Distribution Parameters Research Articles

Bayesian Frequency Estimation Under Local Differential Privacy With an Adaptive Randomized Response Mechanism

Frequency estimation plays a critical role in many applications involving personal and private categorical data. Such data are often collected sequentially over time, making it valuable to estimate their distribution online while preserving privacy. We propose AdOBEst-LDP, a new algorithm for adaptive, online Bayesian estimation of categorical distributions under local differential privacy (LDP). The key idea behind AdOBEst-LDP is to enhance the utility of future privatized categorical data by leveraging inference from previously collected privatized data. To achieve this, AdOBEst-LDP uses a new adaptive LDP mechanism to collect privatized data. This LDP mechanism constrains its output to a subset of categories that ‘predicts’ the next user's data. By adapting the subset selection process to the past privatized data via Bayesian estimation, the algorithm improves the utility of future privatized data. To quantify utility, we explore various well-known information metrics, including (but not limited to) the Fisher information matrix, total variation distance, and information entropy. For Bayesian estimation, we utilize posterior sampling through stochastic gradient Langevin dynamics, a computationally efficient approximate Markov chain Monte Carlo (MCMC) method. We provide a theoretical analysis showing that (i) the posterior distribution of the category probabilities targeted with Bayesian estimation converges to the true probabilities even for approximate posterior sampling, and (ii) AdOBEst-LDP eventually selects the optimal subset for its LDP mechanism with high probability if posterior sampling is performed exactly. We also present numerical results to validate the estimation accuracy of AdOBEst-LDP. Our comparisons show its superior performance against non-adaptive and semi-adaptive competitors across different privacy levels and distributional parameters.

Modelling the spatio-temporal dynamics of youth unemployment in Africa: A Bayesian approach

Youth unemployment has remained one of the major social and economic problems facing many African countries despite persistent efforts by governments and other stakeholders to mitigate the problem. We deployed a two-parameter beta geospatial model within a distributional regression framework that enables us to link covariates to the mean and variance parameters of the response distribution, to study the spatio-temporal patterns of unemployment combining multiple African countries, while accounting for the impact of temperature and rainfall as climatic variables. We also examined the pattern of relationship between unemployment and gross domestic product of each of the countries over the study period. The data for the study was sourced from the World Bank Development Indicator database covering 1991 to 2020 while Bayesian inference was based on Markov chain Monte Carlo simulation. The findings reveal rising unemployment rates with increase in temperature and rainfall, and that in most cases, neighbouring African countries show similar unemployment pattern over the study period.

Parameter estimation for stable distributions and their mixture

In this paper, we consider estimating the parameters of univariate α-stable distributions and their mixtures. First, using a Gaussian kernel density distribution estimator, we propose an estimation method based on the characteristic function. The optimal bandwidth parameter was selected using a plug-in method. We highlight another estimation procedure for the Maximum Likelihood framework based on the False position algorithm to find a numerical root of the log-likelihood through the score functions. For mixtures of α-stable distributions, the EM algorithm and the Bayesian estimation method have been modified to propose an efficient and valuable tool for parameter estimation. The proposed methods can be generalised to multiple mixtures, although we have limited the mixture study to two components. A simulation study is carried out to evaluate the performance of our methods, which are then applied to real data. Our results appear to accurately estimate mixtures of α-stable distributions. Applications concern the estimation of the number of replicates in the Mayotte COVID-19 dataset and the distribution of the N-acetyltransferase activity of the Bechtel et al. data for a urinary caffeine metabolite implicated in carcinogens. We compare the proposed methods, together with a detailed discussion. We conclude with the limitations of this study, together with other forthcoming work and a future implementation of an R package or Python library for the proposed methods in data modelling.

Probabilistic Time Series Forecasting Based on Similar Segment Importance in the Process Industry

Probabilistic time series forecasting is crucial in various fields, including reducing stockout risks in retail, balancing road network loads, and optimizing power distribution systems. Building forecasting models for large-scale time series is challenging due to distribution differences, amplitude fluctuations, and complex patterns across various series. To address these challenges, a probabilistic forecasting method with two different implementations that focus on historical segment importance is proposed in this paper. First, a patch squeeze and excitation (PSE) module is designed to preprocess historical data, capture segment importance, and distill information. Next, an LSTM-based network is used to generate maximum likelihood estimations of distribution parameters or different quantiles for multi-step forecasting. Experimental results demonstrate that the proposed PSE module significantly enhances the base model’s prediction performance, and direct multi-step forecasting offers more detailed information for high-frequency data than recursive forecasting.

