof is constructive, providing a universal algorithm which only needs to access the values of the characteristic function of the chamber at any requested point.

On the first zero of an empirical characteristic function

1991 ◽  
Vol 28 (3) ◽  
pp. 593-601 ◽  
Author(s):  
H. U. Bräker ◽  
J. Hüsler
Keyword(s):  
Characteristic Function ◽  
Limit Distribution ◽  
Random Variable ◽  
Empirical Characteristic Function ◽  
The Real ◽  
Exponential Decrease ◽  
Characteristic Process

We deal with the distribution of the first zero Rn of the real part of the empirical characteristic process related to a random variable X. Depending on the behaviour of the theoretical real part of the underlying characteristic function, cases with a slow exponential decrease to zero are considered. We derive the limit distribution of Rn in this case, which clarifies some recent results on Rn in relation to the behaviour of the characteristic function.

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