Affiliations: Faculty of Mathematics, Federal University of Uberlândia, Uberlândia, Brazil | E-mail: [email protected]
Corresponding author: Faculty of Mathematics, Federal University of Uberlândia, Uberlândia, Brazil. E-mail: [email protected].
Abstract: The α-stable distribution can describe a degree of concentration of the observations around the mean as well as their asymmetry, regardless of sample size. As the α stability index is the most interesting parameter in the applications, several estimators have been proposed for α. Here we develop an estimator for α (called STNRW-ECF) based on the empirical characteristic function and the Seismic Trace Noise Reduction by Wavelets and Double Threshold Estimation method (STNRW). We analyze the proposed estimator using Monte Carlo simulations and prove its asymptotic Gaussian distribution. Electrocardiography (ECG) is the process of recording the electrical activity of the heart over a period of time using electrodes placed on the skin. The time intervals between its various peaks, may contain useful information about the nature of disease afflicting the heart. To analyze this kind of data can be tiring and more prone to errors when interpreted by human beings, since there is a huge amount information to be processed. Here we propose the STNRW-ECF estimator to be an additional diagnostic tool that may provide an indication of cardiac arrhythmia, and we also propose a test based on the principal wavelet shrinkage to confirm whether or not the STNRW-ECF estimator should be used for this purpose.