Scale Parameter Research Articles

New classes of goodness‐of‐fit tests for the one‐sided Lévy distribution

New estimators for the scale parameter of the one‐sided Lévy distribution are proposed, which are used for constructing new classes of goodness‐of‐fit (gof) tests, based on the ratio of two estimators of the scale parameter. A Monte Carlo study examines the performance of the new gof tests in controlling type I error rate and evaluates their power performance. The performance of the new classes of gof test is also compared with existing tests. Finally, the applicability of the new gof tests is illustrated using three real data sets.

Quantified asymptotic analysis for the relativistic quantum mechanical system with electromagnetic fields

We study the asymptotic analysis of a relativistic quantum mechanical system interacting with self-consistent electromagnetic fields, with a specific focus on the Maxwell–Klein–Gordon (MKG) system. Firstly, we show that the MKG system is globally well-posed under the Coulomb gauge condition, even in the presence of self-interacting potential. Furthermore, to derive the asymptotic analysis, we consider the non-relativistic and semi-classical regime simultaneously, introducing a single scaling parameter that serves to parameterize both the speed of light and the Planck constant. As the scaling parameter approaches zero, we obtain rigorous and quantified estimates on the asymptotic convergence of the electrostatic MKG system toward the classical Euler–Poisson system. Our analytical framework relies on the modulated energy estimate.

A new adaptive EWMA chart for two‐parameter exponential distribution based on type‐II censored data

AbstractIn this article, we propose a new adaptive exponentially weighted moving average (AEWMA) chart for monitoring the joint shifts in the location and scale parameters of the two‐parameter exponential distribution, namely the AEWMA‐II chart. A key feature of the proposed chart is its straightforward post‐signal diagnostics. The Monte Carlo simulation method is used to compute the steady‐state run‐length profiles of the proposed chart. The run‐length properties include the average run‐length and standard deviation of the run‐length. Through a comprehensive run‐length comparison, it is found that the AEWMA‐II chart performs better than the existing AEWMA chart. Moreover, with post‐signal diagnostics, the proposed chart also surpasses the existing chart. Finally, a real dataset is applied to illustrate the excellent performance and practical application of the proposed chart.

Asymmetric Laplace scale mixtures for the distribution of cryptocurrency returns

AbstractRecent studies about cryptocurrency returns show that their distribution can be highly-peaked, skewed, and heavy-tailed, with a large excess kurtosis. To accommodate all these peculiarities, we propose the asymmetric Laplace scale mixture (ALSM) family of distributions. Each member of the family is obtained by dividing the scale parameter of the conditional asymmetric Laplace (AL) distribution by a convenient mixing random variable taking values on all or part of the positive real line and whose distribution depends on a parameter vector $$\varvec{\theta }$$ θ providing greater flexibility to the resulting ALSM. Advantageously concerning the AL distribution, our family members allow for a wider range of values for skewness and kurtosis. For illustrative purposes, we consider different mixing distributions; they give rise to ALSMs having a closed-form probability density function where the AL distribution is obtained as a special case under a convenient choice of $$\varvec{\theta }$$ θ . We examine some properties of our ALSMs such as hierarchical and stochastic representations and moments of practical interest. We describe an EM algorithm to obtain maximum likelihood estimates of the parameters for all the considered ALSMs. We fit these models to the returns of two cryptocurrencies, considering several classical distributions for comparison. The analysis shows how our models represent a valid alternative to the considered competitors in terms of AIC, BIC, and likelihood-ratio tests.

Reliability Estimation of Scale Parameter in Type II Generalized Half-Logistic Distribution from Doubly Censored Samples Based on Monte Carlo Simulation

Objectives: This article deals with estimation of the reliability function for one-parameter Type II Generalized Half- Logistic distribution (Type II GHLD). Methods: The Maximum likelihood (ML) and Approximate Maximum likelihood (AML) methods provided by Jilani et.al. 1 . Findings: Comparisons between the estimators were made using Monte Carlo Simulation based on statistical indicter bias and mean squared error (MSE). We have generated 3000 random samples of size n=10(5)20 from a standard one-parameter Type II GHLD with = 0.5, 1.5 and 2.0. Each sample is then ordered and from this sample a doubly (including left and right) censored sample is considered, by censoring r smallest observations and s largest observations with all possible choices of r and s corresponding to this resultant sample we compute MLEs (using Newton-Raphson method), the LAMLE and unbiased LAMLE . Finally, the results are explained with tables. Novelty: This study has empirically proves that all the three reliability estimators have the same asymptotic variance. Hence, in this case, any one of the three estimators can be used but preferable estimator based unbiased estimator. Keywords: Maximum likelihood estimation, Approximate Maximum likelihood estimation, Bias, Mean squared error, Variances

