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Due to the escalating demand for conventional potassium sources, and their unavailability in many African countries, there is a growing interest in hydrothermally treated igneous rocks as viable alternatives. These materials exhibit promising potential in enhancing potassium release, comparable to traditional sources like muriate of potash (M.O.P.). However, it remains uncertain whether they can adequately fulfill the nutrient requirements of plants. In this study, we evaluated nutrient balance in ryegrass (Lolium multiflorum) using raw and hydrothermally treated K-bearing silicate rocks as fertilizers. The Compositional Nutrient Diagnostic (CND) approach was used to assess the plants' nutrient status, involving identification of high-yield subpopulations, and setting a yield cutoff. We derived a theoretical threshold for nutrient imbalance (CNDr2) using statistical methods like the chi-square distribution function and low-yield subpopulation proportion. CNDr2 was validated via Cate–Nelson partition and sum of squared individual nutrient indexes. Results showed a yield cutoff of 37.759 kg ha−1, distinguishing low-yield and high-yield subpopulations based on cumulative variance ratio functions from survey data. The theoretical threshold derived using the chi-square function was 10.1, subsequently validated by the Cate–Nelson method. Critical CND nutrient indices were symmetrical around zero, but their sum indicated foliar nutrient imbalance, notably zinc, potassium, and copper excess, attributed to 20 interactions identified (4 synergetic and 16 antagonistic). This study underscores hydrothermal treatment's efficacy in improving nutrient availability and achieving a balanced nutrient profile compared to raw materials. It offers a promising solution for enhancing agricultural productivity, especially in tropical regions like Africa, where traditional sources are scarce. [ABSTRACT FROM AUTHOR]

Particle emission fluctuation was studied experimentally with a free convection diffusion flame, which used primary reference fuels consisting of n-heptane and iso-octane. The smokeless weak turbulent flame was turned into a smoky strong turbulent flame by disturbing it with a tangential airflow. A diffusion charger (DC) particle sensor was used to measure the transient particle mass (PM) emissions. The turbulence increased the PM significantly, particularly for a higher fraction of iso-octane fuel. Statistical results showed that the PM fluctuation follows the chi-square distribution. Furthermore, the theoretical analysis proved that the PM is related with the square of the fluctuation velocity. [ABSTRACT FROM AUTHOR]

This study aimed to determine whether the Relative Age Effect (RAE) was present in different sexes and age categories in 12 elite-level international amateur boxing competitions. A total of 4813 athletes competing between 2013 and 2022 were analysed. Athletes were split into four quartiles according to their birth date and compared to the expected (equal) birth date distribution using chi-squared goodness of fit. The results revealed greater RAE prevalence in youth compared to the senior group. RAE was more prominent in males compared to females, with the female group showing an inverse RAE trend. Odds ratio (OR) showed an overrepresentation of male boxers born in Q1 compared to Q4 (OR > 1.19-1.33), while senior female boxers presented an inverse trend (OR < 0.95). Odds Ratios for medallists within the youth group were greater than 1.07 (except Q3 × Q4 = 0.93) highlighting an overrepresentation of boxers born earlier in the year. A shift in strategy to reduce the RAE in young boxers whereby coaches focus less on the short-term pursuit of sporting success is encouraged. Organisations and coaches should increase awareness and provide systematic education around RAE, whilst creating equal competitive opportunities for all young boxers to reduce the extent of RAE in boxing. [ABSTRACT FROM AUTHOR]

Recently, the Gini distance correlation (GDC), ρ g , was proposed to measure dependence between numerical and categorical variables (Dang et al. 2021). This new dependence measure can mutually characterize independence between the random variables. That is, ρ g = 0 if and only only the categorical variable and the numerical variable are independent. Limiting distributions of the naive estimator of GDC have been established in Dang et al. (2021). It has been shown that under independence, the empirical GDC admits a degenerating limit which is an infinite weighted sum of Chi-squared distributions. In this paper, we propose a modified estimator of the GDC that is asymptotically normal under independence between the numerical and the categorical variables. We also extend this method to the generalized GDC Zhang et al. (2019) in reproducing kernel Hilbert space (RKHS). Both the modified GDC and generalized GDC can be applied to test the K-sample problem. Simulations studies are conducted to examine the finite sample performance of the new K-sample test based on the modified estimators. [ABSTRACT FROM AUTHOR]

To study the symmetry and asymmetry of the model error under multiplicative distortion measurement errors setting, we propose a correlation coefficient-based measure between the distribution function and the root of density function. The unknown distribution function and density function are estimated from four kinds of residuals: the conditional mean calibration-based residuals, the conditional absolute mean calibration-based residuals, the conditional variance calibration-based residuals, and the conditional absolute logarithmic calibration-based residuals. We study the asymptotic results of the estimators of correlation coefficient-based measure under four calibrations. Next, we consider statistical inference of the correlation coefficient-based measure by using the empirical likelihood method. The empirical likelihood statistics are shown to be an asymptotically standard chi-squared distribution. Simulation studies demonstrate the performance of the proposed estimators and test statistics. A real example is analyzed to illustrate its practical usage. [ABSTRACT FROM AUTHOR]