Maximum lq-likelihood estimator of the heavy-tailed distribution parameter

Studying the extreme value theory (EVT) involves multiple main objectives, among them the estimation of the tail index parameter. Some estimation methods are used to estimate the tail index parameter like maximum likelihood estimation (MLE). Additionally, the Hill estimator is one type of maximum likelihood estimator, which is a more robust with a large sample than a small sample. This research proposes the construction of an alternative estimator for the parameter of the heavy-tailed distribution using the maximum lq-likelihood estimation (MLqE) approach in order to adapt the ML and Hill estimator with the small sample. Furthermore, the maximum lq-likelihood estimator asymptotic normality is established. Moreover, several simulation studies in order to compare the MLq estimator with the ML estimators are provided. In the excesses over high suitable threshold values the number of the largest observation k will lead to an efficient estimate of the Hill estimator. For this, selection of k in the Hill estimator was investigated using the method of the quantile type 8 which is effective with the hydrology data. The performance of the Hill estimator and the lq-Hill estimator is subsequently compared by employing real relies with the distribution of hydrology data.

The formative time delay and electron avalanche number distributions for multielectron initiation of streamer breakdown

Electron avalanche statistics were mainly studied with a single electron initiation and there was no mathematical transition reported to the formative time delay distribution. This paper deals with the transition from the electron avalanche number distribution to the formative time delay distribution for multielectron initiation and streamer breakdown mechanism. The goal of the research is a detailed analysis of the formative time delay of electrical breakdown for different applications, such as spark counters, resistive plate chambers, gas-discharge switches, and high voltage systems with gas as an insulator. The electron avalanche number distribution for multielectron initiation is described by negative binomial distribution (NBD). Regarding the newly derived formative time delay distribution, when the number of initiating electrons k is small, the formative time delay distributions are asymmetric with the pronounced right tail. With increasing k, the formative time distributions shift to the shorter formative times and become narrower and higher, more symmetric and Gauss-like. As statistical tests show, for k≳20 the hypothesis that the formative time delay distributions are Gaussians cannot be rejected. As illustrations, the formative time delay distributions in neon and air at low reduced electric field are shown and briefly discussed. The distributions for methylal, ether and methane are presented in order to compare the estimated distribution parameters with available experimental data and to model the measured distributions.

Truly Multivariate Structured Additive Distributional Regression

Generalized additive models for location, scale and shape (GAMLSS) are a popular extension to mean regression models where each parameter of an arbitrary parametric distribution is modelled through covariates. While such models have been developed for univariate and bivariate responses, the truly multivariate case remains extremely challenging for both computational and theoretical reasons. Alternative approaches to GAMLSS may allow for higher-dimensional response vectors to be modelled jointly but often assume a fixed dependence structure not depending on covariates or are limited with respect to modelling flexibility or computational aspects. We contribute to this gap in the literature and propose a truly multivariate distributional model, which allows one to benefit from the flexibility of GAMLSS even when the response has dimension larger than two or three. Building on copula regression, we model the dependence structure of the response through a Gaussian copula, while the marginal distributions can vary across components. Our model is highly parameterized but estimation becomes feasible with Bayesian inference employing shrinkage priors. We demonstrate the competitiveness of our approach in a simulation study and illustrate how it complements existing approaches along the examples of childhood malnutrition and a yet unexplored data set on traffic detection in Berlin.