Different Transformation Methods of the Lomax Distribution: A Review

Over the years, several scholars have attempted to create models for occurrences in which the data distribution exhibits varying degrees of heavy-tailedness. Various generalizations or expansions of the Lomax distribution have been suggested in order to achieve this objective. The behavior of the system is determined by two fundamental parameters: the form shape parameter and the scale parameter. The Lomax distribution effectively represents many failure patterns found in real-world situations. The versatility and wide range of applications make it an essential instrument in the investigation of dependability and survival modeling. This paper provides a comprehensive overview of several techniques for extending Lomax distribution. The included extensions include Lomax distribution, Inverse Transformation, and Alpha Power Transformations. Multiple novel and comparable distributions were deliberated and scrutinized. The research has the potential to serve as a valuable standard and encourage the development of improved distributions that can accurately represent complex events.

Accurate birth weight prediction from fetal biometry using the Gompertz model

ObjectivesMonitoring of fetal growth and estimation of birth weight is of clinical importance. During pregnancy, ultrasound fetal biometry values including femur length, head circumference, abdominal circumference, biparietal diameter are measured and used to place fetuses on “growth charts”. There is no simple growth-model-based, predictive formula in use for fetal biometry. Estimation of fetal weight at birth currently depends on ultrasound data taken a short time before birth. Study designOur cohort (“Seethapathy cohort”) consists of ultrasound biometry measurements and other data for 774 pregnant women in Chennai, India, 2015–2017. We use the Gompertz model, a standard model for constrained growth, with just three intuitive parameters, to model the growth of fetal biometry, and a machine learning (ML) model trained on these parameters to predict birth weight (BW). ResultsThe Gompertz model convincingly fits the growth of fetal biometry values. Two Gompertz parameters—t0 (inflection time) and c (rate of decrease of growth rate)—seem universal to all fetuses, while the third, A, is an overall scale specific to each fetus, capturing individual variation. On the Seethapathy cohort we can infer A for each fetus from ultrasound data available by the 24 or 35 weeks. Our ML model predicts birth weight with < 8 % error, outperforming published methods that have access to late-term ultrasound data. The same model gives an 8.4 % error in BW prediction on an independent validation cohort of 365 women. ConclusionsThe Gompertz model fits fetal biometry growth and enables birth weight estimation without need of late-term ultrasounds. Aside from its clinical predictive value, we suggest its use for future growth standards, with almost all variation described by a single scale parameter A.

A Gauss kernel non-local stress-driven plate theory

This study presents a novel stress-driven formulation, incorporating Kirchhoff’s plate assumptions and accounting for the non-local size-dependent feature in both plate geometric axes, which is practical, especially near the origin of the axis in the polar coordinates. The presented formulation does not impose any additional constraints on the elastic radial curvatures, which are known as constitutive boundary conditions. Therefore, taking into account the non-local behavior in both radial and circumferential directions does not lead to an overconstrained problem. The study focuses on the analysis of a circular plate with an outer radius (R), thickness (h), and the length scale parameter (L). The governing differential equations are derived in Cartesian coordinates and then transformed to the polar coordinates to analyze circular plates. When R tends to infinity, the governing equation is solved analytically. Using the Galerkin technique, a finite element solution is presented for the analysis of a bounded circular plate with a clamped boundary condition at the outer radius R. The study discusses the size effects and the gradient properties of functionally graded plates in stress-driven non-local theory. It reveals that while increasing the non-local parameter results in a reduction of transverse displacement, the moments remain unaffected.

