Slash Truncation Positive Normal Distribution and Its Estimation Based on the EM Algorithm

In this paper, we present an extension of the truncated positive normal (TPN) distribution to model positive data with a high kurtosis. The new model is defined as the quotient between two random variables: the TPN distribution (numerator) and the power of a standard uniform distribution (denominator). The resulting model has greater kurtosis than the TPN distribution. We studied some properties of the distribution, such as moments, asymmetry, and kurtosis. Parameter estimation is based on the moments method, and maximum likelihood estimation uses the expectation-maximization algorithm. We performed some simulation studies to assess the recovery parameters and illustrate the model with a real data application related to body weight. The computational implementation of this work was included in the tpn package of the R software.

Fatigue Test of 6082 Aluminum Alloy under Random Load with Controlled Kurtosis

This paper presents the results of experimental tests carried out on an electromagnetic shaker where the excited element was a specimen with additional weight attached to the slip table. The load was random with a different kurtosis parameter value, i.e., it was performed for non-Gaussian loads. The experiment was accompanied by basic fatigue calculations in the frequency domain and their verification with experimental results. A significant decrease in fatigue life was found to take place with an increase in kurtosis and the maintenance of the same standard deviation of the specimen load. The fatigue effect, caused by the deviation from the normal distribution that was described by the kurtosis parameter, on the fatigue life of aluminum alloy 6082 was presented. An analysis revealed the different amplitude probability distributions for the loading signal and the recorded deformation signal. It was concluded that there was a lack of sensitivity of the numerical model to the change in the kurtosis parameter of the distribution of random loads.

Efficient Spectral Allocation for Cognitive Full Duplex Relay Network Systems Based Soft Computing Technique

Background: Due to the huge development of wireless devices and mobile data traffic had gained attention towards identifying accurate solutions for more proficient utilization of the wireless spectrum. An essential issue confronting the future in wireless systems is to identify the appropriate spectrum bands to satisfy the request of future administrations. While the greater part of the radio spectrum is allocated to various services, applications and users show that spectrum usage is quite low. Materials and Methods: The spectrum sensing is performed at the start of each time slot before the data transmission. As a promising framework to improve the spectrum utilization, Cognitive Radio (CR) technique has the immense potential to meet such a necessity by permitting unlicensed users to exist together in licensed bands. In this paper Cognitive radio and Full-Duplex (FD) based two-way relay communications are developed to enhance spectrum utilization for multichannel and to decrease the false alarm rate. Results: To solve the optimization problems in spectral efficiency, soft computing techniques is proposed to minimize the self-interference and delay to the licensed users. In this proposed work the kurtosis parameter is used for channel detection to determine whether the signal is present or not. Conclusion: The performance results of the proposed method are evaluated in terms of spectral allocation and outage probability which achieves better performance than the existing Multi- Objective Genetic Algorithm (MOGA) optimization.

Reconstruction of the ground-layer adaptive-optics point spread function for MUSE wide field mode observations

Context. Here we describe a simple, efficient, and most importantly fully operational point-spread-function (PSF)-reconstruction approach for laser-assisted ground layer adaptive optics (GLAO) in the frame of the Multi Unit Spectroscopic Explorer (MUSE) wide field mode. Aims. Based on clear astrophysical requirements derived by the MUSE team and using the functionality of the current ESO Adaptive Optics Facility we aim to develop an operational PSF-reconstruction (PSFR) algorithm and test it both in simulations and using on-sky data. Methods. The PSFR approach is based on a Fourier description of the GLAO correction to which the specific instrumental effects of MUSE wide field mode (pixel size, internal aberrations, etc.) have been added. It was first thoroughly validated with full end-to-end simulations. Sensitivity to the main atmospheric and AO system parameters was analysed and the code was re-optimised to account for the sensitivity found. Finally, the optimised algorithm was tested and commissioned using more than one year of on-sky MUSE data. Results. We demonstrate with an on-sky data analysis that our algorithm meets all the requirements imposed by the MUSE scientists, namely an accuracy better than a few percent on the critical PSF parameters including full width at half maximum and global PSF shape through the kurtosis parameter of a Moffat function. Conclusions. The PSFR algorithm is publicly available and is used routinely to assess the MUSE image quality for each observation. It can be included in any post-processing activity which requires knowledge of the PSF.

Kurtosis Based Empirical Mode Decomposition for Rolling Bearing Fault Detection

A bearing fault diagnosis approach based on spectral kurtosis and empirical mode decomposition (EMD) is proposed. EMD is a signal decomposition technique, which can adaptively separate a number of intrinsic mode functions (IMFs) from the vibration signal according to the architectural characteristics of the data. The spectral kurtosis parameter takes as signal impulsive indicator. Firstly, EMD is utilized to process the sampling vibration signal. And then spectral kurtosis is calculated to select the optimal intrinsic mode functions, so as to suppress the noise and highlight the transient impact feature. Finally, the envelope spectrum is computed and the fault characteristic is recognized. The experimental results show that the proposed approach can identify bearing defects effectively and provide a reliable method for gearbox fault monitoring and diagnosis.

Adaptive rank tests for location with generalizaed Lambda distribution scores

We propose adaptive rank tests for the location alternative in one sample, using as score function the percentile function of the Generalized Lambda Distribution (GLD ). We give expressions for its eciency as functions of the kurtosis parameters of the distribution used for the score function and those of the sampled distribution. A simulation study shows that the proposed tests maintain its nominal size and that this test using scores functions with small kurtosis parameter, are very ecient for samples coming from distributions with large kurtosis, overtaking the sign test and the Wilcoxon test. Reciprocally, tests which use scores from GLD distributions with large kurtosis are more ecient when the sample comes from GLD distributions with small kurtosis.