Refined speckle contrast estimation in OCT based on compensation of scattering-related distortions of speckle pattern parameters

Abstract Speckle contrast (SC) parameters in optical coherence tomography (OCT) scans are formed by the interplay of several factors—local level of optical wave backscattering by the material inhomogeneities, parameters of spatial distribution of the latter and the degree of cumulative optical wave attenuation during its fourth-and-back propagation. For the optical wavelengths used in OCT, this attenuation is usually dominated by the influence of scattering in the visualized turbid tissues rather than by absorption. For sufficiently high concentrations of scatterers (at least a few scatterers in the coherence volume) characterized by comparable scattering strengths and a fairly homogeneous distribution in space, the interference of locally scattered waves should be characterized by a Rayleigh distribution of speckle amplitudes, for which the local SC tends to 0.52. Equivalently, in terms of speckle intensities, the local SC tends to unity. Local spatial inhomogeneities or strongly uneven scattering strengths lead to the appearance of increased values of SC, which may serve as a diagnostic feature of some tissue components in OCT images. At the same time, in comparison to surface speckles formed by coherent-light scattering from rough surfaces, OCT-beam attenuation during its fourth-and-back propagation may introduce intensity inhomogeneities in OCT scans even for homogeneous tissue areas. This effect results in artefactual distortion of the visible SC in comparison with the above-mentioned expected value. Moreover, the presence of individual strong scatterers may additionally non-locally distort SC values due to the appearance of elongated shadows below such scatterers, which causes lateral inhomogeneities in OCT scans. Here, we propose a refined SC parameter, which is cleaned from distorting scattering-related effects in both axial and lateral directions. Depth-resolved estimation of the optical attenuation coefficient is used to restore attenuation-free OCT scans, for which the refined SC is estimated. The efficiency of the proposed approach is demonstrated using both digital OCT phantoms with highly controlled properties and experimental OCT data.

Modified two-sample Anderson-Darling test statistic

Two-sample testing hypothesis has been used and discussed in several scientific fields. However, the underlying theoretical distribution cannot be assumed to have a specific parametric distribution such as a normal distribution. When it is difficult to assume an underlying distribution, non parametric statistical methods are preferable. Such methods are typically robust and require fewer assumptions regarding the underlying distribution. As it is difficult to determine the number of parameters in an unknown distribution, we are interested in testing whether two independent samples of distributions are equal. Although the power of the Kolmogorov-Smirnov test statistic is not high, it is the standard test statistic for this general alternative. However, there are some advantages in using the Anderson-Darling test statistic instead of the Kolmogorov-Smirnov test statistic. We introduce two modified Anderson-Darling test statistics and list the exact critical values for small sample sizes. Moreover, we derive the limiting distribution of the proposed test statistic. Furthermore, we investigate the power performances of the proposed test statistic in various scenarios using Monte-Carlo simulations. Simulation studies and real data analysis reveal that the proposed test statistic is a good competitor to existing omnibus test statistics and has some advantages in certain situations.

Research on unsteady flow characteristics of turbocharger turbine stage with coupling inlet and exhaust casings

The inlet and exhaust casings of marine turbochargers are closely coupled to the axial flow turbine. These are crucial parts that work with the axial flow turbine and have the ability to raise the power plant’s output power even higher. Their final stage of the axial flow turbine and the exhaust casing’s complex flow due to their close relationship will have a significant effect on each other’s aerodynamic performance. However, most existing studies have not paid sufficient attention to this coupled transient interaction. In this paper, the flow interaction between the axial flow turbine and the inlet and exhaust casings is studied. Particular attention is paid to the study of the coupled flow characteristics under design and variable operating conditions. This study is carried out using coupled computational fluid dynamics (CFD) simulation. The computational domain consists of an inlet casing, 28 stator blades, 43 rotor blades, and an exhaust casing. The commercial CFD software ANSYS CFX solver and the SST turbulence model are used to simulate the unsteady flow field of the turbocharger axial turbine coupled to the inlet and exhaust casings. In this paper, the turbine flow field and the inlet and exhaust casings flow fields are analyzed, and the influence of the exhaust casing on rotor surface pressure fluctuation is discussed. In addition, the flow field distribution and performance parameters of the axial flow turbine coupled with the inlet and exhaust casings under three different operating conditions have been calculated and analyzed. The results show that the inlet casing affects the circumferential distribution of the stator leading edge pressure, while the asymmetric back pressure caused by the exhaust casing flow field causes the low-frequency pressure fluctuation at the rotor blade surface. At the trailing edge of the suction surface, the complex flow separation and vortex structure in the exhaust casing are the main factors causing rotor-stator interaction. The low-frequency fluctuation amplitude caused by the exhaust casing is greater than that caused by the high-frequency fluctuation of the rotor-stator interaction. Moreover, as the flow coefficient increases, the low-frequency fluctuation amplitude is much greater than the high-frequency fluctuation amplitude.

