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Journal articles on the topic 'Fractional moments'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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1

Novi Inverardi, Pierluigi, Giorgio Pontuale, Alberto Petri, and Aldo Tagliani. "Hausdorff moment problem via fractional moments." Applied Mathematics and Computation 144, no. 1 (2003): 61–74. http://dx.doi.org/10.1016/s0096-3003(02)00391-0.

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2

Gzyl, H., and A. Tagliani. "Hausdorff moment problem and fractional moments." Applied Mathematics and Computation 216, no. 11 (2010): 3319–28. http://dx.doi.org/10.1016/j.amc.2010.04.059.

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3

Gzyl, H., and A. Tagliani. "Stieltjes moment problem and fractional moments." Applied Mathematics and Computation 216, no. 11 (2010): 3307–18. http://dx.doi.org/10.1016/j.amc.2010.04.057.

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4

Novi Inverardi, Pierluigi, Alberto Petri, Giorgio Pontuale, and Aldo Tagliani. "Stieltjes moment problem via fractional moments." Applied Mathematics and Computation 166, no. 3 (2005): 664–77. http://dx.doi.org/10.1016/j.amc.2004.06.060.

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5

Johansen, Søren, and Morten Ørregaard Nielsen. "A NECESSARY MOMENT CONDITION FOR THE FRACTIONAL FUNCTIONAL CENTRAL LIMIT THEOREM." Econometric Theory 28, no. 3 (2011): 671–79. http://dx.doi.org/10.1017/s0266466611000697.

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We discuss the moment condition for the fractional functional central limit theorem (FCLT) for partial sums of xt = Δ−dut, where $d\, \in \,\left({ - {1 \over 2}\,,\,{1 \over 2}} \right)$ is the fractional integration parameter and ut is weakly dependent. The classical condition is existence of q ≥ 2 and $q\, > \,\left( {d\, + \,{1 \over 2}} \right)^{ - 1} $ moments of the innovation sequence. When d is close to $ - {1 \over 2}$ this moment condition is very strong. Our main result is to show that when $d\, \in \,\left({ - \,{1 \over 2},\,0} \right)$ and under some relatively weak condition

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6

Ninh, Anh, and András Prékopa. "The discrete moment problem with fractional moments." Operations Research Letters 41, no. 6 (2013): 715–18. http://dx.doi.org/10.1016/j.orl.2013.09.001.

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7

Tagliani, A. "Hausdorff moment problem and fractional moments: A simplified procedure." Applied Mathematics and Computation 218, no. 8 (2011): 4423–32. http://dx.doi.org/10.1016/j.amc.2011.10.019.

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8

Dutt, Vinayak, and James F. Greenleaf. "Speckle Analysis Using Signal to Noise Ratios Based on Fractional Order Moments." Ultrasonic Imaging 17, no. 4 (1995): 251–68. http://dx.doi.org/10.1177/016173469501700401.

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The SNR (signal-to-noise ratio) of the echo envelope image is a monotonically-increasing function of scatterer number density. Various SNRs, like amplitude SNR and intensity SNR, can be used to quantify the scatterer density. The problem of using a SNR based on higher order moments like the intensity SNR is that they require large sample sizes to obtain estimates with high confidence (the variance of the estimate becomes large for higher moments). In this paper, we consider SNRs based on fractional order moments (moments of order less than 1), and obtain mathematical analyses of their properti

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9

Gholizadeh, Mahdieh, Mohammad Hossein Gholizadeh, Hossein Ghayoumi Zadeh, and Mostafa Danaeian. "The noise reduction of medical radiography images using fractional moments." Medical Journal of Tabriz University of Medical Sciences and Health Services 42, no. 6 (2021): 649–58. http://dx.doi.org/10.34172/mj.2021.005.

