Statistical Moments Research Articles

On the theory of order statistics of the flexible Lomax distribution

This paper studies the flexible Lomax distribution’s order statistics with graphical and numerical findings. Along with the quantitative measurements, some plots are furnished, including those for the skewness and kurtosis measures. We will dwell on the numerous results that relate to statistics of moments of order. We consider the single and product moment of order statistics from the new distribution. Further, we establish some recurrence relation for single moments of order statistics. We have sought to apply the derived relations to empirically evaluate the moments of smallest (largest) order statistics to establish well-known moments and related measures. For order statistics of a flexible Lomax distribution, exact analytical expressions of entropy, residual entropy, and past latent entropy are determined.

УСУНЕННЯ ЗАВАД У ДИНАМІЧНИХ СПЕКТРАХ ЗА НАЯВНОСТІ ПОТУЖНОГО СИГНАЛУ. Частина 2. ВУЗЬКОСМУГОВІ ЗАВАДИ УМОВНО-СТАЦІОНАРНОГО ХАРАКТЕРУ

Subject and Purpose. A new method for detecting narrow band interferences is discussed, with the use of an example record of Jovi- an Io-C decametric radio storm as obtained with the UTR-2 array on April 10, 2020. We aimed at developing an efficient and simple algorithm based on a detailed analysis of the effect the radio interference environment and the frequency response of the telescope may have on the efficiency of the interference mitigation procedure. Methods and Methodology. The ‘orthogonal detection’ method proposed for identifying linear interference patterns in dynamic spectra of powerful radio sources has been adapted for application to narrow band interferences of various spectral widths and variable brightness, which often happen to be located close to (or intersect with) the signal of interest. In order to minimize the impact of the telescope’s frequency response, a discretized frequency-scanning technique is used, which permits a steady approximation of the averaged spectrum by low order polynomials, as well as removal of the frequency trend which hinders distinguishing between the low-level interference signals and those coming from the source. Results. An efficient approach to the problem of detecting long lasting, narrowband interferences in dynamical spectra (con- ditionally stationary interferences) is proposed. The algorithm has been tested on the example of a powerful storm of Jovian radio emission. The proposed technique can be especially useful in situations where the signal of interest overlaps with the interference in the time-frequency domain. Conclusions. The new approach to the problem of interference mitigation, based on the development of combined algorithms of signal separation in the time-frequency domain, has been shown to offer an effective method of signal processing. In contrast to the previously used methods based on calculation of statistical moments for amplitudes, the new approach allows avoiding use of the same statistical indicators for both interference detection and subsequent steps of data analysis intended for building physical models and interpreting the observational data.

Prediction of elastic deformation and elastic wave velocity of perovskite MgSiO3 with cubic structure at high pressure up to 140 GPa and high temperature up to 4000K from statistical moment method

Based on the structural and thermodynamic theory of cubic perovskite built on the SMM published in previous works, we construct the theory of elastic deformation and elastic wave velocity of cubic perovskite. We apply the obtained theory to numerical calculations for MgSiO3 at extreme conditions of temperature up to 4000K and pressure up to 140 GPa. The SMM calculation results for MgSiO3 are consistent with the current calculation and experimental results for CaSiO3. Our results are predictive of the thermodynamic properties of MgSiO3 in the context of scarce data on this material.

Study on Thermodynamic Properties and Elastic Deformation of Full-Heusler Alloys Co2TaGa and Co2VGa by Statistical Moment Method

Heusler alloy is a ferromagnetic alloy based on the Heusler phase. It is an intermetallic alloy between metallic and non-metallic elements that can be non-ferromagnetic and has a BCC crystal structure. This paper presents the theory of thermodynamics and elastic deformation of full-Heusler A2BC alloy with BCC structure built on the basis of statistical moment method (SMM). The paper presents numerical results for the temperature and pressure dependence of the mean nearest neighbor distance between two atoms, the density, the volume, the thermal expansion coefficient, the isotherm and adiabatic compressibilities, the isothermal elastic modulus, the heat capacities at constant volume and pressure, Young’s modulus, the bulk modulus, longitudinal and transverse wave velocities of alloys Co2TaGa and Co2VGa when using the coordination sphere method and the Mie–Lennard-Jones pair interaction potential. Some SMM calculation results agree well with available ab initio calculation results.