The Lorenz curve portrays income distribution inequality. In this article, we develop three modified empirical likelihood (EL) approaches, including adjusted empirical likelihood, transformed empirical likelihood, and transformed adjusted empirical likelihood, to construct confidence intervals for the generalized Lorenz ordinate. We demonstrate that the limiting distribution of the modified EL ratio statistics for the generalized Lorenz ordinate follows scaled Chi-Squared distributions with one degree of freedom. We compare the coverage probabilities and mean lengths of confidence intervals of the proposed methods with the traditional EL method through simulations under various scenarios. Finally, we illustrate the proposed methods using real data to construct confidence intervals. [ABSTRACT FROM AUTHOR]

In capture–recapture experiments, the presence of overdispersion and heterogeneity necessitates the use of the negative binomial regression model for inferring population sizes. However, within this model, existing methods based on likelihood and ratio regression for estimating the dispersion parameter often face boundary and nonidentifiability issues. These problems can result in nonsensically large point estimates and unbounded upper limits of confidence intervals for the population size. We present a penalized empirical likelihood technique for solving these two problems by imposing a half-normal prior on the population size. Based on the proposed approach, a maximum penalized empirical likelihood estimator with asymptotic normality and a penalized empirical likelihood ratio statistic with asymptotic chi-square distribution are derived. To improve numerical performance, we present an effective expectation-maximization (EM) algorithm. In the M-step, optimization for the model parameters could be achieved by fitting a standard negative binomial regression model via the R basic function glm.nb(). This approach ensures the convergence and reliability of the numerical algorithm. Using simulations, we analyze several synthetic datasets to illustrate three advantages of our methods in finite-sample cases: complete mitigation of the boundary problem, more efficient maximum penalized empirical likelihood estimates, and more precise penalized empirical likelihood ratio interval estimates compared to the estimates obtained without penalty. These advantages are further demonstrated in a case study estimating the abundance of black bears (Ursus americanus) at the U.S. Army's Fort Drum Military Installation in northern New York. [ABSTRACT FROM AUTHOR]

We derive an equation system for finding Maximum Likelihood Estimators (MLEs) for the parameters of a p-dimensional t-distribution with ν degrees of freedom, t p , ν , and use the MLEs for testing covariance structures for the t p , ν -distributed population. The likelihood ratio test (LRT), Rao score test (RST) and Wald test (WT) statistics are derived under the general null-hypothesis H 0 : Σ = Σ 0 , using a matrix derivative technique. Here the p × p -matrix Σ is a dispersion/scale parameter. Convergence to the asymptotic chi-square distribution under the null hypothesis is examined in extensive simulation experiments. Also the convergence to the chi-square distribution is studied empirically in the situation when the MLEs of a t p , ν -distribution are changed to the corresponding estimators for a normal population. Type I errors and the power of the tests are also examined by simulation. In the simulation study the RST behaved more adequately than all remaining statistics in the situation when the dimensionality p was growing. [ABSTRACT FROM AUTHOR]

This study aimed to assess, for the first time, how self-reported sleep, mental toughness, and reaction time are impacted by a professional padel tournament. In addition, we evaluated whether sex, age, and/or ranking play a role in this possible effect of a tournament on these variables. Twenty-three professional players (15 men, Mage= 24 ± 6 years; eight women, Mage= 21 ± 5 years) were evaluated on two occasions: (a) baseline, in a noncompetitive week and (b) postmeasure, the morning after an individual was eliminated from the tournament. The Pittsburgh Sleep Quality Index, the Mental Toughness Questionnaire, and the psychomotor vigilance task were used to evaluate the dependent variables. Wilcoxon tests or paired samples t tests were employed to assess the effect of participating in the tournament. To test correlations between variables, Pearson correlation coefficients (quantitative variables) or chi-square distributions (qualitative variables) were employed. Results showed that self-reported sleep (p <.01), mental toughness (p =.01), and reaction time (p =.04) were significantly impaired by the tournament. Exploring moderating variables, results showed that mental toughness did not correlate with sleep impairments (p >.05). In contrast, a nearly significant correlation between sleep impairments and higher reaction times was found (p =.066). No significant effects of age, sex, and ranking were observed. In conclusion, participating in a padel competition impairs the self-reported sleep, mental toughness, and reaction time of professional padel players. A trend toward a significant correlation between the competition-related impairment in sleep and reaction time was observed, whereas age, ranking, and sex were not found to be moderators of any of these impairments. [ABSTRACT FROM AUTHOR]