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Background: This paper presents a method to improve medical radiography images based on the use of statistical signal moments. Methods: In this paper, the image with noise is considered as a statistical signal, and the noise reduction is performed by using fractional moments. The fractional moment’s method, on the one hand, has a speed similar to the moment method, and, on the other hand, has not the limitations of the moment method, which sometimes achieves inaccurate results. The proposed method is ultimately examined on radiographic images (CT). Results: The information obtained from the fr

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10

Farouk, R. M. "Image Reconstruction Based on Novel Sets of Generalized Orthogonal Moments." Journal of Imaging 6, no. 6 (2020): 54. http://dx.doi.org/10.3390/jimaging6060054.

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In this work, we have presented a general framework for reconstruction of intensity images based on new sets of Generalized Fractional order of Chebyshev orthogonal Moments (GFCMs), a novel set of Fractional order orthogonal Laguerre Moments (FLMs) and Generalized Fractional order orthogonal Laguerre Moments (GFLMs). The fractional and generalized recurrence relations of fractional order Chebyshev functions are defined. The fractional and generalized fractional order Laguerre recurrence formulas are given. The new presented generalized fractional order moments are tested with the existing orth

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11

Alieva, T., and M. J. Bastiaans. "On fractional Fourier transform moments." IEEE Signal Processing Letters 7, no. 11 (2000): 320–23. http://dx.doi.org/10.1109/97.873570.

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12

Dzhabbarov, I. Sh. "Fractional moments of the ?-function." Mathematical Notes of the Academy of Sciences of the USSR 38, no. 4 (1985): 771–78. http://dx.doi.org/10.1007/bf01158400.

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13

Hristova, Snezhana, and Krasimira Ivanova. "Caputo Fractional Differential Equations with Non-Instantaneous Random Erlang Distributed Impulses." Fractal and Fractional 3, no. 2 (2019): 28. http://dx.doi.org/10.3390/fractalfract3020028.

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The p-moment exponential stability of non-instantaneous impulsive Caputo fractional differential equations is studied. The impulses occur at random moments and their action continues on finite time intervals with initially given lengths. The time between two consecutive moments of impulses is the Erlang distributed random variable. The study is based on Lyapunov functions. The fractional Dini derivatives are applied.

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14

Agarwal, Ravi, Snezhana Hristova, Donal O’Regan, and Peter Kopanov. "p-Moment Mittag–Leffler Stability of Riemann–Liouville Fractional Differential Equations with Random Impulses." Mathematics 8, no. 8 (2020): 1379. http://dx.doi.org/10.3390/math8081379.

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Fractional differential equations with impulses arise in modeling real world phenomena where the state changes instantaneously at some moments. Often, these instantaneous changes occur at random moments. In this situation the theory of Differential equations has to be combined with Probability theory to set up the problem correctly and to study the properties of the solutions. We study the case when the time between two consecutive moments of impulses is exponentially distributed. In connection with the application of the Riemann–Liouville fractional derivative in the equation, we define in an

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15

Farouk, R. M., and Qamar A. A. Awad. "Image representation based on fractional order Legendre and Laguerre orthogonal moments." International Journal of ADVANCED AND APPLIED SCIENCES 8, no. 2 (2021): 54–59. http://dx.doi.org/10.21833/ijaas.2021.02.007.

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In this paper, we have introduced new sets of fractional order orthogonal basis moments based on Fractional order Legendre orthogonal Functions (FLeFs) and Fractional order Laguerre orthogonal Functions (FLaFs) for image representation. We have generated a novel set of Fractional order Legendre orthogonal Moments (FLeMs) from fractional order Legendre orthogonal functions and a new set of Fractional order Laguerre orthogonal Moments (FLaMs) from the fractional order Laguerre orthogonal functions. The new presented sets of (FLeMs) and (FLaMs) are tested with the recently introduced Fractional o

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16

Nolan, John P. "Truncated fractional moments of stable laws." Statistics & Probability Letters 137 (June 2018): 312–18. http://dx.doi.org/10.1016/j.spl.2018.02.009.

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17

Fomenko, O. M. "Fractional moments of automorphic $L$-functions." St. Petersburg Mathematical Journal 22, no. 2 (2011): 321. http://dx.doi.org/10.1090/s1061-0022-2011-01143-4.

