Statistical Properties Research Articles

Advanced Excitation Symmetry Analysis Method (ESAM) for improved automated ultrasonic testing of polished materials

One of the strategic plans of the international NDT community is to define standards for developing advanced and digitalized non-destructive testing for automated set-up in mass production [1,2]. Excitation Symmetry Analysis Method (ESAM) are new coded signal processing tools exploring symmetry properties [3]. ESAM method aims to extract the nonlinearity from an ultrasound output by studying the property of symmetry of the transfer function. More precisely, the extraction of nonlinearity is done using basis function associated to a group which is associated to an a priori transfer function. As soon as the linear tomography uses the invariant properties of amplitude dependence, nonlinear tomography should exploit the invariance properties (or symmetry properties) of the complex system. Consequently, the invariance of the stationary properties of a complex medium would be supposed to be associated to a signature of the degradation, that will be extracted with advanced signal processing tools. The idea remains the same: studying the symmetry and more precisely the time reversal one and the inversion. A signal processing is used to measure discrepancies in the autocorrelation function (output signal called chirp coda) for two inputs: a signal and its inversion (pulse inversion). The experiments were done on different sample with and without cracks. It has been shown that when the nonlinearities are extracted from the chirp coda amplitude are non- negligible in crack area and nonlinearities are out of phase. Then, mixing symmetries like time reversal and pulse inversion enable the detection of defect that are difficult to detect with conventional ultrasound method. Indeed, for such crack a destructive mechanical analysis called Jomini is done where the material is polished and examined with microscope. The sensitivity improvement of chirp-coded signal processing has been validated in various domains. Coded excitation techniques, used in communication systems such as radar and sonar provide improved SNR without increasing the amplitude of excitation. The typical test equipment consists of a preamplifier Juvitek TRA-02 (0.02 - 5 MHz) connected to a computer, an amplifier ENI model A150 (55 dB at 0.3-35 MHz), a shear wave transducer Technisonic (2.25 MHz), and a longitudinal wave transducer Panametrics V155 (5 MHz). The experimental device was tested with the V3 calibration block, improved, and specially scaled in order to access to a wide range of multivalued parameters: mechanical properties, ultrasonic parameters (celerity and attenuation) and local geometric data.

Effect of Macroeconomic Factors on Economic Growth: A Case Study of Bangladesh

Macroeconomic factors strongly influence the economy. It affects countries and businesses equally. The relationship between different macroeconomic factors is an area of widespread study for policymakers and economists. The ultimate purpose of this study is to assess the impact of macroeconomic factors on the economic growth. This research has taken GDP as a substitute variable for the development of the economy as well as endogenous (dependent) variable and FDI, inflation (INF), money supply (M2), public and private domestic investment (DINVEST), and foreign exchange reserve (FExR) as independent variables. Moreover, this study used time series secondary data starting from 2005-06 to 2022-23 for all econometric analysis. On the other side, we utilized the ADF (Augmented Dickey-Fuller) test to study the unit root (stationary property) of data, the Durbin Watson (DW) statistic technique to verify the autocorrelation of variables, the VIF test technique to examine the multicollinearity among independent variables and multiple linear regression to scrutinize the overall effect of macroeconomic factors on growth of the economy. Study findings show that DINVEST and FDI positively affect the growth of the economy. i.e., if macroeconomic variables- DINVEST and FDI are increased by 1 unit, they increase economic growth by 2.96 units and 0.62 units, respectively. However, inflation, money supply, and foreign exchange reserves have a positive effect on economic growth, but it is statistically insignificant. The study implies that economists, researchers, academicians, and policymakers can use the findings of the study for future research and decision-making regarding the effect of macroeconomic factors on economic growth.

The LOFAR – eFEDS survey: The incidence of radio and X-ray AGN and the disk–jet connection

