Fourth Central Moment Research Articles

Landslide type inference based on statistical analysis of a high-resolution digital elevation model in Gorce National Park, Poland

High-resolution digital elevation models are commonly utilized for detecting and classifying landslides. In this study, we aim to refine landslide detection and classification by analyzing the geometry of landslides using slope and aspect, coupled with descriptive statistics up to the fourth central moment (kurtosis). Employing the Monte Carlo method for creating terrain topography probability distributions and ANOVA tests for statistical validation, we analyzed 364 landslides in Gorce National Park, Poland, revealing significant kurtosis differences across landslide types and lithologies. This methodology offers a novel approach to landslide classification based on surface geometry, with implications for enhancing scientific research and improving landslide risk management strategies.

Smoothing level selection for density estimators based on the moments

This paper introduces an approach to select the bandwidth or smoothing parameter in multiresolution (MR) density estimation and nonparametric density estimation. It is based on the evolution of the second, third and fourth central moments and the shape of the estimated densities for different bandwidths and resolution levels. The proposed method has been applied to density estimation by means of multiresolution densities as well as kernel density estimation (MRDE and KDE respectively). The results of the simulations and the empirical application demonstrate that the level of resolution resulting from the moments method performs better with multimodal densities than the Bayesian Information Criterion (BIC) for multiresolution densities estimation and the plug-in for kernel densities estimation.

Multiple Fault Detection in Induction Motors through Homogeneity and Kurtosis Computation

In the last few years, induction motor fault detection has provoked great interest among researchers because it is a fundamental element of the electric-power industry, manufacturing enterprise, and services. Hence, considerable efforts have been carried out on developing reliable, low-cost procedures for fault diagnosis in induction motors (IM) since the early detection of any failure may prevent the machine from suffering a catastrophic damage. Therefore, many methodologies based on the IM startup transient current analysis have been proposed whose major disadvantages are the high mathematical complexity and demanding computational cost for their development. In this study, a straightforward procedure was introduced for identifying and classifying faults in IM. The proposed approach is based on the analysis of the startup transient current signal through the current signal homogeneity and the fourth central moment (kurtosis) analysis. These features are used for training a feed-forward, backpropagation artificial neural network used as a classifier. From experimentally obtained results, it was demonstrated that the brought-in scheme attained high certainty in recognizing and discriminating among five induction motor conditions, i.e., a motor in good physical condition (HLT), a motor with one broken rotor bar (1BRB), a motor with two broken rotor bars (2BRB), a motor with damage on the bearing outer race (BRN), and a motor with an unbalanced mechanical load (UNB).

Antineutrino detection for temporal monitoring of fuel burnup in a large nuclear reactor

The objective of this work is to determine if coherent-elastic-neutrino-nucleus scatter (CEνNS) in natural germanium detectors can be used to detect antineutrinos from an AP1000-type fission reactor. In this work, we first modeled the AP1000 core using Monte Carlo N-Particle Transport Code 6.2 (MCNP) to estimate the number of fissions from each fissile isotope in the core. Next, the reactor antineutrino spectrum was computed using the summation method for fuel burnup from 10 to 60 GWd/MTU. It was found that with the increasing fuel burnup, as the 239Pu inventory builds-up in the fuel and the 235U inventory depletes, the contributions from 239Pu to fission is enhanced. Thus, the antineutrino energy spectrum begins to skew more towards lower energies as seen by the quantification of third and fourth central moments. Increased fuel burnup also results in greater antineutrino production. The detection setup assumes a 100-kg CEνNS based natural germanium detector, which is placed outside the reactor containment, 25 m away from the core. The detector has a 100-eV nuclear recoil (NR) threshold and experiences a background level of 100 differential rate units (DRU), per kg.keV.day, due to surrounding radiation interacting in the detector. We then computed the differential pulse height distribution responses for two 235U enrichment cases: 3.3-wt-% and 4.4-wt-% at burnup levels of 10, 20, 40, and 60 GWd/MTU. Overall, the detection rate decreases when the burnup increases. This study indicates that germanium pulse height distribution end-point energies decrease with increasing fuel burnup and become less separable. Thus, we note that the CEνNS detector resolution would need to be higher for more burned fuel. A 16-eV NR is sufficient for distinguishing fresh fuel from that burned to 20 GWd/MTU. We also investigate the ability to detect a difference between burnups: 10 and 20 GWd/MTU, 10 and 40 GWd/MTU, 10 and 60 GWd/MTU, based on the integral detector counts after accounting for background and detection threshold. We determined that fuel burnup deviations can be detected with confidence much greater than 20%, as required by the IAEA, for low likelihood events. For 3.3-wt-% 235U enrichment, the confidence levels to distinguish burnup between 10 and 20 GWd/MTU, 10 and 40 GWd/MTU, 10 and 60 GWd/MTU are 80.60%, 100%, and 100%, respectively. For 4.4-wt% 235U enrichment, but the same three burnup comparisons, the confidence levels decreased marginally to 65.52%, 100%, and 100%, respectively.

