Journal articles: 'MOMENTS METHOD'

1

Jurczek, E. "Orthogonalized-moments method." Physical Review B 32, no. 6 (September 15, 1985): 4208–11. http://dx.doi.org/10.1103/physrevb.32.4208.

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Morrison, Hugh, Matthew R. Kumjian, Charlotte P. Martinkus, Olivier P. Prat, and Marcus van Lier-Walqui. "A General N-Moment Normalization Method for Deriving Raindrop Size Distribution Scaling Relationships." Journal of Applied Meteorology and Climatology 58, no. 2 (February 2019): 247–67. http://dx.doi.org/10.1175/jamc-d-18-0060.1.

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AbstractA general drop size distribution (DSD) normalization method is formulated in terms of generalized power series relating any DSD moment to any number and combination of reference moments. This provides a consistent framework for comparing the variability of normalized DSD moments using different sets of reference moments, with no explicit assumptions about the DSD functional form (e.g., gamma). It also provides a method to derive any unknown moment plus an estimate of its uncertainty from one or more known moments, which is relevant to remote sensing retrievals and bulk microphysics schemes in weather and climate models. The approach is applied to a large dataset of disdrometer-observed and bin microphysics-modeled DSDs. As expected, the spread of normalized moments decreases as the number of reference moments is increased, quantified by the logarithmic standard deviation of the normalized moments, σ. Averaging σ for all combinations of reference moments and normalized moments of integer order 0–10, 42.9%, 81.3%, 93.7%, and 96.9% of spread are accounted for applying one-, two-, three-, and four-moment normalizations, respectively. Thus, DSDs can be well characterized overall using three reference moments, whereas adding a fourth reference moment contributes little independent information. The spread of disdrometer-observed DSD moments from uncertainty associated with drop count statistics generally lies between values of σ using two- and three-moment normalizations. However, this uncertainty has little impact on the derived DSD scaling relationships or σ when considered.

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Kliche, Donna V., Paul L. Smith, and Roger W. Johnson. "L-Moment Estimators as Applied to Gamma Drop Size Distributions." Journal of Applied Meteorology and Climatology 47, no. 12 (December 1, 2008): 3117–30. http://dx.doi.org/10.1175/2008jamc1936.1.

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Abstract The traditional approach with experimental raindrop size data has been to use the method of moments in the fitting procedure to estimate the parameters for the raindrop size distribution function. However, the moment method is known to be biased and can have substantial errors. Therefore, the L-moment method, which is widely used by hydrologists, was investigated as an alternative. The L-moment method was applied, along with the moment and maximum likelihood methods, to samples taken from simulated gamma raindrop populations. A comparison of the bias and the errors involved in the L-moments, moments, and maximum likelihood procedures shows that, with samples covering the full range of drop sizes, L-moments and maximum likelihood outperform the method of moments. For small sample sizes the moment method gives a large bias and large error while the L-moment method gives results close to the true population values, outperforming even maximum likelihood results. Because the goal of this work is to understand the properties of the various fitting procedures, the investigation was expanded to include the effects of the absence of small drops in the samples (typical disdrometer minimum size thresholds are 0.3–0.5 mm). The results show that missing small drops (due to the instrumental constraint) can result in a large bias in the case of the L-moment and maximum likelihood fitting methods; this bias does not decrease much with increasing sample size. Because the very small drops have a negligible contribution to moments of order 2 or higher, the bias in the moment methods seems to be about the same as in the case of full samples. However, when moments of order less than 2 are needed (as in the case of modelers using moments 0 and 3), the moment method gives much larger bias. Therefore a modification of these methods is needed to handle the truncated-data situation.

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Headrick, Todd C. "A Characterization of Power Method Transformations throughL-Moments." Journal of Probability and Statistics 2011 (2011): 1–22. http://dx.doi.org/10.1155/2011/497463.

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Power method polynomial transformations are commonly used for simulating continuous nonnormal distributions with specified moments. However, conventional moment-based estimators can (a) be substantially biased, (b) have high variance, or (c) be influenced by outliers. In view of these concerns, a characterization of power method transformations byL-moments is introduced. Specifically, systems of equations are derived for determining coefficients for specifiedL-moment ratios, which are associated with standard normal and standard logistic-based polynomials of order five and three. Boundaries forL-moment ratios are also derived, and closed-formed formulae are provided for determining if a power method distribution has a valid probability density function. It is demonstrated thatL-moment estimators are nearly unbiased and have relatively small variance in the context of the power method. Examples of fitting power method distributions to theoretical and empirical distributions based on the method ofL-moments are also provided.