Context. Radio jets are present in a diverse sample of AGN. However, the mechanisms of jet powering are not fully understood, and it remains unclear to what extent they obey mass-invariant scaling relations similar to those found for the triggering and fuelling of X-ray-selected AGN. Aims. We use the multi-wavelength data in the eFEDS field observed by eROSITA/Spectrum-Roentgen-Gamma (SRG) and LOFAR to study the incidence of X-ray and radio AGN as a function of several stellar mass (M*)-normalised AGN power indicators. Methods. From the LOFAR – eFEDS survey, we defined a new sample of radio AGN, with optical counterparts from Legacy Survey DR9, according to a radio-excess relative to their host star formation rate. We further divided the sample into compact and complex radio morphologies. In this work, we used the subset matching to the well-characterised, highly complete spectroscopic GAMA09 galaxies (0 < z < 0.4). We release this value-added LOFAR – eFEDS catalogue*. We calculated the fraction of GAMA09 galaxies hosting radio, X-ray, and both radio and X-ray AGN as functions of the specific black hole kinetic (λJet) and radiative (λEdd) power. Results. Despite the soft-X-ray eROSITA-selected sample, the incidence of X-ray AGN as a function of λEdd shows the same mass-invariance and power law slope (−0.65) as that found in previous studies once corrected for completeness. Across the M* range probed, the incidence of compact radio AGN as a function of λJet is described by a power law with constant slope, showing that it is not only high mass galaxies hosting high power jets and vice versa. This slope is steeper than that of the X-ray incidence, which has a value of around −1.5. Furthermore, higher-mass galaxies are more likely to host radio AGN across the λJet range, indicating some residual mass dependence of jet powering. Upon adding complex radio morphologies, including 34 FRIIs, three of which are giant radio galaxies, the incidence not only shows a larger mass dependence but also a jet power dependence, being clearly boosted at high λJet values. Importantly, the latter effect cannot be explained by such radio AGN residing in more dense environments (or more massive dark matter haloes). The similarity in the incidence of quiescent and star-forming radio AGN reveals that radio AGN are not only found in “red and dead” galaxies. Overall, our incidence analysis reveals some fundamental statistical properties of radio AGN samples, but highlights open questions regarding the use of a single radio luminosity–jet power conversion. We explore how different mass and accretion rate dependencies of the incidence can explain the observed results for varying disk–jet coupling models.

Emergence and Criticality in Spatiotemporal Synchronization: The Complementarity Model.

This work concerns the long-term collective excitability properties and the statistical analysis of the critical events displayed by a recently introduced spatiotemporal many-body model, proposed as a new paradigm for Artificial Life. Numerical simulations show that excitable collective structures emerge in the form of dynamic networks, created by bursts of spatiotemporal activity (avalanches) at the edge of a synchronization phase transition. The spatiotemporal dynamics is portraited by a movie and quantified by time varying collective parameters, showing that the dynamic networks undergo a "life cycle," made of self-creation, homeostasis, and self-destruction. The power spectra of the collective parameters show 1/f power law tails. The statistical properties of the avalanches, evaluated in terms of size and duration, show power laws with characteristic exponents in agreement with those values experimentally found in the neural networks literature. The mechanism underlying avalanches is argued in terms of local-to-collective excitability. The connections that link the present work to self-organized criticality, neural networks, and Artificial Life are discussed.

Natural gas, trade openness and economic growth in Peru: 1965–2022

Natural gas is a major fuel in Peru, accounting for nearly 45 % of all energy sources used to generate electricity. This research aims to analyze the dynamic association between economic growth and natural gas consumption (NGC), considering Peru's trade openness (Tr) from 1965 to 2022. The augmented Dickey–Fuller unit root test is utilized to test the stationary properties of the log series of real gross domestic product (GDP), NGC, and real Tr. We used the autoregressive distributed lag (ARDL) cointegration approach to determine the long-run (LR) equilibrium association between the variables. As the second cointegration method, we used the Engle-Granger test. The results of the ARDL test support the cointegration of all variables, we find the opposite case with Engle-Granger method. The Granger causality results support the neutrality hypothesis between GDP and NGC, a two-way causality association between Tr and GDP, and the neutrality hypothesis between NGC and Tr. Nevertheless, in the LR, cointegration confirms the growth hypothesis between GDP and NGC. Similarly, we find that in the LR, the first lag of Tr positively impacts the current GDP value. Meanwhile, in the short run, Tr has a positive effect on Peru's GDP. Then, using the findings of cointegration among all variables, we can conclude that NGC and Tr are the drivers of economic growth in Peru in the LR. Finally, we discuss the policy implications of our results.

ON THE MOMENTS OF THE 3-PARAMETER GOMPERTZ DISTRIBUTION

Gompertz distribution is a classical probability distribution extensively used in actuarial science, reliability, and survival analysis. Gompertz distribution also plays a role in various fields, such as biology, economics, and marketing analysis. Some extensions of this distribution have been studied and applied to various problems. In this article, we are concerned with some statistical properties of a 3-parameter Gompertz distribution. This extension of the Gompertz distribution introduced has been used in studying competing risk survival analysis. Our main results are the derivation of moments of this distribution and other statistical properties related to moments, such as moment generating function, mean residual life function, mean inactivity time and Lorenz curve. These results will serve as a complement to the theoretical aspect of the analysis of the distribution.

