Anderson-Darling Research Articles

Evaluation of the pharmacotherapeutic follow-up effectiveness in patients with dyslipidemia in the secondary health care in the Brazilian Unified Health System (SUS)

Cardiovascular diseases (CVD) are one of the main causes of mortality in the world. Dyslipidemia treatment can reduce the number of deaths caused by CVD, by decreasing the lipid profile. Evaluate the pharmacotherapeutic follow-up effectiveness in patients with dyslipidemia, regarding clinical and laboratory aspects. A quasi-experimental trial was performed in 12 months. The studied population was included patients with dyslipidemia who received a pharmacotherapeutic follow-up, which was evaluated according to the Pharmacotherapy Workup developed by the Brazilian Ministry of Health. Clinical and laboratory evaluations were performed at the baseline, after a 6 and 12-months period. The statistical analyzes were performed with the normality test of Lilliefors, Cramer Von Misses, and Anderson Darling, later the t-paired test. This study demonstrated that after 6-months of intervention, statistically significant results were verified in the reduction of LDL-cholesterol, total cholesterol, increase in HDL-cholesterol, and reduction in the blood pressure. It was observed that for high-risk patients, the achievement of targets in the lipid profile and HbA1C occurred only after 12-months, because, this population needs more aggressive targets and expressive interventions. Pharmacotherapeutic follow-up in patients with dyslipidemia reduced lipid blood levels and promoted positive clinical and laboratory outcomes.

Statistical analysis of correlation of gamma passing results for two quality assurance phantoms used for patient-specific quality assurance in volumetric modulated arc radiotherapy.

Patient-specific quality assurance (QA) data must be migrated from outdated QA systems to new ones to produce objective results that can be understood by oncologists. We aimed to evaluate a method for obtaining a high correlation of dose distributions according to various gamma passing rates among two types of 2D detectors for the migration of patient-specific QA data of volumetric modulated arc therapy (VMAT). The patient-specific QA of 20 patients undergoing VMAT was measured in two different modes: standard single measurement (SM) mode and multiple merged measurements (MM) techniques using ArcCHECK (AC) and OCTAVIUS (OT). The correlation of the measured and calculated dose distributions was evaluated according to varying gamma passing rates (3%/3 mm, 2%/3 mm, 2%/2 mm, and 1%/1 mm). The gamma passing rates were analyzed using the Anderson-Darling normality test. Treatment plan dose distributions were calculated by intentionally shifting the calculation isocenter position (x,y,z ± 0.5, ± 1.0, ± 1.5, and ± 2.0 mm). The highest correlation between the SM and MM was observed with a gamma passing rate of 1%/1 mm with AC (r = 0.866) and 3%/2 mm with OT (r = 0.916). However, SM and MM did not follow a normal distribution with a rate of 3%/2 mm in OT. The second-highest correlation was obtained with a rate of 2%/2 mm (r = 0.900). Among the two 2D detectors, the highest correlation between the calculated and measured dose distributions was obtained for a gamma passing rate of 1%/1 mm using SM in AC and 2%/2 mm using MM in OT (r = 0.716). Adjusting the gamma passing rate and measurement mode of AC and OT resulted in higher correlations between measured and calculated dose distributions. The high correlation between different 2D detectors objectively indicated a potential migration method. This enabled the sharing of more accurate patient-specific QA data from 2D detectors with different phantoms. A high correlation was observed between the two types of detectors in this study (r = 0.716); therefore, the proposed method should be useful for oncologists to share information regarding patient-specific QA for VMAT.

Measuring the Adequacy of Loss Distribution for the Ghanaian Auto Insurance Risk Exposure through Maximum Likelihood Estimation

Loss distribution plays an influential role in evaluating risks from policyholders’ claims. Nevertheless, the auto insurance market in Ghana pays little attention to policyholders’ claims distribution, resulting in the market’s inefficiency. This study investigates the type of loss distribution function that best approximates policyholders’ claims in Ghana. We applied the Kullback-Leibler divergence, Kolmogorov Smirnov, Anderson-Darling statistical tests and maximum likelihood estimation (MLE) to estimate policyholders’ claims. The results suggest that Ghana’s auto policyholder’s claims are better approximated using the lognormal probability distribution. Through the lognormal distribution, the industry can adequately evaluate policyholders’ claims to minimize potential loss. Additionally, this distribution could enable the market reach decisions on premiums and expected profits theoretically.