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Jiade Yuan, Changqing Gu, and Guodong Han. "Efficient Generation of Method of Moments Matrices Using Equivalent Dipole-Moment Method." IEEE Antennas and Wireless Propagation Letters 8 (2009): 716–19. http://dx.doi.org/10.1109/lawp.2009.2024337.

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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 (February 24, 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 fractional moments of the received signal is a criterion to estimate the noise parameters and the gray scales of the main image. One of the limitations of the proposed method is that the image should be sent several times, because in statistical discussions, we cannot make a decision with only one sample. The error of the proposed noise reduction method in terms of the number of times the original image was sent, is about 0.009, 0.0009, 0.0002, and 0.0001, for n = 3, n = 6, n = 9 and n = 14, respectively. Conclusion: The simulation results show that the proposed method is more effective than the most conventional noise reduction methods, both in the low signal to noise ratio and in terms of image quality, and is more powerful than the most notable noise removal methods in restoring the subtleties and image details.

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Dell'Aquila, Rosario. "Generalized Method of Moments." Journal of the American Statistical Association 101, no. 475 (September 2006): 1309–10. http://dx.doi.org/10.1198/jasa.2006.s120.

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Benoit, C., E. Royer, and G. Poussigue. "The spectral moments method." Journal of Physics: Condensed Matter 4, no. 12 (March 23, 1992): 3125–52. http://dx.doi.org/10.1088/0953-8984/4/12/010.

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Mat Jan, Nur Amalina, Ani Shabri, and Ruhaidah Samsudin. "Handling non-stationary flood frequency analysis using TL-moments approach for estimation parameter." Journal of Water and Climate Change 11, no. 4 (August 16, 2019): 966–79. http://dx.doi.org/10.2166/wcc.2019.055.

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Abstract Non-stationary flood frequency analysis (NFFA) plays an important role in addressing the issue of the stationary assumption (independent and identically distributed flood series) that is no longer valid in infrastructure-designed methods. This confirms the necessity of developing new statistical models in order to identify the change of probability functions over time and obtain a consistent flood estimation method in NFFA. The method of Trimmed L-moments (TL-moments) with time covariate is confronted with the L-moment method for the stationary and non-stationary generalized extreme value (GEV) models. The aims of the study are to investigate the behavior of the proposed TL-moments method in the presence of NFFA and applying the method along with GEV distribution. Comparisons of the methods are made by Monte Carlo simulations and bootstrap-based method. The simulation study showed the better performance of most levels of TL-moments method, which is TL(η,0), (η = 2, 3, 4) than the L-moment method for all models (GEV1, GEV2, and GEV3). The TL-moment method provides more efficient quantile estimates than other methods in flood quantiles estimated at higher return periods. Thus, the TL-moments method can produce better estimation results since the L-moment eliminates lowest value and gives more weight to the largest value which provides important information.

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HOSNY, KHALID M. "EFFICIENT COMPUTATION OF LEGENDRE MOMENTS FOR GRAY LEVEL IMAGES." International Journal of Image and Graphics 07, no. 04 (October 2007): 735–47. http://dx.doi.org/10.1142/s021946780700288x.

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Direct computation of Legendre orthogonal moments requires huge arithmetic operations, which is very time consuming. Many works have described methods for reducing the computations involved in evaluating Legendre moments. Nevertheless, reduction computational complexity is still an open problem and needs more investigation. Existing algorithms mainly focused on binary images and compute Legendre moments using a set of geometric moments. We propose a fast and efficient method for computation of Legendre moments for binary and gray level images. A recurrence formula of one-dimensional Legendre moments will be established using the recursive property of Legendre polynomials; then the method will be extended to calculate the two-dimensional Legendre moments. This method is completely independent on geometric moment. The complexity analysis shows that the proposed method computes Legendre moments more efficiently than the direct method and the other conventional methods.

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GOH, HOCK-ANN, CHEE-WAY CHONG, ROSLI BESAR, FAZLY SALLEH ABAS, and KOK-SWEE SIM. "TRANSLATION AND SCALE INVARIANTS OF HAHN MOMENTS." International Journal of Image and Graphics 09, no. 02 (April 2009): 271–85. http://dx.doi.org/10.1142/s0219467809003435.

