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Journal articles on the topic 'Moments method (Statistics)'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 August 2024

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1

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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2

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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3

Orlov, A. I. "Interval statistics: Maximum likelihood method and method of moments." Journal of Mathematical Sciences 88, no. 6 (March 1998): 833–39. http://dx.doi.org/10.1007/bf02365369.

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4

Hyde, Milo W. "Independently Controlling Stochastic Field Realization Magnitude and Phase Statistics for the Construction of Novel Partially Coherent Sources." Photonics 8, no. 2 (February 22, 2021): 60. http://dx.doi.org/10.3390/photonics8020060.

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In this paper, we present a method to independently control the field and irradiance statistics of a partially coherent beam. Prior techniques focus on generating optical field realizations whose ensemble-averaged autocorrelation matches a specified second-order field moment known as the cross-spectral density (CSD) function. Since optical field realizations are assumed to obey Gaussian statistics, these methods do not consider the irradiance moments, as they, by the Gaussian moment theorem, are completely determined by the field’s first and second moments. Our work, by including control over the irradiance statistics (in addition to the CSD function), expands existing synthesis approaches and allows for the design, modeling, and simulation of new partially coherent beams, whose underlying field realizations are not Gaussian distributed. We start with our model for a random optical field realization and then derive expressions relating the ensemble moments of our fields to those of the desired partially coherent beam. We describe in detail how to generate random optical field realizations with the proper statistics. We lastly generate two example partially coherent beams using our method and compare the simulated field and irradiance moments theory to validate our technique.

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5

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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6

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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7

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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8

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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9

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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10

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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11

Adebisi Ade, Ogunde, Oseghale Innocent Osezuwa, Oyebimpe Emmanuel Adeniji, and Olalude Adelekan Gbenga. "Generalized Bur X Lomax Distribution: Properties, Inference and Application to Aircraft Data." Journal of Mathematics Research 14, no. 2 (March 24, 2022): 52. http://dx.doi.org/10.5539/jmr.v14n2p52.

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We proposed and studied a flexible distribution with wider applications called Generalized Burr X Lomax (GBX-L) distribution. Some well-known mathematical properties such as ordinary moments, incomplete moment probability weighted moments, stress-strength model, mean residual lifetime, characteristic function, quantile function, order statistics and Renyi entropy of GBX-L distribution are investigated. The expressions of order statistics are derived. Parameters of the derived distribution are obtained using the maximum likelihood method and simulation studied is carried out to examine the validity of the method of estimation. The applicability of the proposed distribution is exemplified using aircraft data.

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12

Clerk, Luke De, and Sergey Savel’ev. "Nonstationary Generalised Autoregressive Conditional Heteroskedasticity Modelling for Fitting Higher Order Moments of Financial Series within Moving Time Windows." Journal of Probability and Statistics 2022 (May 20, 2022): 1–19. http://dx.doi.org/10.1155/2022/4170866.

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Here, we present a method for a simple GARCH (1,1) model to fit higher order moments for different companies’ stock prices. When we assume a Gaussian conditional distribution, we fail to capture any empirical data when fitting the first three even moments of financial time series. We show instead that a mixture of normal distributions is needed to better capture the higher order moments of the data. To demonstrate this point, we construct regions (parameter diagrams), in the fourth- and sixth-order standardised moment space, where a GARCH (1,1) model can be used to fit moment values and compare them with the corresponding moments from empirical data for different sectors of the economy. We found that the ability of the GARCH model with a double normal conditional distribution to fit higher order moments is dictated by the time window our data spans. We can only fit data collected within specific time window lengths and only with certain parameters of the conditional double Gaussian distribution. In order to incorporate the nonstationarity of financial series, we assume that the parameters of the GARCH model can have time dependence. Furthermore, using the method developed here, we investigate the effect of the COVID-19 pandemic has upon stock’s stability and how this compares with the 2008 financial crash.