MODERN METHODS OF QUANTITATIVE ASSESSMENT OF THE STRUCTURE OF HYDROCARBON RESOURCES OF LARGE PETROLEUM BASINS

The article discusses modern methods of quantitative assessment of the elements of hydrocarbon resource structure in large oil and gas (petroleum) basins. The assessment is based on the law of mass distribution of hydrocarbon accumulations, i.e., the truncated Pareto distribution. The procedure developed is used for: estimation of the truncated Pareto distribution parameters and cumulative hydrocarbon volumes concentrated in pools, prediction of their number and size distribution and total resources within each size-class interval; simulation of spatial distributions of hydrocarbon accumulations with transformation of a population of HC pools into a population of fields; prediction of the number and size-class distribution of total HC resources in pools and fields, and fields distribution by the number of HC pools. The involved analytical approach based on the simulation mathematical modeling is described.

Modeling and analysis of internal excitation and vibration characteristics of gears with early-stage crack and 3D tooth surface error

Affected by the tooth surface errors, the vibration characteristics of early crack failures are usually various under different tooth surface precision level. Therefore, to reveal the influence of three-dimensional (3D) tooth surface error (TSE) on the internal excitation and vibration characteristics of gears with early-stage crack (ESC), a coupling internal excitation model of gears with ESC and 3D errors is proposed based on a double-layer iterative method. In this model, the influence of meshing phase between tooth pair and along tooth width direction (TWD) on the time-varying mesh stiffness (TVMS) are simultaneously considered, which overcomes the limitations of traditional models that are only suitable for characterizing the coupled excitation of the two-dimensional tooth profile errors and TVMS. Based on verifying the proposed model, the effects of TSE type, parameters, and load on the TVMS, loaded static transmission error (LSTE), load distributions, and torsional deformation of the cracked gear teeth are investigated, and the vibration characteristics of ESC failures under the effects of 3D TSE are also explored. The research results show that the distribution parameters of 3D TSE have a significant effect on the internal excitation and vibration characteristics of gears with ESC, and thus measuring and evaluating the distribution parameters of TSE can help improve the accuracy of gear fault identification and diagnosis methods.

A noodle in a haystack: determining the conservation status of the rare and Data Deficient Ravensthorpe Range slider, Lerista viduata

Context One-seventh of the ~157,000 species assessed by the IUCN Red List of Threatened Species are Data Deficient (DD), with insufficient information to assess their extinction risk. Such a statistic is concerning from a conservation perspective because more than half are predicted to be threatened by extinction, yet they are generally neglected from conservation priority. Aims Here, we aimed to improve ecological knowledge, and inform the conservation status of, the DD Ravensthorpe Range slider (Lerista viduata), a historically rare skink confined to Western Australia’s Ravensthorpe Range. Methods A detailed framework was developed to improve data on attributes integral to the species’ IUCN Red List assessment (e.g. distribution, threats, population size): collation of historical records, fieldwork within and around its known range, preserved specimen analysis, on-ground and spatial analysis of threats, and inference from ecologically similar species. Key results We found that L. viduata is threatened under multiple IUCN Red List criteria (B1ab[i,ii,iii,v], B2ab[i,ii,iii,v], C2ab[ii], D2), and overall should be considered Critically Endangered. This status is based on its Extent of Occurrence (32 km2) being <100 km2, occurrence at one location (defined by the threat of fire), and an inferred continuing decline in its distribution and habitat parameters. The species’ small estimated population size (3,514–9,276 mature individuals) also renders it extinction prone. Conclusions We demonstrate that L. viduata, long perceived as DD, should be reclassified as Critically Endangered, and is of the utmost conservation concern. Implications Our study reiterates the need for DD species to receive greater consideration in conservation research and action.