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Hahn moments are a superset of Tchebichef and Krawtchouk moments. The formulation for Hahn moments is however comparably more complex than other moments. So far only research work on translation and scale invariants for Tchebichef moments has been presented but not on Hahn moments. In this paper, a moment normalization method to achieve translation and scale invariants of Hahn moments is proposed. This method applies the concept of mapping functions used in image normalization. The mapping functions, once determined, are plugged into the moment generating functions to generate moment invariants. The proposed method is simpler and flexible. Experimental results show that faster execution and more precise moment invariants can be achieved using the invariant generating functions.

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Wang, Shi Long, Yu Ru Xu, Lei Wan, and Xu Dong Tang. "A New Feature Extraction Method for Underwater Targets." Advanced Materials Research 171-172 (December 2010): 518–22. http://dx.doi.org/10.4028/www.scientific.net/amr.171-172.518.

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in the complex underwater environment, underwater images are taken by special underwater CCD camera and its S/N is low and the edge is fuzzy. For the four types of characteristic underwater targets, the novel moments called relative boundary moments are proposed, and the affine invariants of discrete moments are constructed. With scale, translating and rotating invariance, the moments can be used as the descriptors of the samples. Experimental results show that compared with the traditional regional moments, the new moment invariants not only can reduce the calculation in data processing to a large extent, but also improve the robustness and timeliness for engineering applications. When applying to the practical engineering, that is particularly approval for AUV to complete a certain mission.

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Ding, Jiu, Noah H. Rhee, and Chenhua Zhang. "On Polynomial Maximum Entropy Method for Classical Moment Problem." Advances in Applied Mathematics and Mechanics 8, no. 1 (December 21, 2015): 117–27. http://dx.doi.org/10.4208/aamm.2014.m504.

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AbstractThe maximum entropy method for the Hausdorff moment problem suffers from ill conditioning as it uses monomial basis {1,x,x2,...,xn}. The maximum entropy method for the Chebyshev moment probelm was studied to overcome this drawback in. In this paper we review and modify the maximum entropy method for the Hausdorff and Chebyshev moment problems studied in and present the maximum entropy method for the Legendre moment problem. We also give the algorithms of converting the Hausdorff moments into the Chebyshev and Lengendre moments, respectively, and utilizing the corresponding maximum entropy method.

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Mačiūnas, Darius, Rimantas Belevičius, and Juozas Kaunas. "MULTI-OBJECTIVE OPTIMIZATION OF GRILLAGES APPLYING THE GENETIC ALGORITHM / DAUGIAKRITERIS SIJYNŲ OPTIMIZAVIMAS GENETINIAIS ALGORITMAIS." Mokslas - Lietuvos ateitis 3, no. 6 (January 3, 2012): 47–52. http://dx.doi.org/10.3846/mla.2011.110.

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The article analyzes the optimization of grillage-type foundations seeking for the least possible reactive forces in the poles for a given number of poles and for the least possible bending moments of absolute values in the connecting beams of the grillage. Therefore, we suggest using a compromise objective function (to be minimized) that consists of the maximum reactive force arising in all poles and the maximum bending moment of the absolute value in connecting beams; both components include the given weights. The variables of task design are pole positions under connecting beams. The optimization task is solved applying the algorithm containing all the initial data of the problem. Reactive forces and bending moments are calculated using an original program (finite element method is applied). This program is integrated into the optimization algorithm using the “black-box” principle. The “black-box” finite element program sends back the corresponding value of the objective function. Numerical experiments revealed the optimal quantity of points to compute bending moments. The obtained results show a certain ratio of weights in the objective function where the contribution of reactive forces and bending moments to the objective function are equivalent. This solution can serve as a pilot project for more detailed design. Santrauka Straipsnyje nagrinėjamas rostverkinių pamatų optimizavimas, siekiant kuo mažesnių reaktyvinių jėgų poliuose duotajam polių skaičiui ir kuo mažesnių absoliutiniu dydžiu lenkimo momentų sijyno jungiančiosiose sijose. Optimizavimo uždavinio tikslo funkciją sudaro didžiausia visuose poliuose atraminė reakcija ir didžiausias absoliutiniu dydžiu lenkimo momentas jungiančiosiose sijose; abu dėmenys imami su tam tikrais svoriais. Uždavinio projektavimo kintamieji yra polių padėtys po jungiančiosiomis sijomis. Optimizavimo uždavinys sprendžiamas genetiniu algoritmu, į kurio formulavimą įtraukiama išankstinė žinoma informacija apie uždavinį. Reakcijų ir momentų skaičiavimo uždavinys skaičiuojamas baigtinių elementų metodu. Ši programa jungiama prie optimizavimo algoritmo juodosios dėžės principu. Optimaliam taškų, kuriuose skaičiuojami lenkimo momentai, skaičiui nustatyti atliekami skaitiniai eksperimentai. Skaitiniais eksperimentais nustatytos sąlygos, kurioms esant reakcija ir momentas turi ekvivalentišką įtaką tikslo funkcijai. Tokie skaičiavimai galėtų būti kaip bandomieji sprendiniai detaliau projektuojant sijyną.

