Continuous Distribution Research Articles

Metallurgical characteristics of AA6061 aluminium and AZ31B magnesium dissimilar joints by fusion welding technique.

Aluminium (Al) and magnesium (Mg) alloys are extensively used in the automobile sector because of their high strength-to-weight ratio, excellent castability low density and simplicity of recycling. Al-Mg structures used in the automotive sector can potentially reduce their weight. Although there is a significant opportunity for substantial cost reduction, the use of magnesium in aluminium structures remains restricted. This study aims to weld 3 mm-thick rolled sheets of AA6061 Al and AZ31B Mg alloy using the cold metal transfer (CMT) arc welding process. Three different filler wires (ER1100, ER4043, and ER5356) were used in the experiment. In this article, the mechanical and microstructure characteristics of Al/Mg dissimilar joints manufactured by CMT are evaluated and discussed in detail. Optical microscope (OM), scanning electron microscopy (SEM), energy dispersive x-ray spectroscopy (EDX), and x-ray diffraction (XRD) were used to analyze the CMT-welded Al/Mg dissimilar joints. Of the three filler wires used, ER4043 (Al-5%Si) filler wire yielded defect-free sound joints due to the presence of Si, which improves the flow ability of molten filler during welding. The presence of Mg-rich intermetallics-Al12Mg17)and Al-rich intermetallics-Al3Mg2 were observed. The fractured area of the CMT-welded Al/Mg dissimilar joints revealed the presence of the Mg-rich intermetallics (Al12Mg17), which is responsible for the decrease in tensile strength. The reduction of intermetallics, particularly of Mg-rich intermetallics (Al12Mg17) is important for improving joint strength. RESEARCH HIGHLIGHTS: Cold metal transfer (CMT) arc welding was used to control the Al-Mg-rich intermetallics in the Al/Mg dissimilar joints. The microstructure, morphology and phase composition of the welded joints were studied by OM, SEM, TEM, EDS and XRD. The weld metal and AL substrate bonded with a strong interface, while weld metal and Mg substrate were joined at the epitaxial solidification area where the intermetallic compounds of Mg2Al3, Mg17Al12 and Mg2Si are generated. The weld metal on the Mg side experienced brittle fracture, with a continuous distribution of Mg2Al3, Mg17Al12 and Mg2Si.

Mathematical diversity of parts for a continuous distribution

The current paper is part of a series exploring how to link diversity measures (e.g., Gini-Simpson index, Shannon entropy, Hill numbers) to a distribution’s original shape and to compare parts of a distribution, in terms of diversity, with the whole. This linkage is crucial to understanding the exact relationship between the density of an original probability distribution, denoted by p(x), and the diversity D in non-uniform distributions, both within parts of a distribution and the whole. Empirically, our results are an important advance since we can compare various parts of a distribution, noting that systems found in contemporary data often have unequal distributions that possess multiple diversity types and have unknown and changing frequencies at different scales (e.g. income, economic complexity ratings, rankings, etc.). To date, we have proven our results for discrete distributions. Our focus here is continuous distributions. In both instances, we do so by linking case-based entropy, a diversity approach we developed, to a probability distribution’s shape for continuous distributions. This allows us to demonstrate that the original probability distribution g 1, the case-based entropy curve g 2, and the slope of diversity g 3 (c (a,x) versus the c(a,x)*lnA(a,x) curve) are one-to-one (or injective). Put simply, a change in the probability distribution, g 1, leads to variations in the curves for g 2 and g 3. Consequently, any alteration in the permutation of the initial probability distribution, which results in a different form, will distinctly define the graphs g 2 and g3 . By demonstrating the injective property of our method for continuous distributions, we introduce a unique technique to gauge the level of uniformity as indicated by D/c. Furthermore, we present a distinct method to calculate D/c for different forms of the original continuous distribution, enabling comparison of various distributions and their components.

A Discrete Odd Lindley Half-Logistic Distribution with Applications

In the reality, the most of lifetime data is discrete in nature, despite it is known that this data is continuous. As a consequence, the tendency to convert the continuous lifetime distributions to its discrete counterpart has raised. The nature of the most lifetime data in real life is discrete, thus, many of researchers interested to convert. This article aims to introduce a new one-parameter discrete distribution, namely Discrete Odd Lindley Half-Logistic (DOLiHL) distribution. The DOLiHL distribution is derived by discretizing the analogue continuous distribution, using a survival discretization technique. An intensive study of this distribution is provided, including characteristic functions and statistical properties. Moreover, the unknown parameter is estimated using different methods of estimation namely, the maximum likelihood method, method of moments, least squares method and Cramer-von Mises minimum distance estimation method. A simulation study is conducted to examine the distribution’s behavior and compare between the estimation methods at different sample sizes. To evaluate the efficiency of this distribution against other competitive distributions, an implementation on real data in different fields is performed. In conclude, the DOLiHL distribution has assured its efficiency of fitting in lifetime and count data from various fields in real life.