Antifp SRF: Identifying Antifungal Peptides by Sequence Statistical Moments and Random Forest Classifier

Numerous types of fungus are unhealthy and can lead to life-threatening conditions in people. A fungal infection that targets specific bodily regions and that the immune system is unable to fight off. Numerous studies have been conducted on the topic, but due to its negative side effects, medications, chemicals, and conventional techniques have not proven effective enough. Due to the rapidly invading fungus species, antimicrobial peptides having antifungal properties emerged as a new and powerful candidate due to their efficiency and selectivity. Many mathematical models are being developed for its identification, including Deep-AntiFP and AntiFP, the most recently. However, it has limited performance in accuracy, sensitivity, precision, and MCC. This study investigates an efficient and accurate computational model for the prediction of antifungal peptides (AFPs) using machine learning approaches. The model uses the statistical moment as feature extraction and Random Forest (RF) as a predictor to predict AFPs from non-AFPs. 10-fold cross-validation, independent tests, and self-consistency tests are used to validate the performance of the model. Three datasets are used for model training and its evaluation, namely Antifp Main, Antifp DS1, and Independent Main. The model achieved an accuracy of 95.73%, 97.01%, and 99.15% for Antifp Main, Antifp DS1, and Independent main respectively through independent testing; 97.4%, 97.3%, and 97.4% by 10-fold cross-validation and 99.74%, 99.87 and 99.83 by self-consistency testing. The proposed model has shown excellent results for all three datasets as compared to the existing models available in the literature.

Stochastic Optimization of Electromagnetic Inertial Mass Dampers in Nonlinear Hybrid Base Isolation Systems Under Seismic Excitations

Recently developed inerter-based dampers have been installed at the base layer to reduce base displacement and simultaneously improve the superstructure’s performance. However, in the existing research on optimizing damper parameters, the nonlinear property of base isolation is simplified and stochastic linearization technique is introduced to approximate such nonlinearity, which would inevitably introduce errors. In this paper, an improved method is proposed for stochastic optimization of electromagnetic inertial mass dampers (EIMD) in nonlinear hybrid isolation systems subject to seismic excitations. First, a stochastic seismic excitation is represented by one elementary random variable adopting the dimension-reduction spectral representation method. Then, statistical moments of nonlinear base-isolated structural responses are estimated using two-point estimation method (2PEM). Finally, the EIMD optimal parameters are obtained via the modified directional bat algorithm (MDBA) recently proposed by the authors through minimizing base layer response moments. This proposed improved method could fully consider the base isolation nonlinearity compared with the previous stochastic linearization technique. Moreover, the proposed stochastic optimization of the EIMD only requires two dynamic analyses to achieve its efficiency. A seven-story base-isolated frame building equipped with an EIMD is investigated in the numerical simulation, and results indicate that EIMD optimized by this proposed method obviously outperforms the results by the stochastic linearization technique and the conventional viscous damper (VD) in the base layer displacement reduction.

A novel extended inverse‐exponential distribution and its application to COVID‐19 data

AbstractThe aim of this article is to define a new flexible statistical model to examine the COVID‐19 data sets that cannot be modeled by the inverse exponential distribution. A novel extended distribution with one scale and three shape parameters is proposed using the generalized alpha power family of distributions to derive the generalized alpha power exponentiated inverse exponential distribution. Some important statistical properties of the new distribution such as the survival function, hazard function, quantile function, moment, Rényi entropy, and order statistics are all derived. The method of maximum likelihood estimation is used to estimate the parameters of the new distribution. The performance of the estimators are assessed through Monte Carlo simulation, which shows that the maximum likelihood method works well in estimating the parameters. The GAPEIEx distribution was applied to COVID‐19 data sets in order to access the flexibility and adaptability of the distribution, and it happens to perform better than its submodels and other well‐known distributions.