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13

Dey, Sanku, Enayetur Raheem, and Saikat Mukherjee. "Statistical properties and different methods of estimation of transmuted Rayleigh distribution." Revista Colombiana de Estadística 40, no. 1 (January 16, 2017): 165–203. http://dx.doi.org/10.15446/rce.v40n1.56153.

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This article addresses the various properties and different methods of estimation of the unknown parameters of the Transmuted Rayleigh (TR) distribution from the frequentist point of view. Although, our main focus is on estimation from frequentist point of view, yet, various mathematical and statistical properties of the TR distribution (such as quantiles, moments, moment generating function, conditional moments, hazard rate, mean residual lifetime, mean past lifetime, mean deviation about mean and median, the stochastic ordering, various entropies, stress-strength parameter and order statistics) are derived. We briefly describe different frequentist methods of estimation approaches, namely, maximum likelihood estimators, moments estimators, L-moment estimators, percentile based estimators, least squares estimators, method of maximum product of spacings, method of Cram\'er-von-Mises, methods of Anderson-Darling and right-tail Anderson-Darling and compare them using extensive numerical simulations. Monte Carlo simulations are performed to compare the performances of the proposed methods of estimation for both small and large samples. Finally, the potentiality of the model is analyzed by means of two real data sets which is further illustrated by obtaining bias and standard error of the estimates and the bootstrap percentile confidence intervals using bootstrap resampling.

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14

Einmahl, John H. J., Andrea Krajina, and Johan Segers. "A method of moments estimator of tail dependence." Bernoulli 14, no. 4 (November 2008): 1003–26. http://dx.doi.org/10.3150/08-bej130.

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15

Gelman, Andrew. "Method of Moments Using Monte Carlo Simulation." Journal of Computational and Graphical Statistics 4, no. 1 (March 1995): 36. http://dx.doi.org/10.2307/1390626.

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16

Piterbarg, V. I. "Massive Excursions of Gaussian Isotropic Fields. Method of Moments." Theory of Probability & Its Applications 63, no. 2 (January 2018): 193–208. http://dx.doi.org/10.1137/s0040585x97t989003.

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17

Nagaev, A. V. "On a Method of Calculating Moments of Ladder Heights." Theory of Probability & Its Applications 30, no. 3 (September 1986): 569–72. http://dx.doi.org/10.1137/1130068.

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18

Kumar, Devendra, Maneesh Kumar, Sapna Yadav, and Anju Goyal. "A new parameter estimation method for the extended power Lindley distribution based on order statistics, with application." Statistics in Transition new series 25, no. 2 (June 5, 2024): 167–84. http://dx.doi.org/10.59170/stattrans-2024-020.

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In this paper, we propose inference procedures for the estimation of parameters by using order statistics. First, we derive some new expressions for single and product moments of the order statistics from the extended power Lindley distribution. We then use these moments to obtain the best linear unbiased estimates (BLUEs) of the location and scale parameters based on Type-II right-censored samples. A real data set is analysed to illustrate the flexibility and importance of the model.

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19

Hashempour, Majid, and Morad Alizadeh. "A New Weighted Half-Logistic Distribution:Properties, Applications and Different Method of Estimations." Statistics, Optimization & Information Computing 11, no. 3 (June 3, 2023): 554–69. http://dx.doi.org/10.19139/soic-2310-5070-1314.

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In this paper, we introduce a new two-parameter lifetime distribution based on arctan function which is called weighted Half-Logistic (WHL) distribution. Theoretical properties of this model including quantile function, extreme value, linear combination for pdf and cdf, moments, conditional moments, moment generating function and mean deviation are derived and studied in details. The maximum likelihood estimates of parameters are compared with various methods of estimations by conducting a simulation study. Finally, two real data sets show that this model p[rovide better fit than other competitive known models.

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20

Baltagi, Badi H. "Panel Data Econometrics: Method-of-Moments and Limited Dependent Variables." Journal of the American Statistical Association 98, no. 463 (September 2003): 769–70. http://dx.doi.org/10.1198/jasa.2003.s291.