End-Launcher Repeatability in Broadband Methods for Characterization of the Propagation Constant of Transmission Lines Using Two-Port Measurements

This work presents an analysis of the influence of connector repeatability in three different methods for estimating the propagation constant of transmission lines from two-port measurements. For this purpose, the repeatability of 16 transitions using 1.85-mm coaxial-to-microstrip end-launcher connectors has been tested. It has shown that using the same pair of connectors instead of the whole set significantly reduces the standard deviation of the transition S-parameters that affect the final estimation of the propagation constant and, especially, the attenuation constant. In addition, the hypothesis that the measured data have a normal probability distribution has been validated by performing an Anderson–Darling test on the estimated S-parameters of the transition. The obtained standard deviation has been included in a sensitivity analysis, generating S-parameters from the normal distribution and performing a Monte Carlo simulation. The objective is to study the standard deviation of the propagation constant obtained using the proposed methods when there are errors related to connector repeatability. In this case, unlike random errors of the analyzer, it has been found that all the compared strategies for the estimation of the propagation constant (traces, eigenvalues, and determinants) work in the same way concerning launcher repeatability errors. Furthermore, it has been seen that the propagation constant obtained also follows a normal distribution. Finally, to validate the presented theory, methods have been applied to several measurements of two lines in the 0.01–67-GHz frequency range using the same kit and different combinations of different connectors. Results show that higher accuracy is obtained when using the same pair of connectors, considerably reducing attenuation constant ripple, which assesses the suitability of the proposed error analysis.

Self-Organizing Multilateration of an Unknown Number of Transmitters

Wireless Sensor Networks (WSNs) that classify the source of detected radio signals require mobile transmitters, physical (PHY) and link layer meta data, and packet sniffing capabilities. These signal classifiers are restricted by assumptions that may be difficult to realize in adversarial Signal of Opportunity (SOP) localization settings, and they do not jointly localize transmitters. In this paper, we present a novel framework that self-organizes to classify and jointly localize sets of stationary transmitters emitting SOP. The framework leverages the underlying Gaussian distribution associated with multilateration estimates via the use of Unsupervised Learning (UL) techniques. Inference of spatial multilateration features allows for the joint estimation of classification outcomes with respect to several unknown parameters, including the number of transmitters, source transmitters for each signal, the underlying multilateration distribution, and the transmitter locations. The proposed framework was evaluated in a two-dimensional trilateration experiment. Signals transmitted by vehicular Tire Pressure Monitoring System (TPMS) wireless beacons were observed by a custom-built WSN test bed to produce Received Signal Strength Indicators (RSS) features. We used a trained Convolutional Neural Network (CNN) to make location estimates from the RSS feature data. An Anderson-Darling test showed that these CNN estimates were statistically indistinguishable from those of a normal distribution. The spatial trilateration estimates were clustered to identify six of the eight TPMS transmitters with a 75% cluster detection rate, which was the result of every statistically different spatial and RSS population as determined by a Kruskal-Wallis (KW) test. The source transmitter of every signal was classified with a 76.4% indicator variable accuracy (93.7% when removing statistically identical RSS populations) and the detected source transmitters were localized with an average of 1.72 m variance and 1.19 m bias within a roughly 15 m square whose perimeter is made up of receivers.

Nucleation in sessile saline microdroplets: induction time measurement via deliquescence-recrystallization cycling.