State Parameter Fusion Estimation for Intelligent Vehicles Based on IMM-MCCKF

The prerequisite for intelligent vehicles to achieve autonomous driving and active safety functions is acquiring accurate vehicle state parameters. Traditional Kalman filters often underperform in non-Gaussian noise environments due to their reliance on Gaussian assumptions. This paper presents the IMM-MCCKF filter, which integrates the interacting multiple model theory (IMM) and the maximum correntropy cubature Kalman filter method (MCCKF), for estimating the state parameters of intelligent vehicles. The IMM-MCCKF successfully suppresses non-Gaussian noise by optimizing a nonlinear cost function using the maximum correntropy criteria, allowing it to capture and analyze signal data outliers accurately. The filter designs various state and measurement noise submodels to adapt to the environment dynamically, thus reducing the impact of unknown noise statistical properties. Accurately measuring the velocity of a vehicle and the angle at which its center of mass drifts sideways is of utmost importance for its ability to maneuver, maintain stability, and ensure safety. These parameters are critical for implementing advanced control systems in intelligent vehicles. The study begins by constructing a nonlinear Dugoff tire model and a three-degrees-of-freedom (3DOF) vehicle model. Subsequently, utilizing low-cost vehicle sensor signals, joint simulations are conducted on the CarSim-Simulink platform to estimate vehicle state parameters. The results demonstrate that in terms of estimation accuracy and robustness in non-Gaussian noise scenarios, the proposed IMM-MCCKF filter consistently outperforms the MCCKF and CKF algorithms.

Dynamics of rapidly rotating Bose–Einstein quantum droplets

This study presents a detailed analysis of the stationary properties and dynamics of an anharmonically trapped, rapidly rotating Bose–Einstein liquid droplet. We investigate the effects of the particle number, confining potential, and rotation speed on the formation of the energetically favored bead, multiple quantized vortex, off-center vortex, and center-of-mass states. The multi-periodic trajectories and breathing provide evidence of the collective excitations of the surface mode in the vortex states. Observation of the self-trapping phenomenon and tendency toward the lowest Landau level in rapid rotation regimes coincides well with the quantum-Hall limit. Modifying the topological charges and destroying the potential flow of the vortex state can occur if an external disturbance is imposed upon the quantum droplet.

Group sparse structural smoothing recovery: model, statistical properties and algorithm

Group sparse structural smoothing recovery: model, statistical properties and algorithm

Finding the Particularity of the Active Episode of SGR J1935+2154 during Which FRB 20200428 Occurred: Implication from Statistics of Fermi/GBM X-Ray Bursts

By using the Fermi/Gamma-ray Burst Monitor data of the X-ray bursts (XRBs) of SGR J1935+2154, we investigate the temporal clustering of the bursts and the cumulative distribution of the waiting time and fluence/flux. It is found that the bursts occurring in the episode hosting FRB 20200428 have obviously shorter waiting times than those in the other episodes. The general statistical properties of the XRBs further indicate they could belong to a self-organized critical system (e.g., starquakes), making them very similar to the earthquake phenomena. Then, according to a unified scaling law between the waiting time and energy of the earthquakes as well as their aftershocks, we implement an analogy analysis on the XRBs and find that the fast radio burst (FRB) episode owns more dependent burst events than the other episodes. It is indicated that the FRB emission could be produced by the interaction between different burst events, which could correspond to a collision between different seismic/Alfvén waves or different explosion outflows. Such a situation could appear when the magnetar enters into a global intensive activity period.

Utilizing the Sentinel-6 Michael Freilich Equivalent Number of Looks for Sea State Applications

Sentinel-6 Michael Freilich (S6-MF) is the first altimeter operating in a continuous high-rate pulse mode, i.e., interleaved mode. This ensures the generation of low-resolution (LR) mode measurements with a pulse repetition frequency (PRF) of ∼9 kHz (variable along the orbit) for the Ku-band as well as the processing of high-resolution (HR) echoes on ground. This operating mode provides an elevated number of highly correlated single looks with respect to the fewer number, weakly correlated echoes of Jason-3 altimeter. A theoretical model is exploited to envisage the correlation properties of S6-MF pulse limited waveform echoes for different sea-state conditions; after that, the model is validated by comparison with the equivalent number of looks (ENL) empirically estimated from real data. The existence of a significant dependence of the statistical properties on the range is verified, and its impact on the precision and on the accuracy in the estimation of the geophysical parameters is assessed in case of the 9 kHz PRF of S6-MF. By applying pulse decimation before the multilook processing, an investigation on new processing techniques is performed, aimed at exploiting the higher ENL in S6-MF low-resolution mode waveforms. It is shown that a bias of less than 0.4 cm is found for SSH and about 1.5 cm for SWH at SWH = 2 m when the decimated waveforms processing is compared with full high-PRF processing.

