Statistical Probability Distribution Research Articles

Part-of-speech Tagging for Low-resource Languages: Activation Function for Deep Learning Network to Work with Minimal Training Data

Numerous natural language processing (NLP) applications exist today, especially for the most commonly spoken languages such as English, Chinese, and Spanish. Popular traditional methods such as Rule based methods, Naive Bayes classifiers, Hidden Markov models, Conditional Random field-based classifiers, and other stochastic methods have contributed to this improvement in the past. Recently, deep learning has led to exciting breakthroughs in several areas of artificial intelligence, including image processing and natural language processing. It is important to label words as parts of speech to begin developing most of the NLP applications. A deep study in this area reveals that many popular approaches used for this purpose require massive training data. Therefore, these approaches have not been helpful for languages not rich in digital resources. Applying these methods with very little training data prompts the need for innovative problem-solving. This article describes our research, which examines the strengths and weaknesses of well-known approaches, such as conditional random fields and state-of-the-art deep learning models, when applied for part-of-speech tagging using minimal training data for Assamese and English. We also examine the factors affecting them. We discuss our deep learning architecture and the proposed activation function, which shows promise with little training data. The activation function categorizes words belonging to different classes with more confidence by using the outcomes of statistical methods with SMTaylor SoftMax in our deep learning model. With minimal training, our deep learning architecture using the proposed modification of SM-Taylor SoftMax improves accuracy upto 4%, for our small dataset. This technique is a combination of SMTaylor SoftMax and statistical probability distribution of words over tags.

Evaluation of the Feasibility of the Prediction of the Surface Morphologiesof AWJ-Milled Pockets by Statistical Methods Based on Multiple Roughness Indicators

Improvement of the surface quality of machined parts is essential in order to avoid excessive and costly post-processing. Although non-conventional processes can efficiently carry out the machining of difficult-to-cut materials with high productivity, they may also, for various reasons, be related to increased surface roughness. In order to optimize the surface quality of generated surfaces in a reliable way, surface profiles obtained during these processes must be adequately modeled. However, given that most studies have focused on Ra or Rz indicators or are based on the assumption of a normal distribution for the profile heights, relevant models cannot accurately represent the surface characteristics that exist in a real machined surface with a high degree of accuracy. Thus, in the present study, a new modeling approach based on the use of a statistical probability distribution for the surface profile height is proposed. After six different distributions were evaluated on the basis of a three-stage procedure involving different roughness indicators pertaining to the abrasive waterjet (AWJ) milling of pockets, it was found that, although it is not possible to model the nominal values of every roughness parameter simultaneously, in several cases, it is possible to approximate the values of critical indicators such as Ra, Rz, Rsk, Rku and Rp/Rv ratio by Weibull distribution with a sufficient degree of accuracy.

Vertical distribution characteristics of the typhoon gust factor based on a 356-m high meteorological gradient tower

The characteristics of typhoon gust factors (GF) are important for the design of high-rise buildings in coastal areas. Most research on GF are based on observational data near the ground. This has made it difficult to meet the increasing demand for high-rise building designs in recent years. Thus, improving the knowledge of the vertical distribution of GF inside the typhoon is necessary and helpful for the design of high-rises and the prevention of gust disasters. In this study, the data from a 365-m high meteorological tower were used to explore the vertical distribution features of the gust factor within the atmospheric boundary layer (ABL) of typhoons in coastal region. The results indicate that: (1) The statistical probability distribution of GF during the typhoon exhibits a non-Gaussian distribution at all observational heights of the tower. While the generalized extreme value distribution (GEV) can well describe the properties of the probability distribution of GF at different heights. (2) The GF have a weak relationship with the average wind speed. However, GF have a strong relationship with turbulence intensity and increases linearly with the turbulence intensity. Notably, the results from the previous empirical model of the GF do not fully match the parameterised results during typhoons in this study. (3) In the typhoon boundary layer, the bulk wind shear plays a significant role in generating turbulent eddies with scales comparable to the observation height, especially at lower layer. Besides, the strong turbulent fluctuations at near-ground layers may be a result of the coupling of several elements. The turbulent momentum flux transported downward from the upper layers has a significant impact on the peak gust, and the downward transported energy may further enhance the turbulent motion in lower layers, which may lead to a higher gust factor near the surface.