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21

Zellner, Arnold. "Remarks on a ‘critique’ of the Bayesian Method of Moments." Journal of Applied Statistics 28, no. 6 (August 2001): 775–78. http://dx.doi.org/10.1080/02664760120059291.

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22

Oh, Dong Hwan, and Andrew J. Patton. "Simulated Method of Moments Estimation for Copula-Based Multivariate Models." Journal of the American Statistical Association 108, no. 502 (June 2013): 689–700. http://dx.doi.org/10.1080/01621459.2013.785952.

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23

Wu, Yihong, and Pengkun Yang. "Optimal estimation of Gaussian mixtures via denoised method of moments." Annals of Statistics 48, no. 4 (August 2020): 1981–2007. http://dx.doi.org/10.1214/19-aos1873.

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24

Otten, Dustin L., and Prakash Vedula. "A quadrature based method of moments for nonlinear Fokker–Planck equations." Journal of Statistical Mechanics: Theory and Experiment 2011, no. 09 (September 30, 2011): P09031. http://dx.doi.org/10.1088/1742-5468/2011/09/p09031.

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25

BRINGMANN, KATHRIN, KARL MAHLBURG, and ROBERT C. RHOADES. "Taylor coefficients of mock-Jacobi forms and moments of partition statistics." Mathematical Proceedings of the Cambridge Philosophical Society 157, no. 2 (July 9, 2014): 231–51. http://dx.doi.org/10.1017/s0305004114000292.

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AbstractWe develop a new technique for deriving asymptotic series expansions for moments of combinatorial generating functions that uses the transformation theory of Jacobi forms and “mock” Jacobi forms, as well as the Hardy-Ramanujan Circle Method. The approach builds on a suggestion of Zagier, who observed that the moments of a combinatorial statistic can be simultaneously encoded as the Taylor coefficients of a function that transforms as a Jacobi form. Our use of Jacobi transformations is a novel development in the subject, as previous results on the asymptotic behavior of the Taylor coefficients of Jacobi forms have involved the study of each such coefficient individually using the theory of quasimodular forms and quasimock modular forms.As an application, we find asymptotic series for the moments of the partition rank and crank statistics. Although the coefficients are exponentially large, the error in the series expansions is polynomial, and have the same order as the coefficients of the residual Eisenstein series that are undetectable by the Circle Method. We also prove asymptotic series expansions for the symmetrized rank and crank moments introduced by Andrews and Garvan, respectively. Equivalently, the former gives asymptotic series for the enumeration of Andrews k-marked Durfee symbols.

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26

GODA, Yoshimi, Masanobu KUDAKA, and Hiroyasu KAWAI. "Use of L-moments Method for Extreme Statistics of Storm Wave Heights." Journal of Japan Society of Civil Engineers, Ser. B2 (Coastal Engineering) 65, no. 1 (2009): 161–65. http://dx.doi.org/10.2208/kaigan.65.161.

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27

Balakrishnan, N., A. Childs, and B. Chandrasekar. "An efficient computational method for moments of order statistics under progressive censoring." Statistics & Probability Letters 60, no. 4 (December 2002): 359–65. http://dx.doi.org/10.1016/s0167-7152(02)00267-5.

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28

Ul Haq, Muhammad Ahsan, G. G. Hamedani, M. Elgarhy, and Pedro Luiz Ramos. "Marshall-Olkin Power Lomax Distribution: Properties and Estimation Based on Complete and Censored Samples." International Journal of Statistics and Probability 9, no. 1 (December 30, 2019): 48. http://dx.doi.org/10.5539/ijsp.v9n1p48.

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We study a new distribution called the Marshall-Olkin Power Lomax distribution. A comprehensive account of its mathematical properties including explicit expressions for the ordinary moments, moment generating function, order statistics, Renyi entropy, and probability weighted moments are derived. The model parameters are estimated by the method of maximum likelihood. Monte Carlo simulation study is carried out to estimate the parameters and the performance of the estimates is judged via the average biases and mean squared error values. The usefulness of the proposed model is illustrated via real-life data set.