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15

Fox, Rodney O. "Optimal Moment Sets for Multivariate Direct Quadrature Method of Moments." Industrial & Engineering Chemistry Research 48, no. 21 (November 4, 2009): 9686–96. http://dx.doi.org/10.1021/ie801316d.

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Andrews, Donald W. K. "Consistent Moment Selection Procedures for Generalized Method of Moments Estimation." Econometrica 67, no. 3 (May 1999): 543–63. http://dx.doi.org/10.1111/1468-0262.00036.

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Xiao, Zhiguo. "The weighted method of moments approach for moment condition models." Economics Letters 107, no. 2 (May 2010): 183–86. http://dx.doi.org/10.1016/j.econlet.2010.01.019.

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Deju, L., S. C. P. Cheung, G. H. Yeoh, and J. Tu. "Study of Isothermal Vertical Bubbly Flow Using Direct Quadrature Method of Moments." Journal of Computational Multiphase Flows 4, no. 1 (March 2012): 23–39. http://dx.doi.org/10.1260/1757-482x.4.1.23.

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In the numerical study, investigation of bubbly flow requires deep understanding of complex hydrodynamics under various flow conditions. In order to simulate the bubble behaviour in conjunction with suitable bubble coalescence and bubble breakage kernels, direct quadrature method of moments (DQMOM) has been applied and validated instead. To examine the predictive results from DQMOM model, the validation has been carried out against experimental data of Lucas et al. (2005) and Prasser et al. (2007) measured in the Forschungszentrum Dresden-Rossendorf FZD facility. Numerical results showed good agreement against experimental data for the local and axial void fraction, bubble size distribution and interfacial area concentration profiles. Encouraging results demonstrates the prospect of the DQMOM two-fluid model against flow conditions with wider range of bubble sizes and rigorous bubble interactions. Moreover, moment sensitivity study also has been carried out to carefully assess the performance of the model. In order to perform the moment sensitivity test three different moment criteria has chosen – as 4 moments, 6 moments and 8 moments. Close agreement between the predictions and measurement was found and it appeared that increasing the number of moments does not have much significance to improve the conformity with experimental data. Nonetheless, increasing the number of moments merely contribute to perform the calculation expensive in terms of computational resource and time. Based on the present study, this preliminary assessment has definitely served to demonstrate and exploit DQMOM model's capabilities to handle wider range of bubble sizes as well as moment resolution required to achieve moment independent solution.

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Afzalifar, Ali, Teemu Turunen-Saaresti, and Aki Grönman. "Non-realisability problem with the conventional method of moments in wet-steam flows." Proceedings of the Institution of Mechanical Engineers, Part A: Journal of Power and Energy 232, no. 5 (October 11, 2017): 473–89. http://dx.doi.org/10.1177/0957650917735955.

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The method of moments offers an efficient way to preserve the essence of particle size distribution, which is required in many engineering problems such as modelling wet-steam flows. However, in the context of the finite volume method, high-order transport algorithms are not guaranteed to preserve the moment space, resulting in so-called ‘non-realisable’ moment sets. Non-realisability poses a serious obstacle to the quadrature-based moment methods, since no size distribution can be identified for a non-realisable moment set and the moment-transport equations cannot be closed. On the other hand, in the case of conventional method of moments, closures to the moment-transport equations are directly calculated from the moments themselves; as such, non-realisability may not be a problem. This article describes an investigation of the effects of the non-realisability problem on the flow conditions and moment distributions obtained by the conventional method of moments through several one-dimensional test cases involving systems that exhibited similar characteristics to low-pressure wet-steam flows. The predictions of pressures and mean droplet sizes were not considerably disturbed due to non-realisability in any of the test cases. However, in one case that was characterised by strong temporal and spatial gradients, non-realisability did undermine the accuracy of the predictions of measures for the underlying size distributions, including the standard deviation and skewness.