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18

Taufer, Emanuele, Sudip Bose, and Aldo Tagliani. "Optimal predictive densities and fractional moments." Applied Stochastic Models in Business and Industry 25, no. 1 (2009): 57–71. http://dx.doi.org/10.1002/asmb.721.

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19

Heath-Brown, D. R. "Fractional moments of Dirichlet L-functions." Acta Arithmetica 145, no. 4 (2010): 397–409. http://dx.doi.org/10.4064/aa145-4-5.

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20

Boyarinov, R. N. "On fractional moments of random variables." Doklady Mathematics 83, no. 1 (2011): 53–55. http://dx.doi.org/10.1134/s1064562411010145.

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21

Viselter, Ami. "Generalized Widder Theorem via fractional moments." Journal of Functional Analysis 256, no. 2 (2009): 594–602. http://dx.doi.org/10.1016/j.jfa.2008.08.002.

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22

Wang, Chunpeng, Hongling Gao, Meihong Yang, Jian Li, Bin Ma, and Qixian Hao. "Invariant Image Representation Using Novel Fractional-Order Polar Harmonic Fourier Moments." Sensors 21, no. 4 (2021): 1544. http://dx.doi.org/10.3390/s21041544.

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Continuous orthogonal moments, for which continuous functions are used as kernel functions, are invariant to rotation and scaling, and they have been greatly developed over the recent years. Among continuous orthogonal moments, polar harmonic Fourier moments (PHFMs) have superior performance and strong image description ability. In order to improve the performance of PHFMs in noise resistance and image reconstruction, PHFMs, which can only take integer numbers, are extended to fractional-order polar harmonic Fourier moments (FrPHFMs) in this paper. Firstly, the radial polynomials of integer-or

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23

Ossant, Frédéric, Frédéric Patat, Matthias Lebertre, Marie-Laure Teriierooiterai, and Léandre Pourcelot. "Effective Density Estimators Based on the K Distribution: Interest of Low and Fractional Order Moments." Ultrasonic Imaging 20, no. 4 (1998): 243–59. http://dx.doi.org/10.1177/016173469802000402.

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The K distribution is an efficient model to the nonRayleigh statistics of the envelope of backscattered signals in random media. This modeling leads to estimate a parameter of effective density by means of the calculation of statistical moments of the envelope signal. In this study, we propose a mathematical analysis of an effective density estimator previously used and based on superior order moments. In order to improve the effective density estimate, we propose several estimators based on low and fractional order moments. The performances of these estimators are evaluated both with simulate

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24

Shiga, Tokuzo, Akinobu Shimizu, and Takahiro Soshi. "Passage-Time Moments for Positively Recurrent Markov Chains." Nagoya Mathematical Journal 162 (June 2001): 169–85. http://dx.doi.org/10.1017/s0027763000007856.

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Fractional moments of the passage-times are considered for positively recurrent Markov chains with countable state spaces. A criterion of the finiteness of the fractional moments is obtained in terms of the convergence rate of the transition probability to the stationary distribution. As an application it is proved that the passage time of a direct product process of Markov chains has the same order of the fractional moments as that of the single Markov chain.

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25

Ramachandra, K. "Fractional moments of the Riemann zeta-function." Acta Arithmetica 78, no. 3 (1997): 255–65. http://dx.doi.org/10.4064/aa-78-3-255-265.

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26

Bingham, N. H., and G. Tenenbaum. "Riesz and Valiron means and fractional moments." Mathematical Proceedings of the Cambridge Philosophical Society 99, no. 1 (1986): 143–49. http://dx.doi.org/10.1017/s0305004100064033.

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27

Matsui, Muneya, and Zbyněk Pawlas. "Fractional absolute moments of heavy tailed distributions." Brazilian Journal of Probability and Statistics 30, no. 2 (2016): 272–98. http://dx.doi.org/10.1214/15-bjps280.

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28

Novi Inverardi, P. L., and A. Tagliani. "Maximum Entropy Density Estimation from Fractional Moments." Communications in Statistics - Theory and Methods 32, no. 2 (2003): 327–45. http://dx.doi.org/10.1081/sta-120018189.