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29

Ball, Frank, and Robin K. Milne. "Simple derivations of properties of counting processes associated with Markov renewal processes." Journal of Applied Probability 42, no. 4 (December 2005): 1031–43. http://dx.doi.org/10.1239/jap/1134587814.

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A simple, widely applicable method is described for determining factorial moments of N̂t, the number of occurrences in (0,t] of some event defined in terms of an underlying Markov renewal process, and asymptotic expressions for these moments as t → ∞. The factorial moment formulae combine to yield an expression for the probability generating function of N̂t, and thereby further properties of such counts. The method is developed by considering counting processes associated with events that are determined by the states at two successive renewals of a Markov renewal process, for which it both simplifies and generalises existing results. More explicit results are given in the case of an underlying continuous-time Markov chain. The method is used to provide novel, probabilistically illuminating solutions to some problems arising in the stochastic modelling of ion channels.

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30

Chapman, S. C., G. Rowlands, and N. W. Watkins. "Extremum statistics: a framework for data analysis." Nonlinear Processes in Geophysics 9, no. 5/6 (December 31, 2002): 409–18. http://dx.doi.org/10.5194/npg-9-409-2002.

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Abstract. Recent work has suggested that in highly correlated systems, such as sandpiles, turbulent fluids, ignited trees in forest fires and magnetization in a ferromagnet close to a critical point, the probability distribution of a global quantity (i.e. total energy dissipation, magnetization and so forth) that has been normalized to the first two moments follows a specific non-Gaussian curve. This curve follows a form suggested by extremum statistics, which is specified by a single parameter a (a = 1 corresponds to the Fisher-Tippett Type I ("Gumbel") distribution). Here we present a framework for testing for extremal statistics in a global observable. In any given system, we wish to obtain a, in order to distinguish between the different Fisher-Tippett asymptotes, and to compare with the above work. The normalizations of the extremal curves are obtained as a function of a. We find that for realistic ranges of data, the various extremal distributions, when normalized to the first two moments, are difficult to distinguish. In addition, the convergence to the limiting extremal distributions for finite data sets is both slow and varies with the asymptote. However, when the third moment is expressed as a function of a, this is found to be a more sensitive method.

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31

Ball, Frank, and Robin K. Milne. "Simple derivations of properties of counting processes associated with Markov renewal processes." Journal of Applied Probability 42, no. 04 (December 2005): 1031–43. http://dx.doi.org/10.1017/s002190020000108x.

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A simple, widely applicable method is described for determining factorial moments of N̂ t , the number of occurrences in (0,t] of some event defined in terms of an underlying Markov renewal process, and asymptotic expressions for these moments as t → ∞. The factorial moment formulae combine to yield an expression for the probability generating function of N̂ t , and thereby further properties of such counts. The method is developed by considering counting processes associated with events that are determined by the states at two successive renewals of a Markov renewal process, for which it both simplifies and generalises existing results. More explicit results are given in the case of an underlying continuous-time Markov chain. The method is used to provide novel, probabilistically illuminating solutions to some problems arising in the stochastic modelling of ion channels.

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32

Zhu, Zhengwei, Jianjiang Zhou, and Hongyu Chu. "Synthetic Aperture Radar Image Background Clutter Fitting Using SKS + MoM-BasedG0Distribution." Mathematical Problems in Engineering 2015 (2015): 1–11. http://dx.doi.org/10.1155/2015/864019.

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G0distribution can accurately model various background clutters in the single-look and multilook synthetic aperture radar (SAR) images and is one of the most important statistic models in the field of SAR image clutter modeling. However, the parameter estimation ofG0distribution is difficult, which greatly limits the application of the distribution. In order to solve the problem, a fast and accurateG0distribution parameter estimation method, which combines second-kind statistics (SKS) technique with Freitas’ method of moment (MoM), is proposed. First we deduce the first and second second-kind characteristic functions ofG0distribution based on Mellin transform, and then the logarithm moments and the logarithm cumulants corresponding to the above-mentioned characteristic functions are derived; finally combined with Freitas’ method of moment, a simple iterative equation which is used for estimating theG0distribution parameters is obtained. Experimental results show that the proposed method has fast estimation speed and high fitting precision for various measured SAR image clutters with different resolutions and different number of looks.