Symmetry, Asymmetry and Studentized Statistics

Inferences on the location parameter λ in location-scale families can be carried out using Studentized statistics, i.e., considering estimators λ˜ of λ and δ˜ of the nuisance scale parameter δ, in a statistic T=g(λ˜,δ˜) with a sampling distribution that does not depend on (λ,δ). If both estimators are independent, then T is an externally Studentized statistic; otherwise, it is an internally Studentized statistic. For the Gaussian and for the exponential location-scale families, there are externally Studentized statistics with sampling distributions that are easy to obtain: in the Gaussian case, Student’s classic t statistic, since the sample mean λ˜=X¯ and the sample standard deviation δ˜=S are independent; in the exponential case, the sample minimum λ˜=X1:n and the sample range δ˜=Xn:n−X1:n, where the latter is a dispersion estimator, which are independent due to the independence of spacings. However, obtaining the exact distribution of Student’s statistic in non-Gaussian populations is hard, but the consequences of assuming symmetry for the parent distribution to obtain approximations allow us to determine if Student’s statistic is conservative or liberal. Moreover, examples of external and internal Studentizations in the asymmetric exponential population are given, and an ANalysis Of Spacings (ANOSp) similar to an ANOVA in Gaussian populations is also presented.

Identification of damage in timber I-beams using continuous wavelet transform of deflection measured with digital image correlation

The article presents a method for detecting damage in timber I-beams based on the continuous wavelet transform (CWT) of their static deflection, measured using the ARAMIS digital image correlation (DIC) system. So far, no detailed uncertainty analysis for this type of identification has been carried out. Filling this gap was the main motivation for the authors to conduct this research. For this purpose, analytical and experimental static deflection CWT analyses were performed for the timber I-beams with softwood flanges and oriented strand board webs, in which local cross-sectional weakenings were artificially introduced for verification purposes. A detailed analysis of the CWT uncertainty resulting from measurement errors and numerical data processing allowed its expression as a function of the beam axis position and the scale parameter. Based on the research, a new methodology was formulated for the diagnostic defect identification in timber beams related to bending stiffness reduction.

Strong evidence for universality in homogeneous compressible turbulence

Quantifying the degree of universality in compressible turbulence is challenging due to the existence of different modes and their complex interactions. For a restricted family of flows, Donzis and John [Phys. Rev. Fluids 5, 084609 (2020)] showed that universal behavior is indeed observed in compressible turbulence if the ratio of dilatational to solenoidal root mean square (rms) velocities (δ=u′d/u′s) is incorporated as a scaling parameter along with the traditional turbulent Mach number (Mt=u′/〈c〉, where u′ is the rms velocity and 〈c〉 is the mean speed of sound). In this paper, we argue for the generality of those results by analyzing a wide range of compressible turbulent flows spanning a variety of flow configurations and setups to assess the degree of universal behavior. These include, among others, reacting flows, flows with solenoidal, thermal, and dilatational forcing, and flows with mean shear and bulk viscosity. We also performed new direct numerical simulations, which include turbulence in situations where vibrational modes of constitutive molecules are not in thermal equilibrium. Collectively, we offer the largest comparison across studies in the literature to date. We find that despite the wide range of forcing conditions and physical processes, universality holds across all these turbulent flows to a very satisfactory degree when both δ and Mt are considered as intrinsic compressibility parameters. The statistics investigated here—single-point statistics up to order four—are chosen such that they represent different ranges across the spectrum of dynamically relevant turbulence scales. We discuss the applicability of the purposed universal behavior for other key statistics in these turbulent flows, including two-point statistics and inhomogeneity effects, and the perspective it opens for modeling them.

Quantum Imitation Learning.

Despite remarkable successes in solving various complex decision-making tasks, training an imitation learning (IL) algorithm with deep neural networks (DNNs) suffers from the high-computational burden. In this work, we propose quantum IL (QIL) with a hope to utilize quantum advantage to speed up IL. Concretely, we develop two QIL algorithms: quantum behavioral cloning (Q-BC) and quantum generative adversarial IL (Q-GAIL). Q-BC is trained with a negative log-likelihood (NLL) loss in an offline manner that suits extensive expert data cases, whereas Q-GAIL works in an inverse reinforcement learning (IRL) scheme, which is online, on-policy, and is suitable for limited expert data cases. For both QIL algorithms, we adopt variational quantum circuits (VQCs) in place of DNNs for representing policies, which are modified with data reuploading and scaling parameters to enhance the expressivity. We first encode classical data into quantum states as inputs, then perform VQCs, and finally measure quantum outputs to obtain control signals of agents. Experiment results demonstrate that both Q-BC and Q-GAIL can achieve comparable performance compared to classical counterparts, with the potential of quantum speedup. To our knowledge, we are the first to propose the concept of QIL and conduct pilot studies, which paves the way for the quantum era.