Some approximation properties of new ( p,q ) -analogue of Bal\xe1zs\u2013Szabados operators

In this paper, a new ( p,q ) -analogue of the Balázs–Szabados operators is defined. Moments up to the fourth order are calculated, and second order and fourth order central moments are estimated. Local approximation properties of the operators are examined and a Voronovskaja type theorem is given.

Cyclical labour income risk in Great Britain

SummaryThis paper provides new evidence on the cyclical behaviour of household labour income risk in Great Britain and the role of social insurance policy in mitigating against this source of income risk. To achieve this, we decompose stochastic idiosyncratic household income into its transitory and persistent components. We focus our analysis of income risk captured by the second to fourth moments of the probability distribution of shocks to the persistent component of income. We find that household labour income risk increases during contractions via changes in third and fourth central moments of persistent shocks to labour income, whereas the variance remains acyclical. We also find that economic policy has reduced the level of risk exposure and its increase during contractions via benefits rather than tax policies.

Approximation Properties of New Modified Gamma Operators

This paper is aimed at constructing new modified Gamma operators using the second central moment of the classic Gamma operators. And we will compute the first, second, fourth, and sixth order central moments by the moment computation formulas, and their quantitative properties are researched. Then, the global results are established in certain weighted spaces and the direct results including the Voronovskaya-type asymptotic formula, and point-wise estimates are investigated. Also, weighted approximation of these operators is discussed. Finally, the quantitative Voronovskaya-type asymptotic formula and Grüss Voronovskaya-type approximation are presented.

Properties and Applications of a New Family of Skew Distributions

We introduce two families of continuous distribution functions with not-necessarily symmetric densities, which contain a parent distribution as a special case. The two families proposed depend on two parameters and are presented as an alternative to the skew normal distribution and other proposals in the statistical literature. The density functions of these new families are given by a closed expression which allows us to easily compute probabilities, moments and related quantities. The second family can exhibit bimodality and its standardized fourth central moment (kurtosis) can be lower than that of the Azzalini skew normal distribution. Since the second proposed family can be bimodal we fit two well-known data set with this feature as applications. We concentrate attention on the case in which the normal distribution is the parent distribution but some consideration is given to other parent distributions, such as the logistic distribution.

Solving High-Order Portfolios via Successive Convex Approximation Algorithms

The first moment and second central moments of the portfolio return, a.k.a. mean and variance, have been widely employed to assess the expected profit and risk of the portfolio. Investors pursue higher mean and lower variance when designing the portfolios. The two moments can well describe the distribution of the portfolio return when it follows the Gaussian distribution. However, the real world distribution of assets return is usually asymmetric and heavy-tailed, which is far from being a Gaussian distribution. The asymmetry and the heavy-tailedness are characterized by the third and fourth central moments, i.e., skewness and kurtosis, respectively. Higher skewness and lower kurtosis are preferred to reduce the probability of extreme losses. However, incorporating high-order moments in the portfolio design is very difficult due to their non-convexity and rapidly increasing computational cost with the dimension. In this paper, we propose a very efficient and convergence-provable algorithm framework based on the successive convex approximation (SCA) algorithm to solve high-order portfolios. The efficiency of the proposed algorithm framework is demonstrated by the numerical experiments.