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33

Martin, Vance L., Andrew R. Tremayne, and Robert C. Jung. "EFFICIENT METHOD OF MOMENTS ESTIMATORS FOR INTEGER TIME SERIES MODELS." Journal of Time Series Analysis 35, no. 6 (August 14, 2014): 491–516. http://dx.doi.org/10.1111/jtsa.12078.

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34

Bravo, Francesco. "Improved generalized method of moments estimators for weakly dependent observations." Journal of Time Series Analysis 32, no. 6 (March 21, 2011): 680–98. http://dx.doi.org/10.1111/j.1467-9892.2011.00726.x.

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35

Fedotenkov, Igor. "A bootstrap method to test for the existence of finite moments." Journal of Nonparametric Statistics 25, no. 2 (June 2013): 315–22. http://dx.doi.org/10.1080/10485252.2012.752487.

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36

Sulewski, Piotr. "Easily Changeable Kurtosis Distribution." Austrian Journal of Statistics 52, no. 3 (July 18, 2023): 1–24. http://dx.doi.org/10.17713/ajs.v52i3.1434.

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The goal of this paper is to introduce the easily changeable kurtosis (ECK) distribution. The uniform distribution appears as a special cases of the ECK distribution. The new distribution tends to the normal distribution. Properties of the ECK distribution such as PDF, CDF, modes, inflection points, quantiles, moments, moment generating function, Moors’ measure, moments of order statistics, random number generator and the Fisher Information Matrix are derived. The unknown parameters of the ECK distribution are estimated by the maximum likelihood method. The Shannon, Renyi and Tsallis entropies are calculated. Illustrative examples of applicability and flexibility of the ECK distribution are given. The most important R codes are presented in the Appendix.

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37

Hussain, Sajid, Muhammad Sajid Rashid, Mahmood Ul Hassan, and Rashid Ahmed. "The Generalized Alpha Exponent Power Family of Distributions: Properties and Applications." Mathematics 10, no. 9 (April 23, 2022): 1421. http://dx.doi.org/10.3390/math10091421.

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Here, a new method is recommended to characterize a new continuous distribution class, named the generalized alpha exponent power family of distributions (GAEPFDs). A particular sub-model is presented for exemplifying the objective. The basic statistical properties, such as ordinary moments, the probability weighted moments, mode, quantile, order statistics, entropy measures, and moment generating functions, etc., were explored. To gauge the GAEPPRD parameters, the ML technique was utilized. The estimator behaviour was studied by a Monte Carlo simulation study (MCSS). The effectiveness of GAEPFDs was demonstrated observationally through lifetime data. The applications show that GAEPFDs can offer preferable results over other competitive models.

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38

Wagner, Vincent, and Nicole Radde. "The impossible challenge of estimating non-existent moments of the Chemical Master Equation." Bioinformatics 39, Supplement_1 (June 1, 2023): i440—i447. http://dx.doi.org/10.1093/bioinformatics/btad205.

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Abstract Motivation The Chemical Master Equation (CME) is a set of linear differential equations that describes the evolution of the probability distribution on all possible configurations of a (bio-)chemical reaction system. Since the number of configurations and therefore the dimension of the CME rapidly increases with the number of molecules, its applicability is restricted to small systems. A widely applied remedy for this challenge is moment-based approaches which consider the evolution of the first few moments of the distribution as summary statistics for the complete distribution. Here, we investigate the performance of two moment-estimation methods for reaction systems whose equilibrium distributions encounter fat-tailedness and do not possess statistical moments. Results We show that estimation via stochastic simulation algorithm (SSA) trajectories lose consistency over time and estimated moment values span a wide range of values even for large sample sizes. In comparison, the method of moments returns smooth moment estimates but is not able to indicate the non-existence of the allegedly predicted moments. We furthermore analyze the negative effect of a CME solution’s fat-tailedness on SSA run times and explain inherent difficulties. While moment-estimation techniques are a commonly applied tool in the simulation of (bio-)chemical reaction networks, we conclude that they should be used with care, as neither the system definition nor the moment-estimation techniques themselves reliably indicate the potential fat-tailedness of the CME’s solution.