A novel maximum entropy method based on the B-spline theory and the low-discrepancy sequence for complex probability distribution reconstruction

The maximum entropy method (MEM) is a powerful tool for the recovery of unknown probability density functions (PDF) and has growing popularity in the reliability analysis community. However, MEM may be inaccurate for PDFs with a complex shape (e. g. multiple modals or a long tail), influencing the accuracy of the reliability analysis greatly. To overcome this deficiency, this study proposes a novel MEM paradigm based on the B-spline theory and the low-discrepancy sequence. Firstly, to enhance the performance of MEM for complex PDFs, the B-spline functions are used to construct the MEM PDF. Correspondingly, the iteration formulation is derived for the undetermined parameter estimation of the B-spline-based MEM PDF based on the closed solution for minimizing the Kullback-Leibler divergence. Then, we adopt the low-discrepancy sequence to calculate the objective function of minimizing the Kullback-Leibler divergence efficiently. Compared with MEM and other moment-based reliability analysis methods, the proposed method does not require the statistical moments, and integrates the advantages of the B-spline theory and MEM. To illustrate the benefits of our method, five examples are analyzed and compared with some classical reliability analysis methods.

Uncertainty modelling and assessment of shear resistance in reinforced concrete beams without shear reinforcement

ABSTRACT In structural concrete, diagonal tension failure is a significant mode of shear failure in slender flexural members. As a result, an accurate estimate of the slender beam’s resistance to shear is required. This study presents a statistical characterisation of the uncertainty associated with various resistance predictive models for slender stirrupless beams with a distinct mode of failure (diagonal tension failure). The investigated models include code- and literature-based shear models. Through a comparative analysis of statistical moments and probabilistic representative models of the uncertainty factor using a substantial number of test cases, the study found that the mechanical model proposed by Tran (2020) demonstrated the best consistency in predicting shear strength. It exhibited a mean of 1.02, standard deviation of 0.16, and coefficient of variation of 16%. To effectively manage the uncertainties identified in the EC2 and AS3600–18 shear models, model uncertainty partial and reduction factors following the EN1990 guidelines were proposed for design practices. However, concerns remain regarding the performance of other shear models, necessitating further reliability investigation.

Determination of Nonstationary Stochastic Response of Linear Oscillators With Fractional Derivative Elements of Rational Order

Abstract In this paper, a technique is developed for determining the nonstationary response statistics of linear oscillators endowed with fractional derivative elements. Notably, fractional operators are particularly effective in modeling solid mechanics problems as they offer the option of influencing both the elasticity and the energy dissipation capacity of the system. In this paper, particular attention is devoted to the case of fractional derivatives of rational order that approximates reasonably well any real order model. The oscillators are subjected to stationary stochastic excitations, and the pertinent nonstationary response statistical moments are determined by first introducing a finite number of oscillator response related states; this is afforded by the rational number order of the fractional operator. Next, the technique involves proceeding to treating the problem in the Laplace transform domain. This leads to multiple convolution integrals determined by representing the transfer function of the oscillator in a partial fraction form by a pole-residue formulation. In this manner, the response evolutionary power spectral density of the fractional oscillator is derived in a closed form, while nonstationary second-order statistics can be obtained by mundane numerical integration in the frequency domain. Applications to oscillators comprising one or two fractional derivative elements are presented, considering the case of a white noise excitation and of a random process possessing the classical Kanai–Tajimi spectrum. Reliability of the developed technique is assessed by juxtaposing its analytical results with pertinent Monte Carlo simulation data.