Induction time, a measure of how long one will wait for nucleation to occur, is an important parameter in quantifying nucleation kinetics and its underlying mechanisms. Due to the stochastic nature of nucleation, efficient methods for measuring large numbers of independent induction times are needed to ensure statistical reproducibility. In this work, we present a novel approach for measuring and analyzing induction times in sessile arrays of microdroplets via deliquescence/recrystallization cycling. With the help of a recently developed image analysis protocol, we show that the interfering diffusion-mediated interactions between microdroplets can be eliminated by controlling the relative humidity, thereby ensuring independent nucleation events. Moreover, possible influence of heterogeneities, impurities, and memory effect appear negligible as suggested by our 2-cycle experiment. Further statistical analysis (k-sample Anderson-Darling test) reveals that upon identifying possible outliers, the dimensionless induction times obtained from different datasets (microdroplet lines) obey the same distribution and thus can be pooled together to form a much larger dataset. The pooled dataset showed an excellent fit with the Weibull function, giving a mean supersaturation at nucleation of 1.61 and 1.85 for the 60 pL and 4 pL microdroplets respectively. This confirms the effect of confinement where smaller systems require higher supersaturations to nucleate. Both the experimental method and the data-treatment procedure presented herein offer promising routes in the study of fundamental aspects of nucleation kinetics, particularly confinement effects, and are adaptable to other salts, pharmaceuticals, or biological crystals of interest.

HYDROLOGICAL REGIONALIZATION OF THE ANNUAL MAXIMUM STREAMFLOWS OF THE UPPER AND MIDDLE PARAOPEBA RIVER – MG USING THE INDEX-FLOOD TECHNIQUE

Estimating peak streamflows in a basin is an essential issue in hydrology, especially for projects and management of hydraulic infrastructures such as dams, spillways, and bridges. In this context, this article presents a regionalization of annual maximum streamflows for the upper and middle Paraopeba River region in Minas Gerais, proposing a regional equation to calculate maximum streamflows using the index-flood technique by the generalized extreme value (GEV) distribution. GEV distribution parameters were estimated using the L-moments method, and the adjustment of the statistical model was performed by applying the Anderson-Darling test. The results of the hydrological regionalization were compared with those obtained by the local frequency analysis, performed for the considered fluviometric stations, observing absolute deviations from 11.91 to 58.78%.

Evaluation of Probability Distribution Functions for Modeling Forest Tree Diameters on Agricultural Landscapes in Ogun State, Nigeria

The use of probability distribution functions for describing tree diameter at breast height provides useful information for forest resource evaluation and quantification. A series of probability distribution functions have been widely developed and applied for managing forest trees in conventional forest reserves without much consideration for trees outside forest reserves. The aim of this study is to evaluate and propose a suitable probability distribution function for trees in Agricultural landscapes. The study examined 3-parameter lognormal, Lognormal, 3-parameter Gamma, Gamma, 3-parameter Weibull and Weibull distribution functions, using the Maximum Likelihood method for fitting tree diameter at breast height. Three hundred and thirty-two temporary farmlands were randomly selected from which stem diameter of all living trees, with diameter ≥ 10.0 cm, were measured. Results of the statistical analysis showed that the 3-parameter lognormal distribution gave a superior description of the stem diameter with the least values of Anderson Darling (1.627) and Akaike Information Criterion (5962.0) statistics. Hence, the 3-parameter lognormal distribution function was found suitable for the stem diameter of trees in Agricultural landscapes in the study area.

A New Probability Heavy‐Tail Model for Stochastic Modeling under Engineering Data

The main aim of the paper is to propose and study a new heavy‐tail model for stochastic modeling under engineering data. After studying and analyzing its mathematical properties, different classical estimation methods such as the ordinary least square, Cramér‐von Mises, weighted least square, maximum likelihood, and Anderson–Darling estimation along with its corresponding left‐tail and right‐tail estimation methods are considered. Comprehensive numerical simulation studies are performed for comparing estimation methods in terms of some criterions. Three engineering and medical real‐life data sets are considered for measuring the applicability flexibility of the new model and to compare the competitive models under uncensored scheme. Two engineering real‐life data of them are also used to compare the classical methods. A modified Nikulin‐Bagdonavicius goodness‐of‐fit is presented and applied accordingly for validation under censorship case. Finally, right censored lymphoma data set is analyzed under the modified statistic test for checking the validation of the reciprocal Weibull model in modeling the right censored data.