Exploring and analyzing the role of hybrid spectrum sensing methods in 6G-based smart health care applications

Background Researchers are focusing their emphasis on quick and real-time healthcare and monitoring systems because of the contemporary modern world’s rapid technological improvements. One of the best options is smart healthcare, which uses a variety of on-body and off-body sensors and gadgets to monitor patients’ health and exchange data with hospitals and healthcare professionals in real time. Utilizing the primary user (PU) spectrum, cognitive radio (CR) can be highly useful for efficient and intelligent healthcare systems to send and receive patient health data. Methods In this work, we propose a method that combines energy detection (ED) and cyclostationary (CS) spectrum sensing (SS) algorithms. This method was used to test spectrum sensing in CR-based smart healthcare systems. The proposed ED-CS in cognitive radio systems improves the precision of the spectrum sensing. Owing to its straightforward implementation, ED is initially used to identify the idle spectrum. If the ED cannot find the idle spectrum, the signals are found using CS-SS, which uses the cyclic statistical properties of the signals to separate the main users from the interference. Results In the simulation analysis, the probability of detection (Pd), probability of a false alarm (Pfa), power spectral density (PSD), and bit error rate (BER) of the proposed ED-CS is compared to those of the traditional Matched Filter (MF), ED, and CS. Conclusions The results indicate that the suggested strategy improves the performance of the framework, making it more appropriate for smart healthcare applications.

A unified linear intrinsic alignment model for elliptical and disc galaxies and the resulting ellipticity spectra

Alignments of disc galaxies were thought to result from tidal torquing, where tidal field of the cosmic large-scale structure exert torquing moments onto dark matter haloes, determining their angular momentum and ultimately the orientation of galactic discs. In this model, resulting intrinsic ellipticity correlations are typically present on small scales, but neither observations nor simulations have found empirical evidence; instead, simulations point at the possibility that alignments of disc galaxies follow a similar alignment model as elliptical galaxies, but with a weaker alignment amplitude. In our article we make the case for the theory of linear alignments resulting from tidal distortions of the galactic disc, investigate the physical properties of this model and derive the resulting angular ellipticity spectra, as they would appear as a contribution to weak gravitational lensing in surveys such as Euclid’s. We discuss in detail on the statistical and physical properties of tidally induced alignments in disc galaxies, as they are relevant for mitigation of alignment contamination in weak lensing data, comment on the consistency between the alignment amplitude in spiral and elliptical galaxies and finally, estimate their observability with a Euclid-like survey.

Constructive approach and randomization of a two-parameter chaos system for securing data

Secure communication techniques are important due to the increase in the number of technology users across the world. Likewise, a more random encryption algorithm suitable to secure data from unauthorised users is highly expected. This paper proposes a two-parameter nonlinear chaos map that is sensitive to the trio seed (s0, \alpha, \lambda) and has better information encryption. We introduce the parameter \alpha to linearise the conventional chaos system, which in turn brings a delay in the cryptosystems. The delay is a phenomenon that changes the chaotic features of a system. A small delay in the system leads to more aperiodicity and the unpredictability of the chaotic attractions. We normalise the new chaos map and use the Lipschitz and pseudo-contractive operators to obtain its irregularity region in Hilbert spaces. We also analyse the chaos map in terms of trajectory, Lyapunov exponent, complexity, and information entropy. Results obtained show that the new chaos map has a wide chaotic range and better statistical properties. It also maintains low complexity due to its linearity and produces more key spaces than most existing chaotic maps.

Testing independence: count data case

ABSTRACT This paper proposes several novel classes of independence tests specially designed for count data. The tests are based on the difference between joint and marginal probability generating functions and can be applied to count data of any arbitrary fixed dimension. The limiting properties of the test statistics are explored. The competitiveness of the novel proposal is demonstrated through an extensive empirical study, while the application is illustrated with a few real-data examples.