Analysis of 5.8 GHz Network for Line of Sight (LOS) and Non-Line of Sight (NLOS) in Suburban Environment

This paper presents the findings of radio wave characterization based on the measurement data at 5.8 GHz. The measurement data were collected by a testbed channel, which links with the following scenarios: a single tree, a row of trees, a row of trees and a road, a row of trees, a road, and a building. These experiments were conducted at University Teknologi Malaysia (UTM) Skudai, Johor to represent the suburban environment. The links consist of pairs of transmitting and receiving antennas that deploy the path of a line of sight (LOS) and non-line of sight (NLOS) radio propagation wave networks. Based on the measurement data analysis, the general issue concerning the statistical probability distribution and the characteristics of LOS and NLOS are examined and discussed. Note that 5.8 GHz technology can be used in both LOS and NLOS scenarios, but its performance varies based on the presence of obstacles and signal propagation characteristics. Other prominent experimental analysis methods, such as hypothesis testing and goodness of fit tests, are implemented to consolidate the findings. The analysis found that the empirical probability density function of LOS and NLOS channels follows Gaussian, Rayleigh, and Rician distribution. Predicting specific future technological developments, such as the availability of 5.8 GHz technology, is challenging because it depends on various factors, including research and development efforts, regulatory decisions, market demand, and technological advancements.

Analysis of 5.8 GHz Network for Line of Sight (LOS) and Non-Line of Sight (NLOS) in Suburban Environment

This paper presents the findings of radio wave characterization based on the measurement data at 5.8 GHz. The measurement data were collected by a testbed channel, which links with the following scenarios: a single tree, a row of trees, a row of trees and a road, a row of trees, a road, and a building. These experiments were conducted at University Teknologi Malaysia (UTM) Skudai, Johor to represent the suburban environment. The links consist of pairs of transmitting and receiving antennas that deploy the path of a line of sight (LOS) and non-line of sight (NLOS) radio propagation wave networks. Based on the measurement data analysis, the general issue concerning the statistical probability distribution and the characteristics of LOS and NLOS are examined and discussed. Note that 5.8 GHz technology can be used in both LOS and NLOS scenarios, but its performance varies based on the presence of obstacles and signal propagation characteristics. Other prominent experimental analysis methods, such as hypothesis testing and goodness of fit tests, are implemented to consolidate the findings. The analysis found that the empirical probability density function of LOS and NLOS channels follows Gaussian, Rayleigh, and Rician distribution. Predicting specific future technological developments, such as the availability of 5.8 GHz technology, is challenging because it depends on various factors, including research and development efforts, regulatory decisions, market demand, and technological advancements.

A digital twin-based analysis method to assess geometric variations for parts in batch production

Background In mass production, engineers are more concerned with the statistical distribution accuracy of parts in mass production rather than just the qualification of individual parts. However, currently, the statistical analysis methods designed for product accuracy are relatively scattered, and most of them focus on nominal part models. Therefore, there is a need to design a statistical analysis method for parts in mass production based on the Digital Twin model. >Methods This paper presents a novel method to analyse the geometric variations of parts in batch production in the production line, which is based on digital twins to model and evaluate deviations contributed by the geometrical condition, assembly condition and material condition. Firstly, the statistical descriptions of the parts, particularly the features of a digital twin for parts in batch production related to the geometry and position, are classified into various hierarchies. Secondly, a covariance method is employed to analyse the law of their shape from the descriptions. Thirdly, the parts' shape feature similarity for different terms is derived, including the linear features of pose constraint, rotation deviation, and geometric deviation and the curve features like a geometric deviation. Finally, the probability distribution of discrete points on the manufacturing error caused by different reasons is calculated. Results Two case studies of reducer and rail highlight the applicability of the proposed approach. The standard deviation of the points has similar trend with sample cases according to normal distribution. Conclusions This paper categorizes the deviations of batch parts into the linear features of pose constraint, rotation deviation, and geometric deviation. When batch parts exhibit any of these deviation types, the eigenvalues and eigenvectors of their covariance matrix show certain patterns, enabling the identification of the deviation type and calculation of the statistical deviation probability distribution for the corresponding features.