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29

Xu, Shujiang, Qixian Hao, Bin Ma, Chunpeng Wang, and Jian Li. "Accurate Computation of Fractional-Order Exponential Moments." Security and Communication Networks 2020 (August 3, 2020): 1–16. http://dx.doi.org/10.1155/2020/8822126.

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Exponential moments (EMs) are important radial orthogonal moments, which have good image description ability and have less information redundancy compared with other orthogonal moments. Therefore, it has been used in various fields of image processing in recent years. However, EMs can only take integer order, which limits their reconstruction and antinoising attack performances. The promotion of fractional-order exponential moments (FrEMs) effectively alleviates the numerical instability problem of EMs; however, the numerical integration errors generated by the traditional calculation methods

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30

Gzyl, Henryk, Pier Luigi Novi Inverardi, and Aldo Tagliani. "Fractional Moments and Maximum Entropy: Geometric Meaning." Communications in Statistics - Theory and Methods 43, no. 17 (2014): 3596–601. http://dx.doi.org/10.1080/03610926.2012.705212.

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31

Zhang, Yong. "Moments for Tempered Fractional Advection-Diffusion Equations." Journal of Statistical Physics 139, no. 5 (2010): 915–39. http://dx.doi.org/10.1007/s10955-010-9965-0.

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32

Xiao, Bin, Linping Li, Yu Li, Weisheng Li, and Guoyin Wang. "Image analysis by fractional-order orthogonal moments." Information Sciences 382-383 (March 2017): 135–49. http://dx.doi.org/10.1016/j.ins.2016.12.011.

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33

Fomenko, O. M. "Fractional moments of automorhic L-FUNCTIONS. II." Journal of Mathematical Sciences 178, no. 2 (2011): 219–26. http://dx.doi.org/10.1007/s10958-011-0541-1.

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34

Kacenas, A., A. Laurincikas, and S. Zamarys. "On Fractional Moments of Dirichlet L-Functions." Lithuanian Mathematical Journal 45, no. 2 (2005): 173–91. http://dx.doi.org/10.1007/s10986-005-0022-7.

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35

TARASOV, VASILY E. "MULTIPOLE MOMENTS OF FRACTAL DISTRIBUTION OF CHARGES." Modern Physics Letters B 19, no. 22 (2005): 1107–18. http://dx.doi.org/10.1142/s0217984905009122.

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In this paper we consider the electric multipole moments of fractal distribution of charges. To describe fractal distribution, we use the fractional integrals. The fractional integrals are considered as approximations of integrals on fractals. In the paper we compute the electric multipole moments for homogeneous fractal distribution of charges.

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36

Mikosch, Thomas, Gennady Samorodnitsky, and Laleh Tafakori. "Fractional Moments of Solutions to Stochastic Recurrence Equations." Journal of Applied Probability 50, no. 04 (2013): 969–82. http://dx.doi.org/10.1017/s0021900200013747.

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In this paper we study the fractional moments of the stationary solution to the stochastic recurrence equationXt=AtXt−1+Bt,t∈Z, where ((At,Bt))t∈Zis an independent and identically distributed bivariate sequence. We derive recursive formulae for the fractional moments E|X0|p,p∈R. Special attention is given to the case whenBthas an Erlang distribution. We provide various approximations to the moments E|X0|pand show their performance in a small numerical study.

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37

Mikosch, Thomas, Gennady Samorodnitsky, and Laleh Tafakori. "Fractional Moments of Solutions to Stochastic Recurrence Equations." Journal of Applied Probability 50, no. 4 (2013): 969–82. http://dx.doi.org/10.1239/jap/1389370094.

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In this paper we study the fractional moments of the stationary solution to the stochastic recurrence equation Xt = AtXt−1 + Bt, t ∈ Z, where ((At, Bt))t∈Z is an independent and identically distributed bivariate sequence. We derive recursive formulae for the fractional moments E|X0|p, p ∈ R. Special attention is given to the case when Bt has an Erlang distribution. We provide various approximations to the moments E|X0|p and show their performance in a small numerical study.