Algorithmic portfolio tilting to harvest higher moment gains

Many financial portfolios are not mean-variance-skewness-kurtosis efficient. We recommend tilting these portfolios in a direction that increases their estimated mean and third central moment and decreases their variance and fourth central moment. The advantages of tilting come at the cost of deviation from the initial optimality criterion. In this paper, we show the usefulness of portfolio tilting applied to the equally-weighted, equal-risk-contribution and maximum diversification portfolios in a UCITS-compliant asset allocation setting.

Approximation properties of modified (<i>p, q</i>)-Szász-Mirakyan-Kantorovich operators

In this paper, we introduce a new kind of modified (p, q)-Szasz-Mirakyan-Kantorovich operators based on (p, q)-calculus. Next, the moments computation formulas, the second and fourth order central moments computation formulas and other quantitative properties are investigated. Then, the approximation properties including local approximation, weighted approximation, rate of convergence and Voronovskaja type theorem are obtained. Finally, we generalize the operators by adding a parameter λ.

A higher-order robust correlation Kalman filter for satellite attitude estimation

A higher-order robust correlation Kalman filtering approach is presented to achieve attitude estimation for satellites with unknown modeling errors. A robust correlation Kalman filter (RCKF) is preliminarily derived by using the sequence orthogonal principle. To improve its performance further, a higher-order sigma version of the RCKF is designed by incorporating a novel sigma point generation algorithm. This modified filter can capture the third and the fourth central moment’s information of the system posteriori probability density function. It is proved that the proposed filter achieves better estimation accuracy and robustness. The effectiveness of the developed filter is demonstrated by simulation results with it applied to the satellite attitude estimation problem.

Noise Suppression for GPR Data Based on SVD of Window-Length-Optimized Hankel Matrix.

Ground-penetrating radar (GPR) is an effective tool for subsurface detection. Due to the influence of the environment and equipment, the echoes of GPR contain significant noise. In order to suppress noise for GPR data, a method based on singular value decomposition (SVD) of a window-length-optimized Hankel matrix is proposed in this paper. First, SVD is applied to decompose the Hankel matrix of the original data, and the fourth root of the fourth central moment of singular values is used to optimize the window length of the Hankel matrix. Then, the difference spectrum of singular values is used to construct a threshold, which is used to distinguish between components of effective signals and components of noise. Finally, the Hankel matrix is reconstructed with singular values corresponding to effective signals to suppress noise, and the denoised data are recovered from the reconstructed Hankel matrix. The effectiveness of the proposed method is verified with both synthetic and field measurements. The experimental results show that the proposed method can effectively improve noise removal performance under different detection scenarios.

Means, moments and Newton's inequalities

It is shown that Newton's inequalities and the related Maclaurin's inequalities provide several refinements of the fundamental arithmetic-geometric-harmonic mean inequality and Sierpinski's inequality in terms of the means and variance of positive real numbers. We also obtain some inequalities involving third and fourth central moments of real numbers.

Algorithmic Portfolio Tilting to Harvest Higher Moment Gains

Many financial portfolios are optimized without taking the higher moments into account. We recommend tilting these portfolios in a direction that increases their estimated mean and third central moment and decreases their variance and fourth central moment. The advantages of tilting come at the cost of deviation from the initial optimality criterion. In this paper, we show the usefulness of portfolio tilting applied to the equally-weighted, equal-risk-contribution and maximum diversification portfolios in a UCITS-compliant asset allocation setting.

