Anderson-Darling Research Articles

Different Estimation Methods for New Probability Distribution Approach Based on Environmental and Medical Data

In this article, we introduce a new extension of the power Lomax (PLo) model by combining the type II exponentiated half-logistic class of statistical models and the PLo model. The new suggested statistical model called type II exponentiated half-logistic-PLo (TIIEHL-PLo) model. However, the new TIIEHL-PLo model is more flexible and applicable than the PLo model and some extensions of THE PLo model, especially those in environmental and medical fields. Some general statistical properties of the TIIEHL-PLo model are computed. Six different estimation approaches, namely maximum likelihood (ML), least-square (LS), weighted least-squares (WLS), maximum product spacing (MPS), Cramér–von Mises (CVM), and Anderson–Darling (AD) estimation approaches, are utilized to estimate the parameters of the TIIEHL-PLo model. The simulation experiment examines the accuracy of the model parameters by employing six different methodologies of estimation. In this study, we analyze three real datasets from the environmental and medical fields to highlight the relevance and adaptability of the proposed approach. The newly suggested model is exceptionally adaptable and outperforms several well-known statistical models.

Statistical Features and Estimation Methods for Half-Logistic Unit-Gompertz Type-I Model

In this study, we propose a new three-parameter lifetime model based on the type-I half-logistic G family and the unit-Gompertz model, which we named the half-logistic unit Gompertz type-I distribution. The key feature of such a novel model is that it adds a new tuning parameter to the unit-Gompertz model using the type-I half-logistic family in order to make the unit-Gompertz model more flexible. Diagrams and numerical results are used to look at the new model’s mathematical and statistical aspects. The efficiency of estimating the distribution parameters is measured using a variety of well-known classical methodologies, including Anderson–Darling, maximum likelihood, least squares, weighted least squares, right tail Anderson–Darling, and Cramer–von Mises estimation. Finally, using the maximum likelihood estimation method, the flexibility and ability of the proposed model are illustrated by means of re-analyzing two real datasets, and comparisons are provided with the fit accomplished by the unit-Gompertz, Kumaraswamy, unit-Weibull, and Kumaraswamy beta distributions for illustrative purposes.

Anderson-Darling test for ground radar environment sensing

A clutter distribution identification method based on the AD (Anderson-Darling) goodness-of-fit test is proposed for the environmental perception and clutter distribution identification of ground radar positions, given the current demand for environment perception by position adaptive technology. The method determines which distribution the clutter obeys by comparing the critical value of the corresponding distribution with the AD statistic. The AD test method is improved by proposing a cell averaging method and a critical value unitisation method to address the problem that the AD parameters of the parameters in ground radar echo sample data fluctuate greatly, and the sample data are accepted by multiple distributions. The measured ground radar echo data was recorded and used for identification. The analysis results show that the improved AD test identification method has a better identification effect in the identification of ground radar’s position environment clutter distribution.

Approximation of the Sum of Independent Lognormal Variates using Lognormal Distribution by Maximum Likelihood Estimation Approached

Three methods of approximating the sum of lognormal variates to a lognormal distribution were studied. They were the Wilkinson approximation, the Monte Carlo version of the Wilkinson approximation and the approximation using estimated maximum likelihood lognormal parameters. The lognormal variates were generated empirically using Monte Carlo simulation based on several conditions such as number of lognormal variates in the sum, number of sample points in the variates, the variates are independent and identically distributed (IID) and also not identically distributed (NIID) with lognormal parameters. Evaluation of all three lognormal approximation methods was performed using the Anderson Darling test. Results show that the approximation using estimated maximum likelihood lognormal parameters produced Type I errors close to the 0.05 target and is considered the best approximation.

A stochastic Petri Net‐based approach for operational performance estimation of quay cranes

AbstractReliability, availability, and maintainability (RAM) of quay cranes (QCs) are essential for an effective port operation. This study estimates operational RAM of QCs using the Stochastic Petri Net (SPN) modelling. Asset Performance Assessment (APA) was performed to conduct the study by a SPN model. Based on the operation and maintenance data, probability distributions of Mean Time Between Failure (MTBF) and Mean Time to Repair (MTTR) is determined by Goodness of Fit Test of Anderson Darling. Subsequently, these distributions are applied in APA to determine the frequencies of failure/breakdowns, duration of downtimes, availability, and reliability with the assistance of the SPN model and Monte Carlo Simulation. The availability of the analysed QC is 0.97 or 97%. The results of this work are verified by the comparison with historical data. The outcomes of this paper contribute to reliability, availability, maintainability, and risk management of QCs.