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38

Gzyl, H., and A. Tagliani. "Recovering a distribution from its translated fractional moments." Statistics & Probability Letters 118 (November 2016): 171–76. http://dx.doi.org/10.1016/j.spl.2016.06.024.

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39

Knight, John L. "Moments of OLS and 2SLS via Fractional Calculus." Econometric Theory 2, no. 2 (1986): 291–93. http://dx.doi.org/10.1017/s0266466600011580.

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40

Bastiaans, Martin J., and Tatiana Alieva. "Wigner distribution moments in fractional Fourier transform systems." Journal of the Optical Society of America A 19, no. 9 (2002): 1763. http://dx.doi.org/10.1364/josaa.19.001763.

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41

Nigmatullin, R. R. "Fractional moments. New source of information in radiospectroscopy." physica status solidi (b) 133, no. 2 (1986): 713–20. http://dx.doi.org/10.1002/pssb.2221330234.

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42

Éminyan, K. M. "Estimate of Fractional Moments of a Trigonometric Sum." Mathematical Notes 76, no. 1/2 (2004): 291–95. http://dx.doi.org/10.1023/b:matn.0000036767.14036.76.

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43

HEATH-BROWN, D. R. "FRACTIONAL MOMENTS OF THE RIEMANN ZETA-FUNCTION, II." Quarterly Journal of Mathematics 44, no. 2 (1993): 185–97. http://dx.doi.org/10.1093/qmath/44.2.185.

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44

Zamarys, S. "On fractional moments of Dirichlet L-functions, II." Lithuanian Mathematical Journal 46, no. 4 (2006): 494–508. http://dx.doi.org/10.1007/s10986-006-0045-8.

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45

Zamarys, S. "On fractional moments of Dirichlet L-functions. III." Lithuanian Mathematical Journal 47, no. 2 (2007): 228–41. http://dx.doi.org/10.1007/s10986-007-0016-8.

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46

Wang, Chunpeng, Qixian Hao, Bin Ma, Jian Li, and Hongling Gao. "Fractional-order quaternion exponential moments for color images." Applied Mathematics and Computation 400 (July 2021): 126061. http://dx.doi.org/10.1016/j.amc.2021.126061.

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47

Yan, Litan, and Xianye Yu. "Asymptotic Behavior for High Moments of the Fractional Heat Equation with Fractional Noise." Journal of Theoretical Probability 32, no. 4 (2019): 1617–46. http://dx.doi.org/10.1007/s10959-019-00899-9.

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48

Dong, Keqiang, and Xiaofang Zhang. "Multiscale Fractional Cumulative Residual Entropy of Higher-Order Moments for Estimating Uncertainty." Fluctuation and Noise Letters 19, no. 04 (2020): 2050038. http://dx.doi.org/10.1142/s0219477520500388.

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The fractional cumulative residual entropy is not only a powerful tool for the analysis of complex system, but also a promising way to analyze time series. In this paper, we present an approach to measure the uncertainty of non-stationary time series named higher-order multiscale fractional cumulative residual entropy. We describe how fractional cumulative residual entropy may be calculated based on second-order, third-order, fourth-order statistical moments and multiscale method. The implementation of higher-order multiscale fractional cumulative residual entropy is illustrated with simulated

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49

Benouini, Rachid, Imad Batioua, Khalid Zenkouar, Azeddine Zahi, Said Najah, and Hassan Qjidaa. "Fractional-order orthogonal Chebyshev Moments and Moment Invariants for image representation and pattern recognition." Pattern Recognition 86 (February 2019): 332–43. http://dx.doi.org/10.1016/j.patcog.2018.10.001.

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50

Di Paola, Mario, and Francesco Paolo Pinnola. "Riesz fractional integrals and complex fractional moments for the probabilistic characterization of random variables." Probabilistic Engineering Mechanics 29 (July 2012): 149–56. http://dx.doi.org/10.1016/j.probengmech.2011.11.003.

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