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Hu, Yi, Xiaohua Xia, Ying Deng, and Dongmei Guo. "Higher Order Mean Squared Error of Generalized Method of Moments Estimators for Nonlinear Models." Discrete Dynamics in Nature and Society 2014 (2014): 1–8. http://dx.doi.org/10.1155/2014/324904.

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Generalized method of moments (GMM) has been widely applied for estimation of nonlinear models in economics and finance. Although generalized method of moments has good asymptotic properties under fairly moderate regularity conditions, its finite sample performance is not very well. In order to improve the finite sample performance of generalized method of moments estimators, this paper studies higher-order mean squared error of two-step efficient generalized method of moments estimators for nonlinear models. Specially, we consider a general nonlinear regression model with endogeneity and derive the higher-order asymptotic mean square error for two-step efficient generalized method of moments estimator for this model using iterative techniques and higher-order asymptotic theories. Our theoretical results allow the number of moments to grow with sample size, and are suitable for general moment restriction models, which contains conditional moment restriction models as special cases. The higher-order mean square error can be used to compare different estimators and to construct the selection criteria for improving estimator’s finite sample performance.

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Kuersteiner, Guido M., and Laszlo Matyas. "Generalized Method of Moments Estimation." Journal of the American Statistical Association 95, no. 451 (September 2000): 1014. http://dx.doi.org/10.2307/2669498.

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22

Burdett, Jeremy K., and Stephen Lee. "Moments method and elemental structures." Journal of the American Chemical Society 107, no. 11 (May 1985): 3063–82. http://dx.doi.org/10.1021/ja00297a011.

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Reinecke, S., and G. M. Kremer. "Method of moments of Grad." Physical Review A 42, no. 2 (July 1, 1990): 815–20. http://dx.doi.org/10.1103/physreva.42.815.

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Yin, Guosheng. "Bayesian generalized method of moments." Bayesian Analysis 4, no. 2 (June 2009): 191–207. http://dx.doi.org/10.1214/09-ba407.

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Yin, Guosheng, Yanyuan Ma, Faming Liang, and Ying Yuan. "Stochastic Generalized Method of Moments." Journal of Computational and Graphical Statistics 20, no. 3 (January 2011): 714–27. http://dx.doi.org/10.1198/jcgs.2011.09210.

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Čížek, Pavel. "Generalized method of trimmed moments." Journal of Statistical Planning and Inference 171 (April 2016): 63–78. http://dx.doi.org/10.1016/j.jspi.2015.11.004.

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Kormann, U., R. Theodorescu, and H. Wolff. "A dynamic method of moments." Statistics 18, no. 1 (January 1987): 131–40. http://dx.doi.org/10.1080/02331888708802002.

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Bisgaard, Torben Maack. "Method of moments on semigroups." Journal of Theoretical Probability 9, no. 3 (July 1996): 631–45. http://dx.doi.org/10.1007/bf02214079.

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Kiełkiewicz, M. "Accuracy of the moments method." Annals of Nuclear Energy 21, no. 3 (March 1994): 189–93. http://dx.doi.org/10.1016/0306-4549(94)90061-2.

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Ortelli, Claudio, and Fabio Trojani. "Robust efficient method of moments." Journal of Econometrics 128, no. 1 (September 2005): 69–97. http://dx.doi.org/10.1016/j.jeconom.2004.08.008.

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Chatelain, Jean-Bernard. "Improving consistent moment selection procedures for generalized method of moments estimation." Economics Letters 95, no. 3 (June 2007): 380–85. http://dx.doi.org/10.1016/j.econlet.2006.11.011.

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Shen, Hong, Longkun Yu, Xu Jing, and Fengfu Tan. "Method for Measuring the Second-Order Moment of Atmospheric Turbulence." Atmosphere 12, no. 5 (April 28, 2021): 564. http://dx.doi.org/10.3390/atmos12050564.