Comparison of different estimation methods for the inverse weighted Lindley distribution

In this paper, different estimation methods are considered for the parameters of the inverse weighted Lindley (IWL) distribution introduced by Ramos et al.(2019). Parameters of the IWL are estimated by the method of maximum likelihood (ML), least squares (LS), weighted least squares (WLS), Cram´er-von Mises (CVM) and Anderson Darling (AD). The performances of the estimators are compared using Monte Carlo simulation study via bias, mean square error and deficiency (Def) criteria. Finally, a real data set is analyzed for illustrative purposes.

Probabilistic constitutive law for masonry veneer wall ties

ABSTRACT In a masonry veneer wall system, tie strengths and stiffnesses vary randomly and so are not consistent for all ties throughout the wall. To ensure an economical and safe design, this paper uses tie calibration experimental approach in accordance with the standard AS2699.1 to investigate the tie failure load under compression and tension loading. Probabilistic wall tie characterisations are accomplished by estimating the mean, coefficient of variation and characteristic axial compressive and tensile strength from 50 specimens. The displacement across the cavity is recorded, which resulted the complete load versus displacement response. Using the maximum likelihood method, a range of probability distributions are fitted to tie strengths at different displacement histogram data sets, and a best-fitted probability distribution is selected for each case. The inverse cumulative distribution function plots are also used along with the Anderson-Darling test to infer a goodness-of-fit for the probabilistic models. An extensive statistical correlation analysis is also conducted to check the correlation between different tie strengths and associated displacement for both compression and tension loading. Based on the findings, a wall tie constitutive law is proposed to define probabilistic tie behaviour in numerical modelling.

The extended Weibull distribution with its properties, estimation and modeling skewed data

The present article introduces a new distribution called the odd log–logistic Lindley-Weibull (OLLLW) distribution that provides greater flexibility in modeling data in applied areas such as medicine and engineering. The OLLLW model provides left-skewed, symmetric, right-skewed, and reversed-J shaped densities. Its hazard function can be bathtub, unimodal, increasing or decreasing. The OLLLW density was expressed as a linear mixture of Weibull densities. Some distributional properties of the introduced model are derived. Its parameters are estimated using five classical estimators called, the maximum likelihood, Anderson–Darling, least-squares, Cramér-von Mises, and weighted least squares estimators. The performance of the proposed estimators is explored by detailed simulation results. The flexibility of the OLLLW distribution is studied by two real data sets from medicine and engineering sciences, showing that its capability to fit the data effectively than the Weibull, Fréchet Weibull, transmuted Weibull, gamma Weibull, transmuted exponentiated Weibull, and modified Weibull distributions.

Evaluation of Generalized Extreme (GEV), Log-Pearson Type 3 (LP3), Pearson Type 3(P3) and Gumbel (EV1) Distributions for Development of IDF Equations for Warri, Nigeria

The application of Gumbel (EVI) to the development of rainfall intensity– duration – frequency (IDF) curves has often been criticized on theoretical and empirical grounds as it may underestimate the largest extreme rainfall amounts. The consequences of underestimation are economic losses, property damages, and loss of life. Therefore, it is important that water resources engineering infrastructure be accurately design to avoid these consequences. This paper evaluates the performances of four probability distributions; GEV, EV1, LP3 and P3 using the annual maxima precipitation series of 26 years for Warri Metropolis obtained from Nigerian Meteorological Agency (NiMet). The strength and weakness of the four probability distributions were examined with the goodness of fit (GOF) module of Easyfit software which implemented Kolmogorov - Smirnov (KS) and Anderson - Darling (AD) tests at 5% significance level. The Easyfit software fitted the precipitation series data to the four probability distributions and ranked the four probability distributions across the fifteen rainfall durations. Results show that for both KS and AD tests, GEV distribution was found to be best-fit distribution and it was applied to the development of IDF curves in Warri Metropolis, Nigeria. Furthermore, the IDF values obtained were applied in the development of three-parameter IDF models for return periods of 10 - , 15 -, 20 -, 25 - , 50 -, and 100-years. The mean absolute error, Nash – Sutcliffe Efficiency (NSE) and Root Mean Square Error (RMSE) indices computed for the IDF models increase with increasing return periods. The IDF curves and models depicted the general attributes of IDF curves and models. This study could be of significant academic value and improvement to professional practice in the design of storm water drainage systems. Therefore, the developed IDF curves and models are recommended to the Warri Urban Authority for inclusion in her stormwater handbooks and manuals.