Decision Making Reliability Approach for Maintainability of Economizer of Coal Based Boiler

This paper investigates the maintainability of economizers of three coal-based boilers for making decision of selection of replacement or maintenance practices. A sudden failure in the economizer can result huge production loss hence, a suitable decision model is essential which provides a strong data base for making optimal decision. A practical model for making decision is developed with respect to failure/repair data of three different economizers and trend with serial correlation tests are conducted. An investigation is carried out to determine the idealized statistical probability distribution providing best fit distribution. Further their Reliability and Maintainability are calculated. The tests of trend and serial correlation show very fast increasing failure rate of economizer # 1&2 with respect to economizer # 3. The present paper highlights that the failure data of economizer # 1 and economizer # 2 follow the NHPP model with poor reliability condition which indicates that these economizers should be replaced to restore boiler system as new as. However, failure data of economizer #3 follows the Lognormal distribution with poor reliability condition which suggests to develop the Preventive Maintenance Interval (PMI) to restore the boiler system. The present model serves a strong ground to decide replacement/preventive maintenance policy for not only to economizers but also to any pressure parts of coal based boilers.

Stellar scintillation statistics and the impact of aperture averaging on space-to-ground optical communications.

Statistical probability distributions characterizing received optical power fluctuations, or scintillation, enable performance predictions of space-to-ground optical communication systems. In this paper, we present measurements of stellar scintillation over a wide range of elevation angles and turbulence conditions collected simultaneously with a 5 cm and 40 cm telescope aperture, which allows a comparison between minimal and significant aperture averaging conditions. The measured data is compared to a reasonable set of candidate probability distribution functions (PDFs), including lognormal, which is most often cited in the literature for weak to moderate scintillation. For scintillation indices (SIs) less than about 0.2, the Nakagami-m distribution provides the best representation of the collected data for both apertures and imposes a greater lasercom link penalty than a lognormal distribution, which has been inaccurately implemented as the default probability distribution in the literature. For larger values of the SI, the scintillation is best characterized by a Gamma-Gamma distribution. Additionally, the measured temporal covariance for weak to moderate scintillation conditions is found to be in reasonably good agreement with theoretical predictions.

A high-throughput technique to evaluate the probability distribution of strength of adhesively bonded joints after moisture absorption

ABSTRACT The reliability of adhesive bond strength influences the applicability of structural adhesives in industries. The statistical probability distribution of the strength of adhesive joints is an essential indicator when designing and choosing adhesives. In this study, we experimentally studied the probability distribution of the strength of adhesive joints. The strength data were collected using a novel high-throughput technique consisting of a sample preparation method and shear testing device. Numerous cylindrical butt shear-joint specimens were prepared by mechanical machining and tested using a self-developed shear testing device. The effect of moisture absorption by the adhesive was specifically considered. The probability distribution of the shear strength of the epoxy adhesive joints was characterized using five probability distribution functions: Normal, Lognormal, Exponential, Weibull, and Gamma. Quantile – quantile plots were employed to determine the suitability of each distribution function. The results suggested that the Weibull and Normal distributions were best suited for describing the probability distribution of the strength of the epoxy adhesive joints. The Weibull distribution is particularly suitable for brittle epoxy adhesives. Moisture absorption reduced both the mean and variance of the shear strength, which might be attributed to the plasticization of the adhesives. The high-throughput method proposed in this study significantly improved the efficiency of testing adhesive joints. It not only contributes to the study of the strength distributions of adhesive joints but also helps to shorten the research and development cycle of new adhesives by facilitating rapid strength evaluation.