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The turbulence moment of order m (μm) is defined as the refractive index structure constant Cn2 integrated over the whole path z with path-weighting function zm. Optical effects of atmospheric turbulence are directly related to turbulence moments. To evaluate the optical effects of atmospheric turbulence, it is necessary to measure the turbulence moment. It is well known that zero-order moments of turbulence (μ0) and five-thirds-order moments of turbulence (μ5/3), which correspond to the seeing and the isoplanatic angles, respectively, have been monitored as routine parameters in astronomical site testing. However, the direct measurement of second-order moments of turbulence (μ2) of the whole layer atmosphere has not been reported. Using a star as the light source, it has been found that μ2 can be measured through the covariance of the irradiance in two receiver apertures with suitable aperture size and aperture separation. Numerical results show that the theoretical error of this novel method is negligible in all the typical turbulence models. This method enabled us to monitor μ2 as a routine parameter in astronomical site testing, which is helpful to understand the characteristics of atmospheric turbulence better combined with μ0 and μ5/3.

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Amani Zakaria, Zahrahtul, Jarah Moath Ali Suleiman, and Mumtazimah Mohamad. "Rainfall frequency analysis using LH-moments approach: A case of Kemaman Station, Malaysia." International Journal of Engineering & Technology 7, no. 2.15 (April 6, 2018): 107. http://dx.doi.org/10.14419/ijet.v7i2.15.11363.

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Statistical analysis of extreme events is often carried out to obtain the probability distribution of floods data and then predict the occurrence of floods for a significant return period. L-moments approach is known as the most popular approach in frequency analysis. This paper discusses comparison of the L-moments method with higher order moments (LH-moments) method. LH-moment, a generalization of L-moment, which is proposed based on the linear combinations of higher-order statistics has been used to characterize the upper part of distributions and larger events in flood data. It is observed from a comparative study that the results of the analysis of observed data and the diagram based on the K3D-II distribution using LH-moments method is more efficient and reasonable than the L-moments method for estimating data of the upper part of the distribution events.

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Rao, K. Srinivasa. "Estimation of Parameters of Pert Distribution by Using Method of Moments." International Journal for Research in Applied Science and Engineering Technology 9, no. 9 (September 30, 2021): 1621–29. http://dx.doi.org/10.22214/ijraset.2021.38239.

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Abstract: The method of moments has been widely used for estimating the parameters of a distribution. Usually lower order moments are wont to find the parameter estimates as they're known to possess less sampling variability. The method of moments may be a technique for estimating the parameters of a statistical model. It works by finding values of the parameters that end in a match between the sample moments and therefore the population moments (as implied by the model). the Method of moment Estimator is used to find out Estimates the parameters of PERT Distribution. We also compare equispaced and unequispaced Optimally Constructed Grouped data by the method of an Asymptotically Relative Efficiency. We also computed Average Estimate (AE), Variance (VAR), Standard Deviation (STD), Mean Absolute Deviation (MAD), Mean Square Error (MSE), Simulated Error (SE) and Relative Absolute Bias (RAB) for both the parameters under grouped sample supported 1000 simulations to assess the performance of the estimators. Keywords: Method of Moments, PERT Distribution, equispaced and unequipped Optimal Grouped sample

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Cai, Zhenning, Ruo Li, and Yanli Wang. "Numerical Regularized Moment Method For High Mach Number Flow." Communications in Computational Physics 11, no. 5 (May 2012): 1415–38. http://dx.doi.org/10.4208/cicp.050111.140711a.

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AbstractThis paper is a continuation of our earlier work [SIAM J. Sci. Comput., 32(2010), pp. 2875-2907] in which a numerical moment method with arbitrary order of moments was presented. However, the computation may break down during the calculation of the structure of a shock wave with Mach number M0≥ 3. In this paper, we concentrate on the regularization of the moment systems. First, we apply the Maxwell iteration to the infinite moment system and determine the magnitude of each moment with respect to the Knudsen number. After that, we obtain the approximation of high order moments and close the moment systems by dropping some high-order terms. Linearization is then performed to obtain a very simple regularization term, thus it is very convenient for numerical implementation. To validate the new regularization, the shock structures of low order systems are computed with different shock Mach numbers.