Evaluation of new Garima data using type-II generalized progressive-hybrid technique and its application to a sodium–sulfur battery

In recent years, several novel modeling applications have been able to better fit complex datasets, and they can provide insights that would not be possible with traditional distributions. A new model developed by mixing the exponential and gamma models, called the Garima model, is discussed in this article. This model exhibits a better behavior fit than exponential and Lindley, among others. When the reliability practitioner wishes to score a specific number of failed units, a generalized progressive-hybrid-censored Type-II technique has been proposed to reduce both the length and expense of a life test. Given the availability of the presented data, the difficulty of estimating the scale parameter and various reliability time aspects of the Garima model is investigated using likelihood and Bayes inferential approaches. In addition, when the Garima parameter is assumed to have gamma density prior, the Markovian-Chain via Monte-Carlo sampler from a symmetric loss is performed to obtain the symmetric Bayes’ infer. Besides the asymptotic confidence intervals, the highest intervals for all unknown subjects are also developed. Simulation comparisons are also carried out, and useful recommendations are provided. A real data application is examined based on genuine datasets from the physical sector to see how the examined approaches may be implemented in real-life situations.

Least squares regression under weak moment conditions

In this paper we consider the robust regression problem when the output variable may be heavy-tailed. In such scenarios, the traditional least squares regression paradigm is usually thought to be not a good choice as it lacks robustness to outliers. By projecting the outputs onto an adaptive interval, we show the regularized least squares regression can still work well when the conditional distribution satisfies a weak moment condition. Fast convergence rates in various norm are derived by tuning the projection scale parameter and regularization parameter in according with the sample size and the moment condition.

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The square-lattice J1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$J_1$$\\end{document}-J2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$J_2$$\\end{document}XXZ model with the ring-exchange interaction K was investigated numerically. As for the hard-core-boson model with the nearest-neighbor hopping J1/2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$J_1/2$$\\end{document}, namely, the J1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$J_1$$\\end{document}-KXY model, it has been reported that the ring exchange leads to a variety of exotic phases such as the valence-bond-solid (VBS) phase. In this paper, we extend the parameter space to investigate the phase boundary between the XY (superfluid) and VBS phases. A notable feature is that the phase boundary terminates at the fully frustrated point, J2/J1→0.5-\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$J_2/J_1 \\rightarrow 0.5^-$$\\end{document}. As a scaling parameter for the multi-criticality, the distance from the multi-critical point δ(≥0)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\delta (\\ge 0)$$\\end{document} is introduced. To detect the phase transition, we employed the high-order fidelity susceptibility χF(3)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\chi ^{(3)}_F$$\\end{document}, which is readily evaluated via the exact-diagonalization scheme. As a demonstration, for a fixed value of δ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\delta $$\\end{document}, the XY-VBS criticality was analyzed by the probe χF(3)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\chi ^{(3)}_F$$\\end{document}. Thereby, with properly scaling δ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\delta $$\\end{document}, the χF(3)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\chi ^{(3)}_F$$\\end{document} data were cast into the crossover-scaling formula to determine the multi-criticality.Graphic abstract

Bayesian Approach for Estimating the Parameters of the Time-To-Failure Distribution and Its Percentiles Under Power Degradation Model

The degradation models are often applied on the degradation data for studying time-to-failure distribution. In this study, the Bayesian approach is applied on the power degradation model for estimating the parameters of the time-to-failure distribution and its percentiles. Two different distributions are assumed for the degradation parameter of the model. The degradation parameter is firstly assumed to follow the skew-normal distribution with three jointly independently distributed parameters such that the gamma prior is assumed for the shape parameter, while the scale and the location parameters are assumed uniform. The second distribution assumed for the degradation parameter is the log-logistic distribution with two jointly independent random parameters where the shape parameter is assumed gamma, while the scale parameter is assumed uniform. Based on the Gibbs sampling method carried out under the JAGS platform, the models considered are applied on the simulated data and the NASA turbofan Jet engine dataset and the results found are compared. In modeling the time-to-failure distribution, it is shown that based on the simulated data and real data, the Bayesian approach for the power degradation model with the skew-normal degradation parameter outperformed the Bayesian approach for the power degradation model with the log-logistic degradation parameter.