Testing dynamic correlations and nonlinearity in bivariate time series through information measures and surrogate data analysis

The increasing availability of time series data depicting the evolution of physical system properties has prompted the development of methods focused on extracting insights into the system behavior over time, discerning whether it stems from deterministic or stochastic dynamical systems. Surrogate data testing plays a crucial role in this process by facilitating robust statistical assessments. This ensures that the observed results are not mere occurrences by chance, but genuinely reflect the inherent characteristics of the underlying system. The initial process involves formulating a null hypothesis, which is tested using surrogate data in cases where assumptions about the underlying distributions are absent. A discriminating statistic is then computed for both the original data and each surrogate data set. Significantly deviating values between the original data and the surrogate data ensemble lead to the rejection of the null hypothesis. In this work, we present various surrogate methods designed to assess specific statistical properties in random processes. Specifically, we introduce methods for evaluating the presence of autodependencies and nonlinear dynamics within individual processes, using Information Storage as a discriminating statistic. Additionally, methods are introduced for detecting coupling and nonlinearities in bivariate processes, employing the Mutual Information Rate for this purpose. The surrogate methods introduced are first tested through simulations involving univariate and bivariate processes exhibiting both linear and nonlinear dynamics. Then, they are applied to physiological time series of Heart Period (RR intervals) and respiratory flow (RESP) variability measured during spontaneous and paced breathing. Simulations demonstrated that the proposed methods effectively identify essential dynamical features of stochastic systems. The real data application showed that paced breathing, at low breathing rate, increases the predictability of the individual dynamics of RR and RESP and dampens nonlinearity in their coupled dynamics.

Kinetic equation for stochastic vector bundles

The kinetic equation is crucial for understanding the statistical properties of stochastic processes, yet current equations, such as the classical Fokker–Planck, are limited to local analysis. This paper derives a new kinetic equation for stochastic systems on vector bundles, addressing global scale randomness. The kinetic equation was derived by cumulant expansion of the ensemble-averaged local probability density function, which is a functional of state transition trajectories. The kinetic equation is the geodesic equation for the probability space. It captures global and historical influences, accounts for non-Markovianity, and can be reduced to the classical Fokker–Planck equation for Markovian processes. This paper also discusses relative issues concerning the kinetic equation, including non-Markovianity, Markov approximation, macroscopic conservation equations, gauge transformation, and truncation of the infinite-order kinetic equation, as well as limitations that require further attention.

Data-driven analysis of annual rain distributions

Rainfall is an important component of the climate system, and its statistical properties are vital for prediction purposes. In this study, we have developed a statistical method for constructing the distribution of annual precipitation. The method is based on the convolution of the measured monthly rainfall distributions and does not depend on any presumed annual rainfall distribution. Using a simple statistical model, we demonstrate that our approach allows for a better prediction of extremely dry or wet years with a recurrence time several times longer than the original time series. The method that has been proposed can be utilized for other climate variables as well. Published by the American Physical Society 2024

A New Three-Parameter Inverse Rayleigh Distribution: Simulation and Application to Real Data

In this paper, we introduce a new three-parameter inverse Rayleigh distribution that extends the inverse Rayleigh distribution, constructed based on the generalized transmuted family of distributions proposed by Alizadeh, Merovci, and Hamedani. We explore statistical properties such as the quantile function, moments, harmonic mean, mean deviation, stress–strength reliability, and entropy. Parameter estimation is performed using various methods, including maximum likelihood, least squares, the method of the maximum product of spacings, and the method of Cramér–von Mises. The usefulness of the new three-parameter inverse Rayleigh distribution is illustrated by modeling a real dataset, demonstrating its superior fit compared to several other distributions.

The Lomax-Exponentiated Odds Ratio–G Distribution and Its Applications

This paper introduces the Lomax-exponentiated odds ratio–G (L-EOR–G) distribution, a novel framework designed to adeptly navigate the complexities of modern datasets. It blends theoretical rigor with practical application to surpass the limitations of traditional models in capturing complex data attributes such as heavy tails, shaped curves, and multimodality. Through a comprehensive examination of its theoretical foundations and empirical data analysis, this study lays down a systematic theoretical framework by detailing its statistical properties and validates the distribution’s efficacy and robustness in parameter estimation via Monte Carlo simulations. Empirical evidence from real-world datasets further demonstrates the distribution’s superior modeling capabilities, supported by compelling various goodness-of-fit tests. The convergence of theoretical precision and practical utility heralds the L-EOR–G distribution as a groundbreaking advancement in statistical modeling, significantly enhancing precision and adaptability. The new model not only addresses a critical need within statistical modeling but also opens avenues for future research, including the development of more sophisticated estimation methods and the adaptation of the model for various data types, thereby promising to refine statistical analysis and interpretation across a wide array of disciplines.