A Solution for the Density Dichotomy Problem of Kuiper Belt Objects with Multispecies Streaming Instability and Pebble Accretion

Kuiper Belt objects (KBOs) show an unexpected trend, whereby large bodies have increasingly higher densities, up to five times greater than their smaller counterparts. Current explanations for this trend assume formation at constant composition, with the increasing density resulting from gravitational compaction. However, this scenario poses a timing problem to avoid early melting by decay of 26Al. We aim to explain the density trend in the context of streaming instability and pebble accretion. Small pebbles experience lofting into the atmosphere of the disk, being exposed to UV and partially losing their ice via desorption. Conversely, larger pebbles are shielded and remain icier. We use a shearing box model including gas and solids, the latter split into ices and silicate pebbles. Self-gravity is included, allowing dense clumps to collapse into planetesimals. We find that the streaming instability leads to the formation of mostly icy planetesimals, albeit with an unexpected trend that the lighter ones are more silicate-rich than the heavier ones. We feed the resulting planetesimals into a pebble accretion integrator with a continuous size distribution, finding that they undergo drastic changes in composition as they preferentially accrete silicate pebbles. The density and masses of large KBOs are best reproduced if they form between 15 and 22 au. Our solution avoids the timing problem because the first planetesimals are primarily icy and 26Al is mostly incorporated in the slow phase of silicate pebble accretion. Our results lend further credibility to the streaming instability and pebble accretion as formation and growth mechanisms.

LSTM‐based post‐processing for noise reduction in SVD‐based particulate matter digital twinning on lightweight embedded devices

AbstractAmong various applications of digital twins, measuring particulate matter in the context of air pollution has become increasingly important due to growing interest in atmospheric environments. By obtaining particle count values from analogue‐to‐digital converter raw data through photodiode and calibrating them, particulate matter values can be acquired. The singular‐value–decomposition is efficient transfer function learning method. However, due to the linear nature of the transfer function of singular‐value–decomposition, it also conveys noise information, necessitating post‐processing to suppress noise. This study proposes a method that utilizes long short‐term memory neural networks to effectively stabilize noise based on the output of continuous dust sensor particulate matter distributions. Using the singular value decomposition based particulate matter shows relative root‐mean‐square error (4.4761, 100%) as a reference, the proposed long short‐term memory post‐processing demonstrates an improved result (2.9328, 65.52%) compared to other post‐processing method: the mean filter (3.6704, 82.00%), low‐pass filter (3.7719, 84.27%) and Kalman filter (3.5550, 79.42%). Furthermore, to address the limitation of initial delay in long short‐term memory to achieve stable data output, a method of iteratively training the initial input data sample is proposed. For the initial input data, the non‐initialization approach exhibited a relative error of 87.57% and it took around 5 samples to predict stable output. In contrast, the proposed iterative training method, applied five times to the initial data sample, achieved a relative error of 9.51% and immediately obtained stable data.

Factor analyzing ordinal items requires substantive knowledge of response marginals.

In the social sciences, measurement scales often consist of ordinal items and are commonly analyzed using factor analysis. Either data are treated as continuous, or a discretization framework is imposed in order to take the ordinal scale properly into account. Correlational analysis is central in both approaches, and we review recent theory on correlations obtained from ordinal data. To ensure appropriate estimation, the item distributions prior to discretization should be (approximately) known, or the thresholds should be known to be equally spaced. We refer to such knowledge as substantive because it may not be extracted from the data, but must be rooted in expert knowledge about the data-generating process. An illustrative case is presented where absence of substantive knowledge of the item distributions inevitably leads the analyst to conclude that a truly two-dimensional case is perfectly one-dimensional. Additional studies probe the extent to which violation of the standard assumption of underlying normality leads to bias in correlations and factor models. As a remedy, we propose an adjusted polychoric estimator for ordinal factor analysis that takes substantive knowledge into account. Also, we demonstrate how to use the adjusted estimator in sensitivity analysis when the continuous item distributions are known only approximately. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

Incentive Mechanism in the Sponsored Content Market With Network Effects

We propose an incentive mechanism for the sponsored content provider (CP) market in which the communication of users can be represented by a graph, and the private information of the users is assumed to have a continuous distribution function. The CP stipulates incentive rewards to encourage users to reveal their private information truthfully and increase their content demand, which leads to an increase in the advertising revenue. We prove that all users gain a nonnegative utility and disclose their private information truthfully. Moreover, we study the effectiveness and scalability of the proposed mechanism in a case study with different network structures.

