Circular Pearson Correlation Using Cosine Series Expansion

2019 ◽  
Author(s):  
Shih-Gu Huang ◽  
Andrey Gritsenko ◽  
Martin A. Lindquist ◽  
Moo K. Chung
Keyword(s):  
Series Expansion ◽  
Pearson Correlation ◽  
Cosine Series

scholarly journals Estimating the Gerber-Shiu Function in Lévy Insurance Risk Model by Fourier-Cosine Series Expansion

Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1402
Author(s):  
Wen Su ◽  
Yunyun Wang
Keyword(s):  
Series Expansion ◽  
Risk Model ◽  
Insurance Risk ◽  
Transform Method ◽  
Fourier Cosine ◽  
Cosine Series ◽  
Surplus Process ◽  
Fourier Cosine Series ◽  
The Fourier Transform ◽  
Better Than

In this paper, we propose an estimator for the Gerber–Shiu function in a pure-jump Lévy risk model when the surplus process is observed at a high frequency. The estimator is constructed based on the Fourier–Cosine series expansion and its consistency property is thoroughly studied. Simulation examples reveal that our estimator performs better than the Fourier transform method estimator when the sample size is finite.

scholarly journals Sigmoidal cosine series on the interval

2006 ◽  
Vol 47 (4) ◽  
pp. 451-475 ◽  
Author(s):  
Beong In Yun
Keyword(s):  
Fourier Series ◽  
Weight Function ◽  
Series Expansion ◽  
Finite Interval ◽  
Present Series ◽  
Fourier Series Expansion ◽  
Numerical Examples ◽  
Cosine Series ◽  
Fourier Series Approximation ◽  
Proper Weight

AbstractWe construct a set of functions, say, composed of a cosine function and a sigmoidal transformation γr of order r > 0. The present functions are orthonormal with respect to a proper weight function on the interval [−1, 1]. It is proven that if a function f is continuous and piecewise smooth on [−1, 1] then its series expansion based on converges uniformly to f so long as the order of the sigmoidal transformation employed is 0 < r ≤ 1. Owing to the variational feature of according to the value of r, one can expect improvement of the traditional Fourier series approximation for a function on a finite interval. Several numerical examples show the efficiency of the present series expansion in comparison with the Fourier series expansion.

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