Probability distribution models for the ultimate strength of tubular T/Y-joints reinforced with collar plates at room and different fire conditions

In this research work, the simulation results of 360 T/Y-joints reinforced with collar plates have been used to propose theoretical probability distribution models for the ultimate capacity at ambient and fire conditions. So far, no study has been carried out on the probability distribution of ultimate strength in joints with collar plates at room or elevated temperature. Therefore, according to the reinforced T/Y-joint models, which were verified with 18 tests, a total of ultimate capacity data sets was produced. In the FE models, the welds along the collar/brace intersection and between the chord and collar have been generated. Also, the Augmented Lagrange method was applied as the contact algorithm for solving the contact between the collar and chord. In the next step, 13 theoretical probability density functions (PDFs) were fitted to the relative frequency histograms of the databases. For obtaining the parameters of each distribution, the maximum likelihood (ML) method was utilized. Assessing the goodness-of-fit based on the Kolmogorov-Smirnov and Anderson Darling tests indicated that the Johnson SB distribution is the best for the ultimate capacity values in the T/Y-joints reinforced with collar plates at 20, 400, 600, and 800 °C. But, for the reinforced joints at 200 °C, the Inverse Gaussian (3P) distribution is the best. In the next step, five fully defined theoretical PDFs were proposed for the collar plate reinforced T/Y-joints at room and different high temperatures. Probability difference and probability-probability graphs indicated that the proposed theoretical probability distributions are well near the given data sets.

Elderly Pedestrians and Road Safety: Findings from the Slovenian Accident Database and Measures for Improving Their Safety

The number of elderly people is increasing worldwide, especially in Europe. Such an aging of the population has numerous consequences for society, many of which relate to transportation: older people, aware of their reduced abilities, prefer walking to driving. This leads to an increase in the elderly walking population and thus the need to understand and address the safety issues of these road users. Although these issues are well known, this topic has been little researched so far. The objective of this research is to provide a deeper insight into the safety level of elderly pedestrians by recognizing repetitive patterns leading to accidents involving them, to highlight the magnitude of the problem by analyzing a 10-year pedestrian crash database, to develop a model predicting—on the basis of the recognized patterns—the severity level of collisions involving older pedestrians, and, finally, on the basis of the highlighted factors, to propose some countermeasures to improve their safety. In order to achieve this goal, first, a statistical analysis of the database is performed, considering 13 factors that lead to accidents. Second, Kolmogorov–Smirnov and Anderson–Darling tests are performed to check if the data follow a normal distribution. Finally, an ordinal logistic regression model is proposed to determine the relationship between the crash severity level and the factors characterizing collisions. Thanks to this model, the statistical influencing factors are highlighted. Finally, based on the previous analysis, some technical and educational countermeasures are proposed.

New Modified Anderson Darling Goodness of Fit Test for Lognormal and Gamma distributions

The purpose of this study is to present the new modified Anderson-Darling goodness of fit test, and compare to the efficiency of three tests; Kolmogorov Smirnov test, Anderson-Darling test and Zhang (2002) test. A simulation study is used to estimate the critical values at a significance level of 0.05. The type I error rate and test power are calculated using Monte Carlo simulation with 10,000 replicates. The data are generated from the specified distribution; i.e., Lognormal and Gamma distributions with sample size of 10, 20, 30, 50, 100 and 200. The results demonstrate that every test has control over the type I error probability. The new test has the highest power for two alternative hypotheses; Loglogistic and Logistic distributions. Moreover, when the alternative distribution is Normal distribution and the sample size is small, the new test has the highest power.

Illicit Activity Detection in Bitcoin Transactions using Timeseries Analysis

A key motivator for the usage of cryptocurrency such as bitcoin in illicit activity is the degree of anonymity provided by the alphanumeric addresses used in transactions. This however does not mean that anonymity is built into the system as the transactions being made are still subject to the human element. Additionally, there is around 400 Gigabytes of raw data available in the bitcoin blockchain, making it a big data problem. HPCC Systems is used in this research, which is a data intensive, open source, big data platform. This paper attempts to use timing data produced by taking the time intervals between consecutive transactions performed by an address and make an identification of the nature of the address (illegal or legal). With the use of three different goodness of fit run tests namely Kolmogorov–Smirnov test, Anderson-Darling test and Cramér–von Mises criterion, two addresses are compared to find if they are from the same source. The BABD-13 dataset was used as a source of illegal addresses, which provided both references and test data points. The research shows that time-series data can be used to represent transactional behaviour of a user and the algorithm proposed is able to identify different addresses originating from the same user or users engaging in similar activity.