Fractional Criticality Theory and Its Application in Seismology

To understand how the temporal non-locality («memory») properties of a process affect its critical regimes, the power-law compound and time-fractional Poisson process is presented as a universal hereditary model of criticality. Seismicity is considered as an application of the theory of criticality. On the basis of the proposed hereditarian criticality model, the critical regimes of seismicity are investigated. It is shown that the seismic process has the property of «memory» (non-locality over time) and statistical time-dependence of events. With a decrease in the fractional exponent of the Poisson process, the relaxation slows down, which can be associated with the hardening of the medium and the accumulation of elastic energy. Delayed relaxation is accompanied by an abnormal increase in fluctuations, which is caused by the non-local correlations of random events over time. According to the found criticality indices, the seismic process is in subcritical regimes for the zero and first moments and in supercritical regimes for the second statistical moment of events’ reoccurrence frequencies distribution. The supercritical regimes indicate the instability of the deformation changes that can go into a non-stationary regime of a seismic process.

Homestead Agroforestry and Tree Species Diversity in Cumilla District of Bangladesh

In Bangladesh, the typical land use structure is homestead agroforestry. It provides people with basic necessities like food, shelter, money, and other things. This study was regulated in the Nangalkot Upazila of the Cumilla district at Bangladesh to identify plant species grown in homestead areas and to explore the relationships between tree diversification and selected characteristics of farmers of the Nangalkot upazila. A total of 50 households from the small, marginal, medium, and large groups were polled. An interview schedule was created using a simple technique and questionnaire to collect data on the selected parameters. The respondents were chosen at random, and data were collected between January 1 and 21, 2021. For statistical analysis, the orthodox descriptive statistical parameters and Product Moment Correlation Coefficient of Pearson (r) were used. A total of twenty seven (27) plant species were identified in the study area's homestead, with 16 being fruit plants and 11 being forest plant species. The most abundant fruit species were mango, coconut, guava, papaya, jackfruit, etc., and the forest plant species were mahogany, bamboo, eucalyptus, neem, akashmoni, etc. On average, 14.38 plant species had been identified in respondents' homestead area. Sixteen agroforestry systems with four layers were identified from the study area. Selected farmers' characteristics, such as family size, farm size, homestead size, knowledge about homestead agroforestry, and socio-economic condition, showed a significant positive relationship with the total number of plant species, which can help in nutritional security of the people in the area of study. The current homestead agroforestry techniques in the Nangalkot Upazila of Cumilla district can be improved using advanced agroforestry approaches, and diversity of medicinal and multipurpose plants should be enhanced in order to maximize farmers' revenue.

An integrated strategy to evaluate active substances of Astragali Radix-Carthami Flos combination on the treatment of cerebral ischemia reperfusion injury based on TQSM polypharmacokinetics and pharmacodynamics.

As a classic herb pair, Astragali Radix-Carthami Flos (AR-CF) has revealed good biological activity in the treatment of cerebral ischemia/reperfusion injury (CI/RI), which remained to be further clarified together with the underlying efficacy related compounds for material basis. In this study, the nine formulations were obtained by L9 (34) orthogonal array design of four active fractions (saponin and flavonoid extracted from AR, safflower yellow and safflower red extracted from CF). The concentrations of eleven components and the levels of four biochemical indicators in rat plasma were continuously detected after intragastric administration of nine formulations, respectively. The collected data were analyzed by sigmoid-Emax function to understand the polypharmacokinetics and pharmacodynamics (PK-PD) behaviors of multi-components. Using the total quantum statistic moment polypharmacokinetics and its similarity method, the importance of four active fractions from AR-CF in relieving CI/RI was discussed and the Q-markers were screened. The results represented that a reliable and robust liquid chromatography tandem mass spectrometry method been successfully established to simultaneously determine the concentrations of eleven components in rat plasma. The AUC and MRT values of components from flavonoid fraction had the greatest contribution to AUCT and MRTT values. The transitivity in vivo of calycosin-7-O-β-Dglucoside (CG), astragaloside IV (AIV) and hydroxysafflor yellow A (HYA) was closer to polypharmacokinetics behavior. All formulations up/down-regulated the levels of GSH-Px and ATP/ET and LDH to varying degrees, among which formulation 7 had the best regulating effect. By drawing the time-concentration-effect curve, clockwise hysteresis loops were presented in the time-concentration-effect relationships between eleven components and LDH/ET, while the relationship between eleven components and ATP/GSH-Px expressed as anticlockwise hysteresis loops. In conclusion, the combination based on the combination principle of formulation 7 produced the best alleviation effect on CI/RI, and flavonoid fraction might played key role in this process. The CG, AIV and HYA were identified as Q-markers. This research offered a novel strategy for exploring the active substances, and provided further understanding regarding the development of drugs for the treatment of cerebral ischemia-reperfusion injury.