Multivariate Density Estimation by Neural Networks.

We propose nonparametric methods to obtain the Probability Density Function (PDF) to assess the properties of the underlying data generating process (DGP) without imposing any assumptions on the DGP, using neural networks (NNs). The proposed NN has advantages compared to well-known parametric and nonparametric density estimators. Our approach builds on literature on cumulative distribution function (CDF) estimation using NN. We extend this literature by providing analytical derivatives of this obtained CDF. Our approach hence removes the numerical approximation error in differentiating the CDF output, leading to more accurate PDF estimates. The proposed solution applies to any NN model, i.e., for any number of hidden layers or hidden neurons in the multilayer perceptron (MLP) structure. The proposed solution applies the PDF estimation by NN to continuous distributions as well as discrete distributions. We also show that the proposed solution to obtain the PDF leads to good approximations when applied to correlated variables in a multivariate setting. We test the performance of our method in a large Monte Carlo simulation using various complex distributions. Subsequently, we apply our method to estimate the density of the number of vehicle counts per minute measured with road sensors for a time window of 24 h.

Characterization of a functionally graded material produced using a new designed blender

Abstract One of the techniques widely used for fabrication of FGMs (Functionally Graded Materials) is powder metallurgy. However, producing a FGM with smooth gradient in its constituents mixture has remained a challenge yet to be met. The purpose of this research is design and manufacturing a blender for producing a functionally graded material with smooth gradient of its constituent materials. The blender was used to mix magnesium and titanium dioxide to produce Magnesium/titanium dioxide FGMs. The powder mixture was then compacted by Instron, drop hammer, and split Hopkinson bar at 600 °C. The microstructure and relative density of the functionally graded samples fabricated at different strain rates were studied in this work. SEM images clearly demonstrated a continuous and functional distribution of Mg and TiO2 particles in the produced FGM samples. It was also shown that increasing the compaction loading rate resulted in a higher relative density in the FGM samples. The maximum relative density (92%) was observed for the samples produced by Hopkinson bar. This level of density was 7% and 17% higher than the densities of the samples fabricated using drop hammer and Instron, respectively. The improvement of relative density in dynamic compaction methods is attributed to the increased compaction pressure and process being adiabatic.

Maximum Entropy Criterion for Moment Indeterminacy of Probability Densities.

We deal with absolutely continuous probability distributions with finite all-positive integer-order moments. It is well known that any such distribution is either uniquely determined by its moments (M-determinate), or it is non-unique (M-indeterminate). In this paper, we follow the maximum entropy approach and establish a new criterion for the M-indeterminacy of distributions on the positive half-line (Stieltjes case). Useful corollaries are derived for M-indeterminate distributions on the whole real line (Hamburger case). We show how the maximum entropy is related to the symmetry property and the M-indeterminacy.

Assessing the Impact of Copula Selection on Reliability Measures of Type P(X < Y) with Generalized Extreme Value Marginals

In reliability studies, we are interested in the behaviour of a system when it interacts with its surrounding environment. To assess the system’s behaviour in a reliability sense, we can take the system’s intrinsic quality as strength and the outcome of interactions as stress. Failure is observed whenever stress exceeds strength. Taking Y as a random variable representing the stress the system experiences and random variable X as its strength, the probability of not failing can be taken as a proxy for the reliability of the component and given as P(Y<X)=1−P(X<Y). This way, in the present paper, it is considered that X and Y follow generalized extreme value distributions, which represent a family of continuous probability distributions that have been extensively applied in engineering and economic contexts. Our contribution deals with a more general scenario where stress and strength are not independent and copulas are used to model the dependence between the involved random variables. In such modelling framework, we explored the proper selection of copula models characterizing the dependence structure. The Gumbel–Hougaard, Frank, and Clayton copulas were used for modelling bivariate data sets. In each case, information criteria were considered to compare the modelling capabilities of each copula. Two economic applications, as well as an engineering one, on real data sets are discussed. Overall, an easy-to-use methodological framework is described, allowing practitioners to apply it to their own research projects.