Statistical fluctuations and quasi phase transition of mesoscopic Bose–Einstein condensation in anharmonic trap

The possibility of quasi phase transition of interacting Bose gas in mesoscopic regime and in the anharmonic trap is studied by a correlated two-body basis function approach. Our methodology accurately describes all measures of statistical fluctuations in anharmonic trap with different anharmonicity. The results addressed here go beyond the mean-field theory, correctly describe finite-sized effect and one unique formalism is valid for entire temperature region. Our main discovery : the lambda-structure in all fluctuation measures near the transition temperature remains same qualitatively in all traps. We also define three characteristic temperatures calculated from the point of inflexion of the lambda-structure of standard deviation, third and fourth central moment. All the three characteristic temperatures smoothly increase with increase in anharmonicity which jointly confirm that the achievement of condensation is more favourable in anharmonic trap. The possibility of true phase transition is ruled out for all traps for the mesoscopic Bose–Einstein condensate. However the additional calculation of transition exponent for the specific heat capacity nicely exhibits that quasi phase transition is more prominent in harmonic trap in comparison with anharmonic traps.

High Order Portfolio Optimization Problem with Transaction Costs

This paper studies a high order moments portfolio optimization model with transaction costs. The model takes kurtosis as objective function and takes the skewness, variance, mean and transaction costs as constraints conditions. Since the optimization problem is of high order and non-convex, it brings some difficulties to the solution of the model. Therefore, this paper transforms the optimization problem into a semi-definite matrix optimization problem by using the moment matrix theory, and then solves it. Through the study of four risky assets in China’s securities market, it is found that transaction costs are significant parts in the study of portfolio model. In addition, sensitivity analysis shows that the kurtosis and skewness are positively correlated with the mean and variance invariant. When mean and skewness are constant, kurtosis and variance are positively correlated. When mean and skewness remain unchanged, the fourth order standard central moment and variance are negatively correlated.

Identifying neutron shielding in neutron multiplicity counting

Neutron Multiplicity Counting (NMC) and passive neutron interrogation is becoming a standard procedure in special nuclear material control and accountability, due to the relative optical transparency of other structure materials to neutron flux, making it very effective for measuring composite poorly-characterized samples. Currently, all applicable neutron multiplicity counting methods assume that both the detection efficiency and the neutron die-away time are system parameters, independent of the sample. Clearly, if the detection efficiency of the system is reduced due to neutron absorption or moderation inside the sample, the measurement will be biased. Therefore, detecting a reduction in the detection efficiency, either accidental or deliberate, is a well motivated problem. In the present study we develop, through both theory and implementation, a new method for detecting a reduced effective detection efficiency in NMC by sampling the fourth central moment of the count distribution. One of the attributes that make the proposed method appealing is that it does not require any additional operation and may be easily applied to any standard NMC counter, assuming that the data is recorded in LIST mode. The method is implemented on a set of 18 measurements, 7 of which are standard NMC measurements, and in the remaining 11 the sample is covered by a moderator, noticeably reducing the effective detection efficiency. The new method successfully discriminates between them.

On limiting distribution of U-statistics based on associated random variables

Let {Xn,n≥1} be a sequence of stationary associated random variables. We discuss another set of conditions under which a central limit theorem for U-statistics based on {Xn,n≥1} holds. We look at U-statistics based on differentiable kernels of degree 2 and above. As applications, we discuss consistent estimators of second, third and fourth central moments, and estimators of skewness and kurtosis based on them.

A new kind of Bernstein-Schurer-Stancu-Kantorovich-type operators based on q-integers

Agrawal et al. (Boll. Unione Mat. Ital. 8:169-180, 2015) introduced a Stancu-type Kantorovich modification of the operators proposed by Ren and Zeng (Bull. Korean Math. Soc. 50(4):1145-1156, 2013) and studied a basic convergence theorem by using the Bohman-Korovokin criterion, the rate of convergence involving the modulus of continuity, and the Lipschitz function. The concern of this paper is to obtain Voronoskaja-type asymptotic result by calculating an estimate of fourth order central moment for these operators and discuss the rate of convergence for the bivariate case by using the complete and partial moduli of continuity and the degree of approximation by means of a Lipschitz-type function and the Peetre K-functional. Also, we consider the associated GBS (generalized Boolean sum) operators and estimate the rate of convergence for these operators with the help of a mixed modulus of smoothness. Furthermore, we show the rate of convergence of these operators (univariate case) to certain functions with the help of the illustrations using Maple algorithms and in the bivariate case, the rate of convergence of these operators is compared with the associated GBS operators by illustrative graphics.