PROBABILISTIC PREDICTIONS OF EQUILIBRIUM RIPPLE GEOMETRY FOR TIME-DEPENDENT SEAFLOOR MODELING

We present a new equilibrium ripple predictor using a machine learning approach that outputs a probability distribution of wave-generated equilibrium wavelengths and statistics including an estimate of ripple height, the most probable ripple wavelength, and sediment and flow parameterizations. The Bayesian Optimal Model System (BOMS) is an ensemble machine learning system that combines two machine learning algorithms and two deterministic empirical ripple predictors with a Bayesian meta-learner to produce probabilistic wave-generated equilibrium ripple wavelength estimates in sandy locations.

A digital twin-based analysis method to assess geometric variations for parts in batch production

Background: In mass production, engineers are more concerned with the statistical distribution accuracy of parts in mass production rather than just the qualification of individual parts. However, currently, the statistical analysis methods designed for product accuracy are relatively scattered, and most of them focus on nominal part models. Therefore, there is a need to design a statistical analysis method for parts in mass production based on the Digital Twin model. Methods: This paper presents a novel method to analyse the geometric variations of parts in batch production in the production line, which is based on digital twins to model and evaluate deviations contributed by the geometrical condition, assembly condition and material condition. Firstly, the statistical descriptions of the parts, particularly the features of a digital twin for parts in batch production related to the geometry and position, are classified into various hierarchies. Secondly, a covariance method is employed to analyse the law of their shape from the descriptions. Thirdly, the parts' shape feature similarity for different terms is derived, including the linear features of pose constraint, rotation deviation, and geometric deviation and the curve features like a geometric deviation. Finally, the probability distribution of discrete points on the manufacturing error caused by different reasons is calculated. Results: Two case studies of reducer and rail highlight the applicability of the proposed approach. The standard deviation of the points has similar trend with sample cases according to normal distribution. Conclusions: This paper categorizes the deviations of batch parts into the linear features of pose constraint, rotation deviation, and geometric deviation. When batch parts exhibit any of these deviation types, the eigenvalues and eigenvectors of their covariance matrix show certain patterns, enabling the identification of the deviation type and calculation of the statistical deviation probability distribution for the corresponding features.

Hidden conditional random field-based equalizer for the 3D-CAP-64 transmission of OAM mode-division multiplexed ring-core fiber communication.

As a key technique for achieving ultra-high capacity optical fiber communications, orbital angular momentum (OAM) mode-division multiplexing (MDM) is affected by severe nonlinear impairments, including modulation related nonlinearities, square-law nonlinearity and mode-coupling-induced nonlinearity. In this paper, an equalizer based on a hidden conditional random field (HCRF) is proposed for the nonlinear mitigation of OAM-MDM optical fiber communication systems with 20 GBaud three-dimensional carrierless amplitude and phase modulation-64 (3D-CAP-64) signals. The HCRF equalizer extracts the stochastic nonlinear feature of the OAM-MDM 3D-CAP-64 signals by estimating the conditional probabilities of the hidden variables, thereby enabling the signals to be classified into subclasses of constellation points. The nonlinear impairment can then be mitigated based on the statistical probability distribution of the hidden variables of the OAM-MDM transmission channel in the HCRF equalizer. Our experimental results show that compared with a convolutional neural network (CNN)-based equalizer, the proposed HCRF equalizer improves the receiver sensitivity by 2 dB and 1 dB for the two OAM modes used here, with l = + 2 and l = + 3, respectively, at the 7% forward error correction (FEC) threshold. When compared with a Volterra nonlinear equalizer (VNE) and CNN-based equalizer, the computational complexity of the proposed HCRF equalizer was found to be reduced by 30% and 41%, respectively. The bit error ratio (BER) performance and reduction in computational complexity indicate that the proposed HCRF equalizer has great potential to mitigate nonlinear distortions in high-speed OAM-MDM fiber communication systems.