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Liang, Chen Hua, and Qing Chang. "Weighted Modified Hu Moment in Human Behavior Recognition." Advanced Materials Research 765-767 (September 2013): 2603–7. http://dx.doi.org/10.4028/www.scientific.net/amr.765-767.2603.

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t has been shown that the traditional seven Hu invariant moment does not have scaling invariance with low recognition rate in human behavior recognition. In order to improve the recognition rate, a human behavior recognition method will be put forward in this paper based on weighted modified Hu moments. Firstly, the traditional seven Hu moments will be extended to ten Hu moments to get more image details. Then, the extended Hu moments will be modified to make the Hu moments has the feature of scaling invariance. Lastly, the weighted modified Hu moment will be obtained through least squares method based on minimum variance criterion. The simulation of the sequence images shows that the weighted modified Hu moment can improve the recognition rate effectively.

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SUN, YANKUI. "LIFTING CONSTRUCTION OF SPLINE DYADIC WAVELET FILTERS WITH ANY NUMBER OF VANISHING MOMENTS." International Journal of Wavelets, Multiresolution and Information Processing 07, no. 05 (September 2009): 693–710. http://dx.doi.org/10.1142/s0219691309003148.

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The dyadic lifting schemes, which generalize Sweldens lifting schemes, have been applied to design dyadic wavelet with higher number of vanishing moments. But the existing dyadic lifting methods cannot give the free parameters (i.e. lifting factors) explicitly under vanishing moment constraints, and the exact vanishing moments of the lifted wavelet is unknown a priori. This paper provides a solution of these problems for spline dyadic wavelets. It proposes a novel constructive method for lifting constructing spline dyadic wavelets with desirable numbers of vanishing moments. This new lifting construction scheme can be applied to design spline dyadic wavelet filters with any number of vanishing moments starting from one single dyadic wavelet with 1 or 2 vanishing moments. Its computational advantage is that the lifting factor parameters can be chosen and given explicitly under vanishing moment constraints. At the end of this paper, some spline dyadic wavelet filters are designed by using our method.

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Chen, Xing Chong, Zun Wen Liu, Yong Liang Zhang, and Lu Pei. "A Method for Checking Eccentricity of Solid Concrete Piers with Low Longitudinal Reinforcement Ratio under a Minor Earthquake." Applied Mechanics and Materials 580-583 (July 2014): 1515–20. http://dx.doi.org/10.4028/www.scientific.net/amm.580-583.1515.

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Solid concrete piers with low longitudinal reinforcement ratio are extensively used in high-speed railway in China. However, how to check such structures is not specified in current technical codes. Checking these structures by eccentricity and stress indexes is discussed hereby. The moment-curvature relationships for piers of various reinforcement ratios are presented by employing the software UCfyber and these moments are compared with moments calculated by allowable stress approach, moments corresponding to the code-specified permissible eccentricity, moments corresponding to the allowable reinforcement stress and stabilizing moments induced by tensile reinforcement and self-weight of the piers, respectively. The results show that the allowable stress approach could be used to check the strength and eccentricity of solid concrete piers with low longitudinal reinforcement ratio in high-speed railway; the restriction on permissible eccentricity may be to a proper extent relaxed for such piers, based on the fact that tensile reinforcement provides an additional stabilizing moment and the reinforcement contributes to the pier’s bearing capacity.

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VENEZIANO, DANIELE, and PIERLUIGI FURCOLO. "A MODIFIED DOUBLE TRACE MOMENT METHOD OF MULTIFRACTAL ANALYSIS." Fractals 07, no. 02 (June 1999): 181–95. http://dx.doi.org/10.1142/s0218348x99000207.

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The Double Trace Moment method for the estimation of parameters of universal multifractal measures is revisited. It is found that the method applies strictly to bare measures but is approximate for dressed measures, which are the only observable ones. The approximation stems from the fact that the double dressed moments used by the method do not scale as required to produce unbiased estimates of the parameters. Modified moments are proposed, which correctly scale for both bare and dressed measures. The original and modified methods are compared theoretically and numerically. Conditions under which the original method gives accurate and heavily biased estimates are identified.

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Shiea, Mohsen, Antonio Buffo, Marco Vanni, and Daniele Marchisio. "Numerical Methods for the Solution of Population Balance Equations Coupled with Computational Fluid Dynamics." Annual Review of Chemical and Biomolecular Engineering 11, no. 1 (June 7, 2020): 339–66. http://dx.doi.org/10.1146/annurev-chembioeng-092319-075814.

