scholarly journals Another approach to the evaluation of a certain multivariate compound distribution

2016 ◽  
Vol 24 (3) ◽  
pp. 339-349
Author(s):  
Elena-Gratiela Robe-Voinea ◽  
Raluca Vernic
Keyword(s):  
Fourier Transform ◽  
Probability Function ◽  
Probability Generating Function ◽  
Recursive Formula ◽  
Aggregate Model ◽  
Insurance Portfolio ◽  
Compound Distribution ◽  
Different Types ◽  
New Form ◽  
The Fourier Transform

AbstractIn this work, we consider the multivariate aggregate model introduced in [11], model that takes into account the case when different types of claims affect in the same time an insurance portfolio under some specific assumptions related to the number of claims. For the probability function of the corresponding multivariate compound distribution, [11] obtained an exact recursive formula proved using the properties of the probability generating function. In this paper, we present a new shorter proof of the same formula that we also extend to a new form. Moreover, we present an alternative approximate method to evaluate the compound distribution based on the Fourier transform, and we compare both methods on a numerical example.

scholarly journals Design and construction of a prototype for the analysis of vibrations in an induction motor for the detection of faults

2020 ◽  
pp. 27-33
Author(s):  
Javier Garrido ◽  
Beatris Escobedo-Trujillo ◽  
Guillermo Miguel Martínez-Rodríguez ◽  
Oscar Fernando Silva-Aguilar
Keyword(s):  
Fourier Transform ◽  
Induction Motor ◽  
Wavelet Transforms ◽  
Data Acquisition System ◽  
Time Frequency ◽  
Different Types ◽  
Control Devices ◽  
The Fourier Transform ◽  
And Control ◽  
Types Of Faults

The contribution of this work is to present the design of a prototype integrated by an induction motor, a data acquisition system, accelerometers and control devices for stop and start, to generate and identify different types of faults by means of vibration analysis. in the domain: time, frequency or frequency-time, through the use of the Fourier Transform, Fast Fourier Transform or Wavelet Transforms (wavelet transform). In this prototype, failures can be generated in the induction motor such as: unbalance, different types of misalignment, mechanical looseness, and electrical failures such as broken bars or short-circuited rings, an example of a misalignment failure is presented to show the process of analysis and detection.

scholarly journals Invariants of optimal integration of rapidly oscillatory functions

2021 ◽  
pp. 121-125
Author(s):  
Valeriy Zadiraka ◽  
Liliya Luts ◽  
Inna Shvidchenko
Keyword(s):  
Fourier Transform ◽  
Wavelet Transform ◽  
Computer Technology ◽  
Quadrature Formulas ◽  
Common Elements ◽  
Optimal Integration ◽  
Different Types ◽  
Bessel Transform ◽  
The Fourier Transform ◽  
Computational Resources

The paper presents some common elements (invariants) of optimal integration of rapidly oscillatory functions for the different types of oscillations, in particular, for calculating the Fourier transform from finite functions, wavelet transform, and Bessel transform. Their brief description is given. The application of the invariants allows to increase the potential of quadrature formulas due to the fullest use of apriori information. Invariants form the basis of computer technology of integration of rapidly oscillatory functions with a given accuracy with limited computational resources.

scholarly journals On the Evaluation of the Distribution of a General Multivariate Collective Model: Recursions versus Fast Fourier Transform

Risks ◽  
2018 ◽  
Vol 6 (3) ◽  
pp. 87
Author(s):  
Raluca Vernic
Keyword(s):  
Fourier Transform ◽  
Fast Fourier Transform ◽  
General Model ◽  
Collective Model ◽  
Point Of View ◽  
Recursive Method ◽  
Collective Models ◽  
Numerical Examples ◽  
Compound Distribution ◽  
Different Types

With the purpose of introducing dependence between different types of claims, multivariate collective models have recently gained a lot of attention. However, when it comes to the evaluation of the corresponding compound distribution, the problems increase with the dimensionality of the model. In this paper, we consider a multivariate collective model that generalizes a model already studied from the point of view of recursive and FFT evaluation of its distribution, and we extend the same study to the general model. With the intention to see which method works better for this general model, we compare the recursive method with the FFT technique, and emphasize the advantages and drawbacks of each one, based on numerical examples.

Amplitude Spectra of Fitness Landscapes

1998 ◽  
Vol 01 (01) ◽  
pp. 39-66 ◽  
Author(s):  
Wim Hordijk ◽  
Peter F. Stadler
Keyword(s):  
Fourier Transform ◽  
Topological Structure ◽  
Empirical Studies ◽  
Amplitude Spectrum ◽  
Fitness Landscapes ◽  
Configuration Spaces ◽  
Amplitude Spectra ◽  
Different Types ◽  
Reliable Procedure ◽  
The Fourier Transform

Fitness landscapes can be decomposed into elementary landscapes using a Fourier transform that is determined by the structure of the underlying configuration space. The amplitude spectrum obtained from the Fourier transform contains information about the ruggedness of the landscape. It can be used for classification and comparison purposes. We consider here three very different types of landscapes using both mutation and recombination to define the topological structure of the configuration spaces. A reliable procedure for estimating the amplitude spectra is presented. The method is based on certain correlation functions that are easily obtained from empirical studies of the landscapes.

scholarly journals Strain Sensitivity Enhancement of Broadband Ultrasonic Signals in Plates Using Spectral Phase Filtering

2021 ◽  
Vol 11 (6) ◽  
pp. 2582
Author(s):  
Lucas M. Martinho ◽  
Alan C. Kubrusly ◽  
Nicolás Pérez ◽  
Jean Pierre von der Weid
Keyword(s):  
Fourier Transform ◽  
Guided Waves ◽  
Strain Level ◽  
Energy Concentration ◽  
Short Time Fourier Transform ◽  
Time Frequency ◽  
Frequency Representation ◽  
The Fourier Transform ◽  
Short Time ◽  
Sensitivity Gain

The focused signal obtained by the time-reversal or the cross-correlation techniques of ultrasonic guided waves in plates changes when the medium is subject to strain, which can be used to monitor the medium strain level. In this paper, the sensitivity to strain of cross-correlated signals is enhanced by a post-processing filtering procedure aiming to preserve only strain-sensitive spectrum components. Two different strategies were adopted, based on the phase of either the Fourier transform or the short-time Fourier transform. Both use prior knowledge of the system impulse response at some strain level. The technique was evaluated in an aluminum plate, effectively providing up to twice higher sensitivity to strain. The sensitivity increase depends on a phase threshold parameter used in the filtering process. Its performance was assessed based on the sensitivity gain, the loss of energy concentration capability, and the value of the foreknown strain. Signals synthesized with the time–frequency representation, through the short-time Fourier transform, provided a better tradeoff between sensitivity gain and loss of energy concentration.

Determination of starch crystallinity with the Fourier-transform terahertz spectrometer

2021 ◽  
Vol 262 ◽  
pp. 117928
Author(s):  
Shusaku Nakajima ◽  
Shuhei Horiuchi ◽  
Akifumi Ikehata ◽  
Yuichi Ogawa
Keyword(s):  
Fourier Transform ◽  
The Fourier Transform ◽  
Starch Crystallinity
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