Practical implications of measuring at historical cost in an inflationary environment

This study aimed to analyze the impacts that can occur in the balance sheets of companies in inflationary environments when these balances sheets are not corrected, independently of whether the inflation rate reaches the level determined by IAS 29. The sample chosen consisted of companies from G20 member states that had already adhered to IFRS. The data distribution was analyzed using the ROA, ROE, EPS, and revenue weighted by total assets of the companies studied, before and after monetary correction, using statistical inference and evaluating the statistical probability distribution using the Kolmogorov-Smirnov and Shapiro-Wilk normality tests, and subsequently applying the Wilcoxon non-parametric test. The main results found were that monetary correction in the financial statements of the companies analyzed shows significance, both in countries with high inflation rates and in those with lower cumulative inflation rates. It is concluded that inflation significantly impacts the results of financial statements above a 10% cumulative rate, so measuring accounting elements at historical cost loses relevance, and it is vital to use corrected historical cost by applying a monetary correction.

Eulerian–Eulerian RSTM-PDF Modeling of Turbulent Particulate Flow

A novel 3D computational model was developed for the turbulent particulate two-phase flow simulation in the rectangular channel. The model is based on the Eulerian approach applied to 3D Reynolds-averaged Navier–Stokes modeling and statistical Probability Distribution Function method. The uniqueness of the method lies in the direct calculation of normal and transverse components of the Reynolds stresses for both gas and particles. Two cases were examined: a conventional channel flow and grid-generated turbulence flow. The obtained numerical results have been verified and validated by the experimental data, received from the turbulent particle dispersion test. The computed values of the particles’ turbulent dispersion and the maximum value of the particulate concentration distribution show good agreement with the experimental results. The examples are ranged from coal and other bulk material pneumatic transport, vertical fluidized beds, coal gasifiers, and chemical reactors.

The New Generalized Exponentiated Fréchet–Weibull Distribution: Properties, Applications, and Regression Model

Statistical probability distributions are commonly used by data analysts and statisticians to describe and analyze their data. It is possible in many situations that data would not fit the existing classical distributions. A new distribution is therefore required in order to accommodate the complexities of different data shapes and enhance the goodness of fit. A novel model called the new generalized exponentiated Fréchet–Weibull distribution is proposed in this paper by combing two methods, the transformed transformer method and the new generalized exponentiated method. This novel modeling approach is capable of modeling complex data structures in a wide range of applications. Some statistical properties of the new distribution are derived. The parameters have been estimated using the method of maximum likelihood. Then, different simulation studies have been conducted to assess the behavior of the estimators. The performance of the proposed distribution in modeling has been investigated by means of applications to three real datasets. Further, a new regression model is proposed through reparametrization of the new generalized exponentiated Fréchet–Weibull distribution using the log-location-scale technique. The effectiveness of the proposed regression model is also investigated with two simulation studies and three real censored datasets. The results demonstrated the superiority of the proposed models over other competing models.

Fitting statistical probability distribution for evaporation in western Brazil

This study aims to find evaporation (ETo) probabilities for the central west region of Brazil, including Campo Grande, Cuiabá, Goiânia and Brasilia. In this case, a maximum likelihood estimation was used for the probability distributions adjusting to the monthly ETo from 1960 to 2020. The work estimates three probability distributions, including the Generalized Extreme Values (GEV), Gumbel (GUM) and Log-Normal (LN). The Kolmogorov-Smirnov test, the Akaike information criterion (AIC), the Bayesian information criterion (BIC), the root mean square error (RMSE) and the coefficient of determination (R2) were applied to measure the quality of the adjustment. The evapotranspiration forecasts were made for the return periods of 10, 30, 50, and 100 years. The GEV and GUM distributions are advised for use during the summer. Altering LN distribution to a sequence of ETo throughout the winter months is the best option. Moreover, deforestation, combustion, extensive fires, aerosol pollutants, and climate change are the primary causes of excessive ETo in the area under study.