High-speed maglev system is a hot research topic nowadays in the field of high-speed ground transportation. Characteristics of the track irregularity of high-speed maglev system is quite different due to its contactless vehicle-rail relationship and segmented track compared with traditional railway. However, research on maglev track irregularity is still insufficient. This paper summarises, for the first time, the track inspection data collected on Shanghai Maglev Demonstration Line (Shanghai Line) since 2006, and describes the main filtering methods and parameters for acceleration and gap signals, taking into account the characteristics of maglev track. Track irregularity is then determined using the inertial measurement principle. The measured track spectrum on Shanghai Line calculated by the Welch method obeys a chi-square distribution with 2 degrees of freedom, indicating that different track qualities can be transformed by probability methods according to the research requirements. Based on the samples obtained over the past 15 years, and referring to the seven-parameter model of the railway system, a high-speed maglev track spectrum is obtained by the fitting method, parameters of which are obtained by applying the damped least squares method. Preliminary vehicle dynamic analysis is conducted utilising the inverted excitations derived from the measured spectrum of the Shanghai Line. [ABSTRACT FROM AUTHOR]

AbstractIn this paper, we develop two procedures for identifying the dynamic trends in the parameters of length-biased lognormal distribution based on likelihood ratio and modified information criterion. These methods mainly consider the test of the existence of the change point and provide the maximum likelihood estimation of the change point when the change point exists. In addition, the asymptotic distribution of test statistic based on likelihood ratio is derived as an extreme value distribution, while the asymptotic distribution of test statistic based on modified information criterion is derived as a chi-square distribution. And the consistency of parameter estimation is proved. Simulations are conducted to study the performance of the proposed method in terms of power, coverage probabilities and average sizes of confidence sets. The proposed methods are applied to a real data to illustrate the detecting procedures. [ABSTRACT FROM AUTHOR]

AbstractWe consider a linear model which can have a large number of explanatory variables, the errors with an asymmetric distribution or the values of the explained variable are missing at random. In order to take in account these several situations, we consider the non parametric empirical likelihood (EL) estimation method. Because a constraint in EL contains an indicator function then a smoothed function instead of the indicator will be considered. Two smoothed expectile maximum EL methods are proposed, one of which will automatically select the explanatory variables. For each of the methods we obtain the convergence rate of the estimators and their asymptotic normality. The smoothed expectile empirical log-likelihood ratio process follow asymptotically a chi-square distribution and moreover the adaptive LASSO smoothed expectile maximum EL estimator satisfies the sparsity property which guarantees the automatic selection of zero model coefficients. In order to implement these methods, we propose four algorithms. [ABSTRACT FROM AUTHOR]

Damage localization is very significant in engineering applications. The existing method based on the chi-square distribution of an autoregressive moving average with exogenous inputs (ARMAX) model residual is not applicable for these realistic excitations except Gaussian excitation. To solve the above problem, this paper presents a structural damage localization method based on the empirical probability mass function (EPMF) of the ARMAX model residual and Kullback–Leibler (KL) divergence. In detail, we employ empirical data analysis (EDA) approach to estimate the EPMF of the ARMAX model residual of the data generated by the arbitrary excitation because EDA does not need any a priori knowledge about the model residual. Moreover, the KL divergence is introduced to measure the dissimilarity of the EPMFs in undamaged and damaged states to prove that our method is effective for arbitrary excitation. Finally, the semi-parametric extreme value theory is used to estimate the reliable threshold for localizing the damage. Numerical simulated and experimental results illustrate that the proposed method localizes the damage under different excitations, respectively. [ABSTRACT FROM AUTHOR]

Diagnostic checking is an important predefined step before using autoregressive models. Although many portmanteau tests were proposed for diagnostic checking, they still struggle with the issue of significant size distortion. In this paper, we develop new diagnostic checking methods based on jackknife empirical likelihood. It is demonstrated that the suggested testing statistics asymptotically have a typical chi-squared distribution. To verify the performance of the finite sample, some simulations are constructed. Additionally, a real example of five agricultural futures is provided to illustrate the merits of our diagnostic checking procedure. [ABSTRACT FROM AUTHOR]