Exploring extreme value analysis of rainfall for some nuclear power plant sites in India

Extreme rainfall is an important consideration for safety of nuclear installations. Literature reported estimation of the same for Indian nuclear power plant sites using Gumbel and Frechet distributions, fitted by least square (graphical) method (LSM). In these reports, the goodness-of-fit was examined graphically by plots on probability papers. In this study, the data for six nuclear sites collected from literature were analysed. For this purpose, in addition to Gumbel and Frechet, other distributions were included and the parameters of the distributions were evaluated using Lieblein technique and maximum likelihood estimation, as well as LSM. The goodness-of-fit was evaluated using the quantitative tool: Anderson-Darling test; and qualitative tools: probability plot and quantile plot – which are suitable for evaluating goodness-of-fit of extreme value distributions. Maximum daily rainfall for return periods of 50, 100 and 1000 years were reported from the fitted distributions. Comparison with the respective values (50 and 100 year return period) from literature demonstrated that the extreme rainfall reported for these sites were quite accurate with maximum variation within ten per cent.

Comparação entre a frequência fundamental acústica da voz e a frequência de vibração das pregas vocais analisada pela videoquimografia digital

ABSTRACT Purpose To compare the frequency of vocal fold opening variation, analyzed by digital kymography, with the fundamental voice frequency obtained by acoustic analysis, in individuals without laryngeal alteration. Methods Observational analytical cross-sectional study. The participants were forty-eight women and 38 men from 18 to 55 years of age. The evaluation was made by voice acoustic analysis, by the habitual emission of the vowel /a/ for 3 seconds, and days of the week, and digital kymography (DKG), by the habitual emission of the vowels /i/ and /ɛ/. The measurements analyzed were acoustic fundamental frequency (f0), extracted by the Computerized Speech Lab (CSL) program, and dominant frequency of the variation of right (R-freq) and left (L-freq) vocal fold opening, obtained through the KIPS image processing program. The mounting of the kymograms consisted in the manual demarcation of the region by vertical lines delimiting width and horizontal lines separating the posterior, middle and anterior thirds of the Rima glottidis. In the statistical analysis, the Anderson-Darling test was used to verify the normality of the sample. The ANOVA and Tukey tests were performed for the comparison of measurements between the groups. For the comparison of age between the groups, the Mann-Whitney test was used. Results There are no differences between the values of the frequency measurement analyzed by digital kymography, with the acoustic fundamental frequency, in individuals without laryngeal alteration. Conclusion The values of the dominant frequency of the vocal folds opening variation, as assessed by digital kymography, and the acoustic fundamental frequency of the voice are similar, allowing comparison between these measurements in the multidimensional evaluation of the voice, in individuals without laryngeal alteration.

Distribution of Computerized Datasets To Fit Weibull, Log-Logistics and Gompertz Survival Models

The lack of detailed and analytic study on the risk factors of Breast cancer in Nigerian presents us with the challenge of not knowing the risk factors distinct to the Nigerian settings. Effectively handling the breast cancer treatment in co-infected patients is delicate. Some challenges to the treatment of breast cancer infection include drug-to-drug interactions between procedures required to treat the cancer cells, thus the hormonal drugs burdens patient’s inability to comply with dosage intake thereby making women with breast cancer prone to developing other forms of cancer. The aim of the research was to analyzed distributed dataset to fit Weibull, Log-logistics and Gompertz survival models. The research methodology involved the collection of data cases on oncological study analyzed using descriptive statistics and parametric survival models. The result shows that the Cramer-von Misses (W), the Anderson Darling (A) and the Kolmogorov Smirnov (D) statistics, Log-logistic distribution has greater p-value than other distributions, hence it is the best fit for survival times of a group of patients given chemotherapy treatment. The research concluded that Gompertz model was the best fitted model to survival times of a group of patients given chemotherapy treatment data, while log-logistic distribution was the best fit distribution for the data. It also concluded that Weibull and log-logistic models perform better than Gompertz model in fatigue fracture data, while log-logistic distribution was the best fit for the data and Gompertz model and the distribution was the best fit to nicotine measurements.