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39

Adeyinka, Femi Samuel. "On the T-X Class of Topp Leone-G Family of Distributions: Statistical Properties and Applications." European Journal of Statistics 2 (November 22, 2021): 2. http://dx.doi.org/10.28924/ada/stat.2.2.

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This article investigates the T-X class of Topp Leone- G family of distributions. Some members of the new family are discussed. The exponential-Topp Leone-exponential distribution (ETLED) which is one of the members of the family is derived and some of its properties which include central and non-central moments, quantiles, incomplete moments, conditional moments, mean deviation, Bonferroni and Lorenz curves, survival and hazard functions, moment generating function, characteristic function and R`enyi entropy are established. The probability density function (pdf) of order statistics of the model is obtained and the parameter estimation is addressed with the maximum likelihood method (MLE). Three real data sets are used to demonstrate its application and the results are compared with two other models in the literature.

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40

Winterstein, Steven R., and Tina Kashef. "Moment-Based Load and Response Models With Wind Engineering Applications." Journal of Solar Energy Engineering 122, no. 3 (May 1, 2000): 122–28. http://dx.doi.org/10.1115/1.1288028.

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A general method is shown here to model wind loads and responses for reliability applications. This method characterizes the short-term loads and responses by a few summary statistics: specifically, by a limited number of statistical moments. A suite of moment-based models are derived and applied here, illustrating how this statistical moment information can best be utilized. Two examples are shown: the fatigue analysis of a wind turbine component, and the vibration response of a fixed structure to nonlinear wind drag loads. [S0199-6231(00)00702-4]

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41

Mano, Shuhei. "Duality Between the Two-Locus Wright–Fisher Diffusion Model and the Ancestral Process with Recombination." Journal of Applied Probability 50, no. 1 (March 2013): 256–71. http://dx.doi.org/10.1239/jap/1363784437.

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Known results on the moments of the distribution generated by the two-locus Wright–Fisher diffusion model, and the duality between the diffusion process and the ancestral process with recombination are briefly summarized. A numerical method for computing moments using a Markov chain Monte Carlo simulation and a method to compute closed-form expressions of the moments are presented. By applying the duality argument, the properties of the ancestral recombination graph are studied in terms of the moments.

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42

Danielsson, Jon, Dennis W. Jansen, and Casper G. De vries. "The method of moments ratio estimator for the tail shape parameter." Communications in Statistics - Theory and Methods 25, no. 4 (January 1996): 711–20. http://dx.doi.org/10.1080/03610929608831727.

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43

Masuda, Hiroki. "Classical Method of Moments for Partially and Discretely Observed Ergodic Models." Statistical Inference for Stochastic Processes 8, no. 1 (2005): 25–50. http://dx.doi.org/10.1023/b:sisp.0000049120.83388.89.

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44

Khan, Muhammad Shuaib, Robert King, and Irene Lena Hudson. "Transmuted Kumaraswamy distribution." Statistics in Transition new series 17, no. 2 (June 1, 2016): 183–210. http://dx.doi.org/10.59170/stattrans-2016-009.

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Abstract:

The Kumaraswamy distribution is the most widely applied statistical distribution in hydrological problems and many natural phenomena. We propose a generalization of the Kumaraswamy distribution referred to as the transmuted Kumaraswamy (TKw) distribution. The new transmuted distribution is developed using the quadratic rank transmutation map studied by Shaw et al. (2009). A comprehensive account of the mathematical properties of the new distribution is provided. Explicit expressions are derived for the moments, moment generating function, entropy, mean deviation, Bonferroni and Lorenz curves, and formulated moments for order statistics. The TKw distribution parameters are estimated by using the method of maximum likelihood. Monte Carlo simulation is performed in order to investigate the performance of MLEs. The flood data and HIV/AIDS data applications illustrate the usefulness of the proposed model.