Residential Harmonic Injection Models Based on Field Measurements

In recent years, harmonic current levels have increased in residential distribution networks due to the growing penetration of nonlinear loads at customer premises. To properly model the harmonic current injection of residences, probabilistic models that account for the stochastic behavior of domestic loads are needed. As a part of the study reported in this paper, a field measurement campaign was performed in 24 dwellings during a one-week period with a one-minute resolution. Harmonic current magnitudes and phase angles of odd harmonic orders up to the 25th as well as the active and reactive power demanded were recorded. By applying two different unsupervised learning techniques (i.e., nonparametric density estimation and Gaussian mixture models) to these measurements, two probabilistic models of harmonic injection of individual residential sites have been derived. Statistical probability distributions have been determined for the magnitude and phase of each harmonic order segmented in different power demand intervals. The developed models are validated on a test feeder by comparing harmonic voltages caused by the injection of the synthetically generated currents with those obtained from measurements. Both field measurement results and the detailed data defining the probabilistic harmonic current models are made public in an Open Science database repository.

Machine Learning-Assisted Rapid Screening of Four Types of New Psychoactive Substances in Drug Seizures.

Over the past few years, new psychoactive substances (NPS) have become a global health and social problem because of their wide variety, constant structural renewal, vague legal definitions, and rapid adaptation to legal restrictions. The rapid structural modifications of NPS have posed significant challenges for the screening and identification of these new substances using traditional mass spectrometric techniques based on reference substances or a mass spectral database. Here, we propose supervised machine learning (ML) classification models such as k-nearest neighbors, support vector machine, random forest, and multigrained cascade forest for the rapid screening of NPS using mass spectrometric data. This approach utilizes ML methods to learn the statistical probability distributions of mass spectral data for NPS and non-NPS. Four classification ML models were generated and evaluated using a data set comprising 567 LC-MS and 732 GC-MS spectra. Through cross validation, we achieved an F1 score of 0.35-0.97. These algorithms were applied in conjunction with mass spectrometry techniques for the detection of six seizures including electronic cigarette oil and suspected powdered substances netted in drug trafficking cases. The models provided warning signals for synthetic cannabinoids, synthetic cathinones, and fentanyl. Thus, an early warning system was successfully established, which provided a useful method for reliable and effective identifications of unknown NPS.

Statistical characteristics, probability distribution, and power potential of sea water velocity in Turkey

Sea currents have the potential to supply electricity from a renewable energy source to coastal regions. The assessment of the potential energy that could be generated is the first step toward developing this resource. In this study, the data was collected at 5 m and 35 m depths below the sea surface level, including sea current velocity and direction. A detailed field measurement, of the probability of sea water velocity at three stations (Antalya, Silivri, Istanbul) for 5 months is carried out. The sea current power density values in these stations were 10.41, 4.92, and 7.91 W/m2 at 5 m depth, respectively. Besides, average sea current power density values were seen to be closely arranged with 11.44, 4.07, and 9.06 W/m2 at 35 depths, respectively. In addition, statistical analysis applying Weibull and Rayleigh models is also presented. It is shown that the use of a Weibull probability distribution facilitates the analysis of sea velocity conditions and is also able to predict the power density with a high degree of accuracy. The results of this study are useful for the understanding of marine hydrodynamics of these areas, where sea current power projects may be started in Turkey.

Bayesiansk kronologisk modellering som redskab i den lovpligtige arkæologi

Bayesiansk kronologisk modellering som redskab i den lovpligtige arkæologi