Brain Age Prediction Using 2D Projections Based on Higher-Order Statistical Moments and Eigenslices from 3D Magnetic Resonance Imaging Volumes.

Brain age prediction from 3D MRI volumes using deep learning has recently become a popular research topic, as brain age has been shown to be an important biomarker. Training deep networks can be very computationally demanding for large datasets like the U.K. Biobank (currently 29,035 subjects). In our previous work, it was demonstrated that using a few 2D projections (mean and standard deviation along three axes) instead of each full 3D volume leads to much faster training at the cost of a reduction in prediction accuracy. Here, we investigated if another set of 2D projections, based on higher-order statistical central moments and eigenslices, leads to a higher accuracy. Our results show that higher-order moments do not lead to a higher accuracy, but that eigenslices provide a small improvement. We also show that an ensemble of such models provides further improvement.

A Provably Convergent Control Closure Scheme for the Method of Moments of the Chemical Master Equation.

In this article, we introduce a novel moment closure scheme based on concepts from model predictive control (MPC) to accurately describe the time evolution of the statistical moments of the solution of the chemical master equation (CME). The method of moments, a set of ordinary differential equations frequently used to calculate the first nm moments, is generally not closed since lower-order moments depend on higher-order moments. To overcome this limitation, we interpret the moment equations as a nonlinear dynamical system, where the first nm moments serve as states, and the closing moments serve as the control input. We demonstrate the efficacy of our approach using three example systems and show that it outperforms existing closure schemes. For polynomial systems, which encompass all mass-action systems, we provide probability bounds for the error between true and estimated moment trajectories. We achieve this by combining the convergence properties of a priori moment estimates from stochastic simulations with guarantees for nonlinear reference tracking MPC. Our proposed method offers an effective solution to accurately predict the time evolution of moments of the CME, which has wide-ranging implications for many fields, including biology, chemistry, and engineering.

3D digital holographic polarimetry of diffuse optically anisotropic biological tissue object fields

The experimental validation of methods for the digital holographic 3D layer-by-layer reconstruction of complex amplitude distributions in different phase planes of diffuse biological tissue histological section microscopic images with a subsequent reconstruction of azimuth and ellipticity polarization maps is presented. Polarization dependencies of the integral and layer-by-layer vector structure of the laser object field azimuth and ellipticity distributions in two types of biological layer samples—the fibrous myocardium and parenchymal liver—have been investigated. Scenarios and dynamics of changes in the values of statistical moments of the first to fourth orders, which characterize the integral and layer-by-layer polarization maps of diffuse biological tissue histological section microscopic images with different morphological structures, have been determined. Criteria for selecting the polarization components of the object field that are formed by acts of scattering of different multiplicities have been identified. An example of biomedical application in cancer detection of biological tissues is provided.