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This review article discusses the solution of population balance equations, for the simulation of disperse multiphase systems, tightly coupled with computational fluid dynamics. Although several methods are discussed, the focus is on quadrature-based moment methods (QBMMs) with particular attention to the quadrature method of moments, the conditional quadrature method of moments, and the direct quadrature method of moments. The relationship between the population balance equation, in its generalized form, and the Euler-Euler multiphase flow models, notably the two-fluid model, is thoroughly discussed. Then the closure problem and the use of Gaussian quadratures to overcome it are analyzed. The review concludes with the presentation of numerical issues and guidelines for users of these modeling approaches.

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Chong, Chee-Way, P. Raveendran, and R. Mukundan. "An Efficient Algorithm for Fast Computation of Pseudo-Zernike Moments." International Journal of Pattern Recognition and Artificial Intelligence 17, no. 06 (September 2003): 1011–23. http://dx.doi.org/10.1142/s0218001403002769.

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Pseudo-Zernike moments have better feature representation capability, and are more robust to image noise than those of the conventional Zernike moments. However, due to the computation complexity of pseudo-Zernike polynomials, pseudo-Zernike moments are yet to be extensively used as feature descriptors as compared to Zernike moments. In this paper, we propose two new algorithms, namely coefficient method and p-recursive method, to accelerate the computation of pseudo-Zernike moments. Coefficient method calculates polynomial coefficients recursively. It eliminates the need of using factorial functions. Individual order or index of pseudo-Zernike moments can be derived independently, which is useful if selected orders or indices of moments are needed as pattern features. p-recursive method uses a combination of lower order polynomials to derive higher order polynomials with the same index q. Fast computation is achieved because it eliminates the requirements of calculating polynomial coefficients, Bpqk, and power of radius, rk, in each polynomial. The performance of the proposed algorithms on moment computation and image reconstruction, as compared to those of the present methods, are experimentally verified using a set of binary and grayscale images.

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O'Brien, Frank, Sherry E. Hammel, and Chung T. Nguyen. "A Method of Moments for Exponentials." Perceptual and Motor Skills 80, no. 3_suppl (June 1995): 1102. http://dx.doi.org/10.2466/pms.1995.80.3c.1102.

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A methodological investigation is reported summarizing a substitution method for deriving probability density functions and moments for a class of exponential functions that could be useful to researchers in a variety of disciplines.

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Little, Thomas, and Vijay Pant. "A PDE method for computing moments." Journal of Computational Finance 4, no. 1 (2000): 5–20. http://dx.doi.org/10.21314/jcf.2000.052.

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Rácz, Sándor, Árpád Tari, and Miklós Telek. "A moments based distribution bounding method." Mathematical and Computer Modelling 43, no. 11-12 (June 2006): 1367–82. http://dx.doi.org/10.1016/j.mcm.2005.07.004.

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Harrington, R. F. "The Method of Moments in Electromagnetics." Journal of Electromagnetic Waves and Applications 1, no. 3 (January 1987): 181–200. http://dx.doi.org/10.1163/156939387x00018.

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Hansen, Bruce E., and Kenneth D. West. "Generalized Method of Moments and Macroeconomics." Journal of Business & Economic Statistics 20, no. 4 (October 2002): 460–69. http://dx.doi.org/10.1198/073500102288618603.

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Frenklach, Michael. "Method of moments with interpolative closure." Chemical Engineering Science 57, no. 12 (June 2002): 2229–39. http://dx.doi.org/10.1016/s0009-2509(02)00113-6.

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Benoit, C. "The moments method and damped systems." Journal of Physics: Condensed Matter 6, no. 17 (April 25, 1994): 3137–60. http://dx.doi.org/10.1088/0953-8984/6/17/006.

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K. Newey, Whitney. "Generalized method of moments specification testing." Journal of Econometrics 29, no. 3 (September 1985): 229–56. http://dx.doi.org/10.1016/0304-4076(85)90154-x.

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Bai, Er-Wei, and Karl E. Lonngren. "Capacitors and the method of moments." Computers & Electrical Engineering 30, no. 3 (April 2004): 223–29. http://dx.doi.org/10.1016/j.compeleceng.2002.10.002.

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Journal articles on the topic 'MOMENTS METHOD'

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