A New Lifetime Distribution with Properties, Characterizations, Validation Testing and Different Estimation Methods

A new lifetime distribution is proposed and its properties are studied. The new density function has a heavy right skew tails with different shapes. The new failure rate function can be “constant”, “bathtub (U)”, “increasing-constant”, “decreasing-constant”, “upside down” and “upside down-U”. Complexity of the most integrals related to statistical properties is solved and numerically analyzed. Simple type copula is presented. Numerical calculations for analyzing the skewness and kurtosis are presented. Different estimation methods such as the maximum likelihood estimation method, Cramer-von-Mises estimation method, ordinary least square estimation method, weighted least square estimation method, Anderson Darling estimation method, right tail Anderson Darling estimation method and left tail-Anderson Darling estimation method are considered. Numerical simulation studies are performed. An example of environmental real data set is employed to compare the estimation methods. Another example is presented to measure importance and flflexibility of the new model. Using the validation approach proposed by Bagdonavicius and Nikulin (2011) for censored data, we propose the construction of modifified chi-square goodness-of-fifit tests for the new model. Based on the maximum likelihood estimators on initial data, the modifified statistics recover the information lost while grouping data and follow chi-square models. All elements of the modifified criteria tests are given explicitly. Numerical example from simulated samples and four real data sets have been analyzed to illustrate the feasibility of the modifified test.

Modified likelihood ratio tests for extreme value distributions

The modified Anderson-Darling test statistics have been suggested in testing the highly skewed distributions to detect more possible departures in the right (or left) tail. In this paper, we propose the corresponding modified likelihood ratio test statistics, and compare their performances for the Gumbel distribution with the modified Anderson-Darling test statistics. We also provide the approximate critical values for the generalized extreme value distribution and generalized Pareto distribution where the unknown shape parameter is present.

Tests for comparing time‐invariant and time‐varying spectra based on the Anderson–Darling statistic

Based on periodogram‐ratios of two univariate time series at different frequency points, two tests are proposed for comparing their spectra. One is an Anderson–Darling‐like statistic for testing the equality of two time‐invariant spectra. The other is the maximum of Anderson–Darling‐like statistics for testing the equality of two time‐varying spectra. Both of two tests are applicable for independent or dependent time series. Several simulation examples show that the proposed statistics outperform those that are also based on periodogram‐ratios but constructed by the Pearson‐like statistics.

Measuring and Locating Zones of Chaos and Irregularity by Application of High Spectral Chaotic Global Variants

The protocol followed was analogous to that by Garner and Ling [2014]. High spectral Entropy and high spectral Detrended Fluctuation Analysis have been established as more sensitive to the chaotic responses in forward problems in subjects with type 1 diabetes mellitus (T1DM), chronic obstructive pulmonary disease (COPD), youth obesity and child malnutrition. From 50 linearly increasing starting points, we applied the objective functions (hsCTF1 to hsCTF7) to attain an optimized value, [Formula: see text] which should increase the chaotic response when substituted back into the appropriate model. The mean percentage increase in Kolmogorov–Sinai Entropy and [Formula: see text]-values when the models were compared statistically by Kruskal–Wallis and One-way analysis of variance (ANOVA1) tests were monitored. Normal distributions were considered by Anderson–Darling, Ryan–Joiner and Lilliefors tests. Effect sizes by Cohen’ [Formula: see text] and Hedges [Formula: see text] were computed as sometimes the ANOVA1 and Kruskal–Wallis tests were not discriminative. The optimal statistical results were Duffing (hsCTF1: 29.4%); Brusselator (hsCTF6: 24.7%); Lorenz (hsCTF6: 28.8%). Multivariate analysis was required to determine which of the seven combinations of chaotic globals were most influential. Following Principal Component Analysis (PCA) hsCTF1 and hsCTF3 were the preferred objective functions delivering the highest increases in mean KS-Entropy with most influential PCA. These methods could be advantageous to increase yields and consequently profits in industrial processes such as yeast glycolysis for alcoholic beverages, Systems Biology, inverse and optimization problems, generally.