Urban Traffic Simulation with Shared Mobility Services: An Approach Using Spatiotemporal Network Kernel Density Estimation and MATSim

The popularity of smartphones and 4G/5G network have enabled various novel transportation modes based on shared mobility, such as app-based ride-hailing services (e.g., Uber and Lyft) and shared micromobility services (e.g., Veo and Gotcha). However, little is known about to what degree their operations impact urban traffic, which is important for transportation planning and policy making. These companies seldom share their ride data due to business and user privacy reasons, and they are young and still exploring and growing their market to new locations. Recently, transportation engineering researchers began to collect data in large cities trying to understand the transportation impacts of shared mobility services, but (1) there does not exist a general analytics framework applicable to any city, and (2) the studies were based on historical data and cannot project the future easily to catch up with the rapid development of shared mobility services. In this paper, we introduce a general framework for multi-modal urban traffic analytics. The goal is to build a digital twin of the transportation in a city, i.e., an accurate agent-based transportation simulation model, based on a medium-sized dataset of the interested transportation modes collected by the research group combined with other open data sources such as US Census Bureau. With this digital twin, transportation engineering researchers can flexibly analyze the impact of shared mobility services under different scenarios, such as “if the number of Uber drivers doubles” or “if the number of deployed e-scooters doubles”. The digital twin may also enable new opportunities, such as being an environment for learning policies with reinforcement learning. Our framework consists of three steps: (1) fitting the spatiotemporal distribution of the shared mobility rides on the underlying road network, (2) generating the travel day-plans of the entire urban population based on the learned spatiotemporal ride distribution and user-specified parameters, and (3) configuring an agent-based simulation software such as MATSim to execute the generated realistic day-plans, which provides detailed transportation data for analytics. At the core of our approach is a new spatiotemporal network kernel density estimation (KDE) method that fixes the flaw of prior methods where the contributions of different data samples are not equal. We also propose a crowdsourcing method to collect app-based ride data that is easy to carry out in any city. Using Birmingham, AL as an example, we demonstrate how our framework can be applied to help transportation engineering researchers analyze the impacts of Uber ride-hailing and Veo e-scooter services.

Effect of Collagen Fiber Tortuosity Distribution on the Mechanical Response of Arterial Tissues.

This study investigated the effect of collagen fiber tortuosity distribution on the biomechanical failure and prefailure properties of arterial wall tissue. An in-silico model of the arterial wall was developed using data obtained from combined multiphoton microscopy imaging and uniaxial tensile testing. Layer dependent properties were prescribed for collagen, elastin, and ground substance. Collagen fibers were modeled as discrete anisotropic elements, while elastin and ground substance were modeled as homogeneous isotropic components. Our parametric analysis, using a finite element approach, revealed that different parameters of collagen fibers tortuosity distribution significantly influence both pre-failure and failure biomechanical properties. Increased fiber tortuosity improved the tissue strength whereas the dispersion in the tortuosity distribution reduced it. This study provides novel insights into the structural-mechanical interdependencies in arterial walls, offering potential targets for clinical assessments and therapeutic interventions aimed at mitigating rupture risks.

Relationship Between Road Traffic Composition and Noise Emission: an Investigation Based on Hungarian National Public Road Traffic Data

Different vehicles contribute to the noise emission of the total road traffic in different ways and degrees. Therefore, emission calculation methods classify road vehicles based on their typical noise emission parameters. This article investigated the role of the four vehicle categories of CNOSSOS-EU method (light motor vehicles, medium heavy vehicles, heavy vehicles, and powered two-wheelers) in generating road traffic noise emissions. Based on traffic data available for national public roads in Hungary, the proportion of each vehicle category in the total road traffic was determined, providing the average distribution and other statistical parameters for each road category. The impact of changes in the traffic composition on noise emission was analysed based on the statistical parameters. The results show the dominance of light vehicles for all road categories (76–89% on average). The average proportion of heavy vehicles is also significant on controlled-access highways (motorways: 21%, expressways: 15%) and main roads (9%). The deviation from the average traffic composition can cause a noticeable difference in road traffic noise emission (up to nearly 3 dB). It was found that the impact of changing the proportion of heavy and light vehicles on noise emission is higher on roads inside built-up areas.