Statistical Analysis of Ceiling and Floor Effects in Medical Trials

Exploratory data analysis and statistical moments were used to investigate the potential impact of ceiling and floor effects in medical trials. A total of 150 treatment-naive eyes were assessed in a retrospective case study of patients who were treated with anti-VEGF injections for wet age-related macular degeneration. The experimental results revealed that ceiling and floor effects are problematic in data analysis and may result in serious errors when using standard parametric tests. The case study provided insights relating to methodology in medical trials, experimental data analysis, and statistical inference, as applied to the interpretation of treatment response limits. Suggestions are provided for statistical data pre-processing and post-processing when significantly skewed distributions are present in response groups.

Baseflow Statistics in Aggregated Catchments

AbstractThis paper employs stochastic analysis to investigate the combined effect of temporal and spatial variability on the temporal variance of baseflow in large catchments. The study makes use of the well‐known aggregated reservoir model, representing the catchment as a network of parallel linear reservoirs. Each reservoir models a sub‐catchment as an independent unit whose discharge temporal variation is characterized by a response time. By treating the rainfall‐generated recharge and the sub‐catchment response times as random variables, the statistical temporal moments of total baseflow are quantified. Comparisons are made between the temporal variance of baseflow in the aggregated reservoir model and that of a single homogeneous reservoir to define an upscaled response time. The analysis of the statistical moments of the random baseflow reveals that the number of reservoirs N has a weak impact on baseflow variance, with ergodic conditions achieved even with a small number of reservoirs. The study highlights that the ratio between the recharge correlation time and the geometric mean of the sub‐catchment response times plays a critical role in baseflow damping and the upscaled response. The results indicate that the dynamics of baseflow generation depend not only on the catchment hydro‐geological structure but also on the variability of the input signal. This research underscores the importance of understanding the combined influences of hydro‐geological factors and recharge input variability for baseflow prediction under uncertainty. The present study should be regarded as a first step, setting the theoretical framework for future research toward incorporating field data.

Automated characterization and monitoring of material shape using Riemannian geometry

Shape affects both the physical and chemical properties of a material. Characterizing the roughness, convexity, and general geometry of a material can yield information on its catalytic efficiency, solubility, elasticity, porosity, and overall effectiveness in the application of interest. However, material shape can be defined in a multitude of conflicting ways where different aspects of a material’s geometry are emphasized over others, leading to bespoke measures of shape that are not easily generalizable. In this paper, we explore the use of Riemannian geometry in the analysis of shape, and show that a Riemannian geometric framework for shape analysis is generalizable, computationally scalable, and can be directly integrated into common data analysis methods. In this framework, material shapes are abstracted as points on a Riemannian manifold. This information can be used to construct statistical moments (e.g., means, variances) and perform tasks such as dimensionality reduction and statistical process control. We provide a practical introduction to the mathematics of shape analysis through Riemannian geometry and illustrate its application on a manufactured/mined granular material dataset provided by Covia Corp. We show that the Riemannian framework can be used to automatically extract and quantify the shape of granular materials in a statistically rigorous manner.

Stochastic characterisation of unstable lean hydrogen–air annular premixed flames

This study is devoted to the characterisation of lean premixed hydrogen–air laminar flames stabilised on an annular burner. The flames studied are chosen to lie close to the lean flammability limit, spanning a range of Damköhler and Reynolds numbers, and correspond to situations where instabilities arise. The experimental characterisation is achieved by examining the statistical moments of the flame hydroxyl radical (OH*) chemiluminescence and schlieren. The standard deviation and the skewness, that are needed to fully characterise the measured probability density functions, are shown to exhibit a non-monotonic behaviour with the distance from the burner surface, first increasing, then decreasing downstream the flame tip. An exponentially modified Gaussian distribution model is proposed to describe the skewed schlieren fluctuations probability density function. This model is closed by developing relations for the probability density function parameters based on the Damköhler and Reynolds numbers, and then used to describe the OH* stochastic behaviour. The relation between the distribution parameters and the transport equation of a reactive scalar gradient is addressed also.