THE INFLUENCE OF BRAND, PRICE AND PRODUCT QUALITY ON SHOPEE E-COMMERCE PURCHASING DECISIONS

The development of information technology in the 4.0 era has changed people's lifestyles, including product purchasing behavior through e-commerce. This research aims to determine the influence of brand, price and product quality variables on Shopee e-commerce purchasing decisions. The research object was carried out in Semarang district with a generation Z population aged 18-27 years. The number of respondents was 95 people with the sampling technique using a non-probability sampling technique with a purposive sampling method. Data collection used a questionnaire with Likert scale parameters. The data analysis technique uses multiple linear regression and is processed using SPSS version 29 software. The results of data analysis show that brand and price variables have a positive and significant effect on Shopee e-commerce purchasing decisions. Meanwhile, the product quality variable does not significantly influence Shopee e-commerce purchasing decisions. The coefficient of determination value shows a value of 32.1% with a significance level of 0.05.

The free vibration of the MEE sandwich microplate with the FG-CNTRC core using the MSGT

This study deals with the free vibration of the sandwich microplate with the core made of functionally graded carbon nanotube-reinforced composites (FG-CNTRC) and magneto-electro-elastic (MEE) face sheets. The governing equation of the microplates is derived by using the refined plate theory (RPT) with two variables and the modified strain gradient theory (MSGT). The Non-Uniform Rational B-Splines (NURBS) basis function of the isogeometric approach (IGA) is used for the approximation of the displacement and electric and magnetic fields of the microplates. The paper studies the effect of the length scale parameters (LSPs), CNTs distributions, CNTs volume fraction, magnetic and electric loads and geometry on the vibrational frequency of the MEE sandwich microplate.

New Lepage-type control charts for joint monitoring of location and scale

This paper introduces two new Shewhart Lepage-type control charts for jointly monitoring the location and scale parameters of continuous processes. The first is based on the van der Waerden (VW) and Ansari-Bradley (AB) tests while the other is on the VW and Mood tests. Statistical performances, in terms of average run length (ARL), of these charts are evaluated numerically and compared with that of their two competitor charts in the existing literature under four distributional models for the process output, namely, the normal, lognormal, Laplace, and logistic. The numerical results show that irrespective of the process distribution, one of the proposed charts (based on VW and Mood tests) has the best performance among all the four charts in the detection of simultaneous shifts in both the parameters of all sizes as well as in the detection of shifts in the scale that have not been accompanied by shifts in the location (only-scale shifts) of all sizes. Moreover, the other proposed chart (based on VW and AB tests) performs better than one of the competitor charts in the existing literature for detecting simultaneous shifts as well as only-scale shifts of all sizes. In addition, it performs better than the other competitor chart for detecting the simultaneous shifts consisting of a large location shift and a small scale shift, however, performs worse than that for detecting the simultaneous shifts consisting of a small location shift and a scale shift of any size, as well as for detecting the only-scale shifts of all sizes. All the four charts perform almost similarly in the detection of only-location shifts of all sizes. Regression models are provided for the proposed charts, which facilitate their designs in practice. Finally, the practical implementation of the proposed charts is illustrated through a real-data example.

Scaling-Up for the Counter-Rotating Twin Screw Extrusion of Polymers.

A novel and original computer scaling-up system for the counter-rotating twin screw extrusion of polymers was developed. In the system, each scaling parameter (scaling criterion) may be considered as an objective function to be minimized for the single parameters or the functional relationships along the length of the screw. Scaling was based on the process simulation, which was performed using the comprehensive (or global) counter-rotating twin screw extrusion program called TSEM (Twin Screw Extrusion Model). The extrusion process was scaled by applying GASESTWIN (Genetic Algorithms Screw Extrusion Scaling) software developed for this purpose using genetic algorithms. Scaling up the extrusion process was carried out to enhance extrusion process throughput according to the scaling criteria specified by the single quantities of polymer melt temperature at the die exit and relative melting length, and by distributions along the screw length of the extrusion parameters of the polymer melt temperature and polymer plasticating. The global objective function had the lowest value for the selected extrusion parameters, which means the minimal differences between the values of the scaled-up processes and extrusion throughput was significantly increased. The solution to the problem of scaling the counter-rotating process presented in this paper complements the existing solutions for optimizing and scaling basic variants of the extrusion process, i.e., flood-fed and starve (metered)-fed single-screw extrusion, as well as co-rotating and counter-rotating twin-screw extrusion.