A Copula-Based Bivariate Composite Model for Modelling Claim Costs

This paper aims to develop a new family of bivariate distributions for modelling different types of claims and their associated costs jointly in a flexible manner. The proposed bivariate distributions can be viewed as a continuous copula distribution paired with two marginals based on composite distributions. For expository purposes, the details of one of the proposed bivarite composite distributions is provided. The dependence measures for the resulting bivariate copula-based composite distribution are studied, and its fitting is compared with other bivariate composite distributions and existing bivariate distributions. The parameters of the proposed bivariate composite model are estimated via the inference functions for margins (IFM) method. The suitability of the proposed bivariate distribution is examined using two real-world insurance datasets, namely the motor third-party liability (MTPL) insurance dataset and Danish fire insurance dataset.

On the role of plastic relaxation in stress assisted grain boundary oxidation

The influence of plasticity on the high-temperature stress-assisted grain boundary oxidation of nickel-based superalloys used in applications such as turbine rotor discs is investigated using the method of discrete dislocation plasticity (DDP). The misfit stress fields of nib-shaped intrusions are captured by a continuous distribution of edge dislocations whose extra half planes represent the volumetric misfit of the oxide, which is implemented in a planar formulation of DDP by invoking the linear superposition principle. DDP simulations show that stresses generated by an intrusion several microns or more in size are large enough to generate dislocation pileups with associated stresses at the intrusion interface on the order of 1 GPa, which in turn lead to localized growth and morphology change of the intrusion by stress-assisted diffusion. This morphology change relaxes the compression stress inside the intrusion near the base, and therefore increases the fracture resistances of the intrusion. The effects of applied loading and background plasticity on the growth rate of the intrusion in defect-free and prestrained samples are predicted. It is found that applied tensile stress generally increases grain boundary oxidation, while in prestrained samples the enhancement of the intrusion growth rate by the applied load is insignificant due to dislocation pile-ups ahead of the oxidation process.

Discrete half-logistic distributions with applications in reliability and risk analysis

AbstractIn the statistical literature, several discrete distributions have been developed so far for modeling non-negative integer-valued phenomena, yet there is still room for new counting models that adequately capture the diversity of real data sets. Here, we first discuss a count distribution derived as a discrete analogue of the continuous half-logistic distribution, which is obtained by preserving the expression of its survival function at each non-negative integer support point. The proposed discrete distribution has a mode at zero and allows for over-dispersion; these two features make it suitable for modeling purposes in many fields (e.g., insurance and ecology), when these conditions are satisfied by the data. In order to widen its spectrum of applications, a discrete analogue is also presented of the type I generalized half-logistic distribution (obtained by adding a shape parameter to the simple one-parameter half-logistic), which allows us to model count data whose mode is not necessarily zero. For these new count distributions, the main statistical properties are outlined, and parameter estimation along with related issues is discussed. Their feasibility is proved on two real data sets taken from the literature, which have already been fitted by other well-established count distributions. Finally, a possible application is illustrated in the insurance field, related to the exact/approximate determination of the distribution of the total claims amount through the well-known Panjer’s recursive formula, within the framework of collective risk models.

Evaluating the influence of coal particle size gradation on the properties of coal–water slurry

This paper presents a comprehensive evaluation of the influence of coal particle size gradation on the properties of coal–water slurry (CWS), including coal concentration, flowability, stability, and rheological behavior. The research findings indicate that coarse coal particles have a dominant effect on improving the coal concentration of CWS, while fine coal particles significantly contribute to enhancing the flowability and stability of CWS. Also, a gradation approach incorporating both coarse and fine components with continuous particle size distributions was explored, successfully achieving a high performance CWS with a high coal concentration of 66.12 wt%, a flow time of 13.37 s indicating excellent flowability, and a water separation rate of 3.49 wt% after standing for 7 days, demonstrating good stability. Furthermore, the validity of these research results was confirmed by zeta potential analyses and scanning electron microscopy (SEM) investigations.

A novel generalized Weibull Poisson G classof continuous probabilisticdistributions with some copulas, properties and applications to real-life datasets.