On the posterior property of the Rician distribution

The Rician distribution, a well-known statistical distribution frequently encountered in fields like magnetic resonance imaging and wireless communications, is particularly useful for describing many real phenomena such as signal process data. In this paper, we introduce objective Bayesian inference for the Rician distribution parameters, specifically the Jeffreys rule and Jeffreys prior are derived. We proved that the obtained posterior for the first priors led to an improper posterior while the Jeffreys prior led to a proper distribution. To evaluate the effectiveness of our proposed Bayesian estimation method, we perform extensive numerical simulations and compare the results with those obtained from traditional moment-based and maximum likelihood estimators. Our simulations illustrate that the Bayesian estimators derived from the Jeffreys prior provide nearly unbiased estimates, showcasing the advantages of our approach over classical techniques. Additionally, our framework incorporates the S.A.F.E. principles – Sustainable, Accurate, Fair, and Explainable – ensuring robustness, fairness, and transparency in predictive modelling.

Gumbel–Logistic Unit Distribution with Application in Telecommunications Data Modeling

The manuscript deals with a new unit distribution that depends on two positive parameters. The distribution itself was obtained from the Gumbel distribution, i.e., by its transformation, using generalized logistic mapping, into a unit interval. In this way, the so-called Gumbel-logistic unit (abbr. GLU) distribution is obtained, and its key properties, such as cumulative distribution function, modality, hazard and quantile function, moment-based characteristics, Bayesian inferences and entropy, have been investigated in detail. Among others, it is shown that the GLU distribution, unlike the Gumbel one which is always positively asymmetric, can take both asymmetric forms. An estimation of the parameters of the GLU distribution, based on its quantiles, is also performed, together with asymptotic properties of the estimates thus obtained and their numerical simulation. Finally, the GLU distribution has been applied in modeling the empirical distributions of some real-world data related to telecommunications.

Exploring statistical and machine learning methods for modeling probability distribution parameters in downtime length analysis: a paper manufacturing machine case study

Manufacturing companies focus on improving productivity, reducing costs, and aligning performance metrics with strategic objectives. In industries like paper manufacturing, minimizing equipment downtime is essential for maintaining high throughput. Leveraging the extensive data generated by these facilities offers opportunities for gaining competitive advantages through data-driven insights, revealing trends, patterns, and predicting future performance indicators like unplanned downtime length, which is essential in optimizing maintenance and minimizing potential losses. This paper explores statistical and machine learning techniques for modeling downtime length probability distributions and correlation with machine vibration measurements. We proposed a novel framework, employing advanced data-driven techniques like artificial neural networks (ANNs) to estimate parameters of probability distributions governing downtime lengths. Our approach specifically focuses on modeling parameters of these distribution, rather than directly modeling probability density function (PDF) values, as is common in other approaches. Experimental results indicate a significant performance boost, with the proposed method achieving up to 30% superior performance in modeling the distribution of downtime lengths compared to alternative methods. Moreover, this method facilitates unsupervised training, making it suitable for big data repositories of unlabelled data. The framework allows for potential expansion by incorporating additional input variables. In this study, machine vibration velocity measurements are selected for further investigation. The study underscores the potential of advanced data-driven techniques to enables companies to make better-informed decisions regarding their current maintenance practices and to direct improvement programs in industrial settings.

Computational Exploration of Limonin as a Potential Inhibitor of DapB in Klebsiella pneumoniae.

Klebsiella pneumoniae has emerged as a significant multidrug-resistant pathogen, classified as a critical priority by the World Health Organization. The rising rates of antibiotic resistance have led to increased therapeutic failures, diminishing the effectiveness of existing antibiotics. Consequently, there is an urgent need for alternative treatments to effectively inhibit the growth of K. pneumoniae and mitigate associated diseases. Phytochemicals have demonstrated potential advantages over traditional antibiotics, prompting their exploration as innovative therapeutic agents. This study aimed to identify phytochemicals that can inhibit dapB, a vital enzyme in the lysine biosynthesis pathway of K. pneumoniae, which is essential for protein synthesis and the cross-linking of the bacterial peptidoglycan cell wall. We screened 17,934 phytochemicals based on Lipinski's Rule of Five, along with their Absorption, Distribution, Metabolism, Excretion properties and toxicological parameters. Next, we conducted triplicate docking studies against dapB to evaluate the library further. The most promising molecules then underwent 100 ns Molecular Dynamics simulations in triplicate, followed by MM/PBSA based binding free energy calculations to identify potential dapB inhibitors. This in silico analysis highlighted limonin as a promising inhibitor of dapB in K. pneumoniae. Further experimental validation is crucial to enhance limonin's potential as a novel therapeutic agent against K. pneumoniae-associated diseases.