Identification Of A Suitable Probability Distribution For Rainfall Analysis Of Bankura District In West Bengal

The daily rainfall data of 22 years (1992 to 1993 and 1997 to 2016) of Bankura district in West Bengal were collected from the Indian Meteorological Department (IMD), Kolkata. The data was then processed to identify the maximum rainfall received on any one day (24 hrs duration), in any week (7 days), in a month (4 weeks), in a monsoon season (4 months), pre-monsoon (4 months), post-monsoon(4 months) and in a year (365 days). The data were analysed to find out the standard deviation and coefficient of variation during all the six periods of study. The data showed that the annual daily maximum rainfall received at any time ranged between 58.7mm (minimum) to 258.8mm (maximum) indicating a large range of fluctuation during the period of study. These data were analysed using Anderson-Darling (AD) statistical goodness of fit teston the basis of probability plot to identify the best fit probability distribution for all the six period of study and the trend has been presented in this study. The lognormal distribution was found as the best fit probability distribution for the annual and monsoon period of study. The weibull (3P) was found as the best fit distribution for pre-monsoon and post-monsoon period of study. Weibull (3P), gamma (2P), lognormal, exponential and largest extreme value were observed in most of the weekly period of study as best fit probability distributions. The scientific results clearly established that the analytical procedure devised and tested in this study may be suitably applied for the identification of the best fit probability distribution of rainfall data.

Update on the indication of a mass-dependent anisotropy above 1018.7 eV in the hybrid data of the Pierre Auger Observatory

We test for an anisotropy in the mass of arriving cosmic-ray primaries associated with the galactic plane. The sensitivity to primary mass is obtained through the depth of shower maximum, X max, extracted from hybrid events measured over a 14-year period at the Pierre Auger Observatory. The sky is split into distinct on-and off-plane regions using the galactic latitude of each arriving cosmic ray to form two distributions of X max, which are compared using an Anderson-Darling 2-samples test. A scan over roughly half of the data is used to select a lower threshold energy of 1018.7 eV and a galactic latitude splitting at |b| = 30°, which are set as a prescription for the remaining data. With these thresholds, the distribution of X max from the on-plane region is found to have a 9.1±1.6−2.2+2.1g/cm2 shallower mean and a 5.9±2.1−2.5+3.5g/cm2 narrower width than that of the off-plane region and is observed in all telescope sites independently. These di↵erences indicate that the mean mass of primary particles arriving from the on-plane region is greater than that of those from the off-plane region. Monte Carlo studies yield a 5.9 ×10−6 random chance probability for the result in the independent data, lowering to a 6.0 × 10−7 post-penalization random chance probability when the scanned data is included. Accounting for systematic uncertainties leads to an indication for anisotropy in mass composition above 1018.7 eV with a 3.3 σ-significance. Furthermore, the result has been newly tested using additional FD data recovered from the selection process. This test independently disfavors the on-and off-plane regions being uniform in composition at the 2.2 σ-level, which is in good agreement with the expected sensitivity of the dataset used for this test.

Parametric Modeling Approach to Covid-19 Pandemic Data

The problem of skewness is common among clinical trials and survival data, which has been the research focus derivation and proposition of different flexible distributions. Thus, a new distribution called Extended Rayleigh Lomax distribution is constructed from Rayleigh Lomax distribution to capture the excessiveness of some survival data. We derive the new distribution by using beta logit function proposed by Jones (2004). Some statistical properties of the distribution such as density, cumulative density, reliability rate, hazard rate, reverse hazard rate, moment generating and likelihood functions; skewness, kurtosis and coefficient of variation are obtained. We also performed the expected estimation of model parameters by maximum likelihood; goodness of fit and model selection criteria, including Anderson Darling, CramerVon Misses, Kolmogorov Smirnov (KS), Akaike Information, Bayesian Information, and Consistent Akaike Information Criterion is employed to select the better distribution from those models considered in the work. The results from the statistics criteria show that the intended distribution performs well and has a good representation of the States in Nigeria’s Covid-19 death cases data than other competing models.

Distribution Nature of Trade Volume and Number of Trades at NEPSE Floor

Investors are concerned with market fluctuation. At NEPSE, market fluctuation is linked to the trade volume and number of shares traded during a specific day. A change in the benchmark index, NEPSE, in the Nepalese stock market depends on the market capitalization. Hence, to estimate the market pattern, a better understanding of the distribution nature of the trade volume and number of trades is beneficial to Nepalese investors. This ultimately helps an investor understand the market mechanism. The paper has followed basic descriptive statistics and a graphical presentation of the PP Plot, QQ Plot, and PDF Plot to test the normality and distribution nature of the NEPSE yearly trade volume and number of trades. Finally, the Sharpio-Wilk test, Jarque-Bera test, Kolmogorov-Smirnov test, and Anderson-Darling (A2) test are applied to test the goodness of fit for the observed and the respective NEPSE yearly trade volume and number of trades. The paper found that the NEPSE's yearly trade volume and number of trades from the year of its establishment to the fiscal year 2021–22 have a leptokurtic distribution. Similarly, the paper shows the distribution of trade volume and the number of trades toward non-normality. The probability distribution function reflects the log-normal (3P) distribution, also known as Galton’s distribution, for both sets of data. The distribution of the NEPSE's yearly trade volume and number of trades is best fitted by Galton’s distribution. The fitting of this specific distribution reflects a compounding effect on the transactions taped during the last two decades and more . Hence, an investor who enters in a NEPSE floor with a small numbers of scrips would multiply the numbers in a period of times.