The current study introduces and examines copula-coupled probability distributions. It explains their mathematical features and shows how they work with real datasets. Researchers, statisticians, and practitioners can use this study's findings to build models that capture complex multivariate data interactions for informed decision-making. The versatility of compound Gfamilies of continuous probability modelsallows them to mimic a wide range of events. These incidents can range from system failure duration to transaction losses to annual accident rates. Due to their versatility, compound families of continuous probability distributions are advantageous. They can simulate many events, even some not well represented by other probability distributions. Additionally, these compound families are easy to use. These compound families can also show random variable interdependencies. This work focuses on the construction and analysis of the novel generalized Weibull Poisson-G family. Combining the zero-truncated-Poisson G family and the generalized Weibull G family creates the compound G family. This family's statistics are mathematically analysed. This study uses Clayton, Archimedean-Ali-Mikhail-Haq, Renyi's entropy, Farlie, Gumbel, Morgenstern, and their modified variations spanning four minor types to design new bivariate type G families. The single-parameter Lomax model is highlighted. Two practical examples demonstrate the importance of the new family.

Archimedean Copulas-Based Estimation under One-Parameter Distributions in Coherent Systems

In the present work we provide a signature-based framework for delivering the estimated mean lifetime along with the variance of the continuous distribution of a coherent system consisting of exchangeable components. The dependency of the components is modelled by the aid of well-known Archimedean multivariate copulas. The estimated results are calculated under two different copulas, namely the so-called Frank copula and the Joe copula. A numerical experimentation is carried out for illustrating the proposed procedure under all possible coherent systems with three components.

Asymptotic properties of [formula omitted]th spacings based on records

In this work, the mth spacings based on record values obtained from continuous distributions are discussed. We first present distributional results for such spacings, and then, by making use of classification of distribution tails, derive asymptotic results for the mth record spacings. We also obtain strong limit results for them and illustrate our theoretical results by examples. Finally, we support our findings by data obtained from simulation experiments.

Regulating the continuous and concentrated distribution of Quasi-2D perovskite phases to achieve Sky-Blue Light-Emitting diodes with efficiency approaching 17%

Blue perovskite light-emitting diodes (PeLEDs) are increasingly crucial for manufacturing high-definition full-color displays due to their outstanding electroluminescent properties. Quasi-two-dimensional (quasi-2D) perovskite stands out as the most promising material for blue light-emitting layer, given its robust quantum/dielectric confinement. In this study, we present the preparation of PeLEDs with a tunable blue emission wavelength using pure bromide perovskite components by adjusting the content of halogenated organic ammonium bromide [2-bromoethylamine hydrobromide (BEABr)]. The bifunctional ligand BEABr not only achieves an excellent phase distribution of quasi-2D perovskite but also reduces the weak van der Waals gap between individual perovskite layers, facilitating effective energy transfer in perovskite films. Additionally, the bifunctional groups passivate perovskite defects and inhibit phase separation, leading to efficient and stable sky-blue luminescence. The BEABr-doped sky-blue PeLED demonstrated superior device performance, achieving a maximum external quantum efficiency of 16.98 % at 493 nm. This work serves as inspiration for further exploration of efficient and stable commercial blue PeLED devices.

Mapping long‐term terrace change in the Chinese Loess Plateau: A new approach by decision tree model with digital elevation model (DEM) and land use

AbstractHuman‐created terraces are distributed extensively in the Chinese Loess Plateau, which play key roles in soil conservation, agricultural production and sustainable development. However, large‐scale and long‐term terrace mapping remains a big challenge due to the complexity of topography, land cover and the deficiency of high‐quality historical spatial data. Facing this task, our study aims to develop a new approach for capturing 30 years (from 1990 to 2020) of terrace patterns at macroscales (the whole Loess Plateau, with an area of 6.4 × 105 km2). The decision tree model (DTM) was integrated with digital elevation model (DEM) and land use data to detect terrace change, and terraced samples were extracted from existing findings for spatial validation. Our study confirmed that this new approach can work successfully on identifying cultivated and grassy terraces, as evidenced by receiver operating characteristic (ROC) curves and area under curve (AUC) values. More notably, a decreasing trend was detected in cultivated terraces with continued uneven distribution from 1990 to 2020, while the areas of grassy terraces increased markedly with more‐concentrated larger patches. This finding indicated that huge areas of terrace abandonment may have already occurred in this region. More attention thus should be paid to the rising risks of cropland utilization and food security. Since it is the first time to get long‐term reliable terrace maps on the Loess Plateau, our efforts can help to better take stock of terrace resources for wiser land use managements and agricultural policy adjustments, finally benefiting socio‐ecological sustainability.