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Loisel, Sébastien, and Marina Takane. "Fast indirect robust generalized method of moments." Computational Statistics & Data Analysis 53, no. 10 (August 2009): 3571–79. http://dx.doi.org/10.1016/j.csda.2009.03.021.

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Körber, K., and L. Klinkenbusch. "Statistical multipole formulations for shielding problems." Advances in Radio Science 10 (September 18, 2012): 233–38. http://dx.doi.org/10.5194/ars-10-233-2012.

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Abstract. A multipole-based method is presented for modelling an electromagnetic field with small statistical variations inside an arbitrary enclosure. The accurate computation of the statistics of the field components from the statistical moments of the multipole amplitudes is demonstrated for two- and three-dimensional examples. To obtain the statistics of quantities which depend non-linearly on the field components, higher-order statistical moments of the latter are required.

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Hörfelt, Per. "Geometric bounds on certain sublinear functionals of geometric Brownian motion." Journal of Applied Probability 40, no. 4 (September 2003): 893–905. http://dx.doi.org/10.1239/jap/1067436089.

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Suppose that {Xs, 0 ≤ s ≤ T} is an m-dimensional geometric Brownian motion with drift, μ is a bounded positive Borel measure on [0,T], and ϕ : ℝm → [0,∞) is a (weighted) lq(ℝm)-norm, 1 ≤ q ≤ ∞. The purpose of this paper is to study the distribution and the moments of the random variable Y given by the Lp(μ)-norm, 1 ≤ p ≤ ∞, of the function s ↦ ϕ(Xs), 0 ≤ s ≤ T. By using various geometric inequalities in Wiener space, this paper gives upper and lower bounds for the distribution function of Y and proves that the distribution function is log-concave and absolutely continuous on every open subset of the distribution's support. Moreover, the paper derives tail probabilities, presents sharp moment inequalities, and shows that Y is indetermined by its moments. The paper will also discuss the so-called moment-matching method for the pricing of Asian-styled basket options.

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Ramalho, Joaquim J. S. "A test statistic equation for obtaining alternative Wald and score statistics in the generalized method of moments framework." Applied Economics Letters 16, no. 5 (March 2, 2009): 489–94. http://dx.doi.org/10.1080/13504850601018676.

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Laribi, Dorsaf, Afif Masmoudi, and Imen Boutouria. "Characterization of generalized Gamma-Lindley distribution using truncated moments of order statistics." Mathematica Slovaca 71, no. 2 (April 1, 2021): 455–74. http://dx.doi.org/10.1515/ms-2017-0481.

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Abstract Having only two parameters, the Gamma-Lindley distribution does not provide enough flexibility for analyzing different types of lifetime data. From this perspective, in order to further enhance its flexibility, we set forward in this paper a new class of distributions named Generalized Gamma-Lindley distribution with four parameters. Its construction is based on certain mixtures of Gamma and Lindley distributions. The truncated moment, as a characterization method, has drawn a little attention in the statistical literature over the great popularity of the classical methods. We attempt to prove that the Generalized Gamma-Lindley distribution is characterized by its truncated moment of the first order statistics. This method rests upon finding a survival function of a distribution, that is a solution of a first order differential equation. This characterization includes as special cases: Gamma, Lindley, Exponential, Gamma-Lindley and Weighted Lindley distributions. Finally, a simulation study is performed to help the reader check whether the available data follow the underlying distribution.

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Soltani, A. R., and H. Homei. "A generalization for two-sided power distributions and adjusted method of moments." Statistics 43, no. 6 (December 2009): 611–20. http://dx.doi.org/10.1080/02331880802689506.

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