Statistical Distribution of Lassa Fever in Edo State, Nigeria

Lassa fever is a severe viral infection caused by the Lassa virus and spread by contact with excretions or secretions of infected rats gaining access to food and water inside human houses and other human activity areas. Sierra Leone, the Republic of Guinea, Nigeria, and Liberia are among the nations where it is endemic with a high number of deaths recorded yearly due to Lassa fever. In Nigeria, one of the states with the highest incidence is Edo. In order to reduce and predict the spread of Lassa fever in Edo state, the trend of the disease needs to be understood. Knowledge of the statistical distribution of a disease is one of the best ways to understand the trend of the disease. Currently, existing research on the statistical distribution of Lassa fever is very rare. The present work is an attempt to initiate research on the statistical distribution of Lassa fever with data obtained on weekly cases of Lassa Fever in Edo State, Nigeria. Based on the Kolmogorov Smirnoff and Anderson Darling’s goodness of fit test for fitting distribution, the Geometric distribution outfitted the weekly confirmed incidences of Lassa fever in Edo State, Nigeria when compared with the Discrete Uniform and Poisson distributions. The study further revealed that on the average, two Lassa fever cases is recorded per week in Edo State within the study period. This number of cases per week is on the high side and should be immediately looked into.

Investigation on the statistical distribution of PM2.5 concentration in Chiang Mai, Thailand

Recently, it is found that Northern Thailand has very high levels of airborne particulates known as PM2.5. PM2.5 particulates can cause breathing problems and may raise the risks of heart disease and even some cancers. According to AirVisual, Chiang Mai, the capital of Northern Thailand which offers for tourists in both business and cultural center, had the highest levels of smog in the world in March 2018, reaching at least 183 on the PM2.5 Air Quality Index scale. The daily average PM2.5 concentration data are determined from July 2016 – June 2018 at two stations in Chiang Mai at Yupparaj Wittayalai school and City Hall. The Weibull, Gamma, Lognormal and Inverse Gaussian distributions are considered for finding the most appropriate probability functions of the daily average PM2.5 concentration. The results show that, as evaluated with the goodness- of-fit measures; Komolgorov-Smirnov and Anderson-Darling test statistics, the Inverse Gaussian distribution is the most suitable probability density functions of the daily average PM2.5 concentration for two stations. Furthermore, the return periods of the PM2.5 concentration are predicted by using the Largest Extreme Value distribution, which can be further applied in air quality management and related policy making.

Estimating the Best-Fitted Probability Distribution for Monthly Maximum Temperature at the Sylhet Station in Bangladesh

The estimation of a suitable probability model depends mainly on the features of available temperature data at a particular place. As a result, existing probability distributions must be evaluated to establish an appropriate probability model that can deliver precise temperature estimation. The study intended to estimate the best-fitted probability model for the monthly maximum temperature at the Sylhet station in Bangladesh from January 2002 to December 2012 using several statistical analyses. Ten continuous probability distributions such as Exponential, Gamma, Log-Gamma, Beta, Normal, Log-Normal, Erlang, Power Function, Rayleigh, and Weibull distributions were fitted for these tasks using the maximum likelihood technique. To determine the model’s fit to the temperature data, several goodness-of-fit tests were applied, including the Kolmogorov-Smirnov test, Anderson-Darling test, and Chi-square test. The Beta distribution is found to be the best-fitted probability distribution based on the largest overall score derived from three specified goodness-of-fit tests for the monthly maximum temperature data at the Sylhet station.