Statistical analysis of excess water on drainage systems in the northern part of Serbia

Drainage systems in Serbia are mainly designed to evacuate excess water generated in the winter-spring period, which occurs as a result of snow accumulation during the long and wet winter and its sudden melting with the parallel appearance of spring rains. Dimensioning of the drainage system is done in such a way as to satisfy the needs of draining the design excess water, which is usually calculated using the water balance. Applying statistical analysis based on distributions of probability, the results of the future occurrence of excess water can be predicted. The paper tests the distribution that best corresponds to the empirical distribution of excess water obtained by applying the water balance. The Kolmogorov-Smirnov, Anderson-Darling, and χ2 tests were used to test a number of theoretical distributions, and basis on those tests Generalized Extreme Value (GEV) distribution was selected, which is often used in hydrological analyzes. The probabilities of excess water on drainage systems for the return period of 5, 10, 50, and 100 years were obtained. The results of the calculations can be used in the reconstruction of existing drainage systems, since most of them were designed more than 50 years ago, or in the planning and design of new drainage systems.

Development of Monte‐Carlo‐based stochastic scenarios to improve uncertainty modelling for optimal energy management of a renewable energy hub

AbstractThe Monte‐Carlo (MC) method for generating stochastic scenarios to model uncertainty has a special role in research related to energy systems, but most studies have not provided a specific criterion for choosing an appropriate probability distribution function for using MC. This paper develops a new process for applying MC to improve uncertainty modelling based on Anderson‐Darling (AD), Kolmogorov‐Smirnov (KS), and Chi‐Square (CS) tests statistical. Moreover, three clustering algorithms of K‐means, Fuzzy c‐means, and Kantorovich distance matrix have been applied to reduce the generated scenarios. To evaluate the performance of the proposed process, a renewable energy hub involving electricity, heat, cooling, natural gas, and biomass fuel carriers, is used employing valid data. The results of numerical studies show that the quality of the scenarios in the proposed process based on statistical tests is much higher than the conventional method. Also, MC‐CS has been superior to the other two proposed methods in various seasons, so that, for example, in summer, its operating cost has decreased by 3% and 4% compared to MC‐KS and MC‐AD, respectively.

Fluctuations spectra of specific kinetic energy, density, and mass flux in Rayleigh–Taylor mixing

Rayleigh–Taylor (RT) interfacial mixing is critically important in a broad range of processes in nature and technology. To understand self-similar RT dynamics, a bias free interpretation of data is in need. This work yields the physics properties and the anomalous scaling of Rayleigh–Taylor mixing based on the analysis of experimental data. Fluctuations spectra are analyzed of the specific kinetic energy of the velocity component in the acceleration direction, the density, and the mass flux. Theoretical foundations and statistical method are developed, under group theory guidance, to investigate unprocessed data, and identify with statistical confidence their spectral shapes. These include the mean values of the spectral shape's parameters, their relative errors, and the goodness of fit. The Anderson–Darling test is employed to inspect the residuals. The intervals of mode numbers are found, where the relative errors of the spectral shape parameters are small and the goodness of fit is excellent. We reveal that spectral shapes of fluctuations in RT mixing experiments can be well described by compound functions, represented by a product of a power law and an exponential. The data analysis based properties unambiguously identifies the dynamic specificity and heterogeneity of RT mixing.

Probability distributions analysis of travel time variability for the public transit system

Travel time variability (TTV) plays a significant role in analysing the reliability of public transit system. The research works carried out on travel time variability under Indian traffic conditions are very few and these studies did not analyse the performance of travel time distribution in detail, considering different temporal and spatial aggregations. In this study, travel time variability is analysed using travel time distributions considering different temporal and spatial aggregations. The Automatic Vehicle Location (AVL) data of four transit routes of Mysore City, Karnataka, India are used to evaluate travel time distributions with respect to temporal aggregations (peak period, off-peak period, 60 minutes, 30 minutes and 15 minutes) and spatial aggregations (route level and segment level). The performance of travel time distributions is analysed using the Anderson-Darling (AD) test. The segments with signalised intersections and different land-use types are analysed to evaluate the distribution fit for various conditions. The results of both route and segment level analysis report highest accuracy and robustness values for Generalised Extreme Value (GEV) distribution. The distribution is proved to be superior in describing travel time variability of public transit.