The aim of our paper is to investigate the properties of the classical phase-dispersion minimization (PDM), analysis of variance (AOV), string-length (SL), and Lomb–Scargle (LS) power statistics from a statistician's perspective. We confirm that when the data are perturbations of a constant function, i.e. under the null hypothesis of no period in the data, a scaled version of the PDM statistic follows a beta distribution, the AOV statistic follows an F distribution, and the LS power follows a chi-squared distribution with two degrees of freedom. However, the SL statistic does not have a closed-form distribution. We further verify these theoretical distributions through simulations and demonstrate that the extreme values of these statistics (over a range of trial periods), often used for period estimation and determination of the false alarm probability (FAP), follow different distributions than those derived for a single period. We emphasize that multiple-testing considerations are needed to correctly derive FAP bounds. Though, in fact, multiple-testing controls are built into the FAP bound for these extreme-value statistics, e.g. the FAP bound derived specifically for the maximum LS power statistic over a range of trial periods. Additionally, we find that all of these methods are robust to heteroscedastic noise aimed to mimic the degradation or miscalibration of an instrument over time. Finally, we examine the ability of these statistics to detect a non-constant periodic function via simulating data that mimics a well-detached binary system, and we find that the AOV statistic has the most power to detect the correct period, which agrees with what has been observed in practice. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Guangxi Normal University - Natural Science Edition is the property of Gai Kan Bian Wei Hui and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Based on the amplitude attribute analysis of ground penetrating radar (GPR) data, this paper applies GPR to the identification of internal damages and abnormal objects in stone walls of Tibetan ruins. The corresponding relationship between the characteristics of internal damages and abnormal objects and the radar data is explored through the Tibetan stone walls (TSWs) simulation test. The identification of location and size of the damages and abnormal objects in TSWs is realized based on the Mahalanobis distance abnormal data discrimination method. Using the normal distribution and the noncentral chi-square distribution, the identification law of types of the damages and abnormal objects is constructed, which takes root mean square (RMS) amplitude and interface reflection coefficient as the characteristic values. The field detection results of TSWs at three Tibetan sites are taken as an extension and supplement to the simulation results, and a set of identification atlas for the location, size and type of the internal damages and abnormal objects in TSWs is established. The application results of the identification atlas were verified by the field detection and the results show that the atlas has a high accuracy, which can significantly improve the efficiency of the identification, and can provide a basis for the performance research, protection and maintenance of TSWs. [ABSTRACT FROM AUTHOR]

In capture-recapture problems, when individuals are categorized into different groups and individuals within each group are suspected to be captured with equal probability, the finite mixture of Poisson distributions is commonly employed to address heterogeneity in capture probabilities. In this study, we propose a penalized likelihood estimation method to estimate population sizes and demonstrate that the penalized likelihood ratio statistic asymptotically follows a standard chi-square distribution. To detect the presence of heterogeneity, we introduce a retooled EM test statistic that asymptotically follows a mixture of chi-square distributions. Our numerical investigations reveal that the proposed maximum penalized likelihood estimator offers increased stability, while the penalized likelihood ratio interval estimator shows enhanced accuracy compared with existing approaches. By carefully selecting an adaptive tuning parameter, the EM test achieves a better balance between the type I error and power than the goodness-of-fit and AIC-based tests. Finally, we apply the proposed method to three real-life datasets: street prostitute data, H5N1 influenza data, and opiate user data. [ABSTRACT FROM AUTHOR]

The length-biased lognormal distribution is a length-biased version of lognormal distribution, which is developed to model the length-biased lifetime data from, for example, biological investigation, medical research, and engineering fields. Owing to the existence of censoring phenomena in lifetime data, we study the change-point-testing problem of length-biased lognormal distribution under random censoring in this paper. A procedure based on the modified information criterion is developed to detect changes in parameters of this distribution. Under the sufficient condition of the Fisher information matrix being positive definite, it is proven that the null asymptotic distribution of the test statistic follows a chi-square distribution. In order to evaluate the uncertainty of change point location estimation, a way of calculating the coverage probabilities and average lengths of confidence sets of change point location based on the profile likelihood and deviation function is proposed. The simulations are conducted, under the scenarios of uniform censoring and exponential censoring, to investigate the validity of the proposed method. And the results indicate that the proposed approach performs better in terms of test power, coverage probabilities, and average lengths of confidence sets compared to the method based on the likelihood ratio test. Subsequently, the proposed approach is applied to the analysis of survival data from heart transplant patients, and the results show that there are differences in the median survival time post-heart transplantation among patients of different ages. [ABSTRACT FROM AUTHOR]

Zero-adjusted generalized linear models (ZAGLMs) are used in many areas to fit variables that are discrete at zero and continuous on the positive real numbers. As in other classes of regression models, hypothesis testing inference in the class of ZAGLMs is usually performed using the likelihood ratio statistic. However, the LR test is substantially size distorted when the sample size is small. In this work, we derive an analytical Bartlett correction of the LR statistic. We also consider two different adjustments for the LR statistic based on bootstrap. Monte Carlo simulation studies show that the improved LR tests have null rejection rates close to the nominal levels in small sample sizes and similar power. An application illustrates the usefulness of the improved statistics. [ABSTRACT FROM AUTHOR]

This paper presents a novel methodology aimed at generating chi-square variates within the framework of neutrosophic statistics. It introduces algorithms designed for the generation of neutrosophic random chi-square variates and illustrates the distribution of these variates across a spectrum of indeterminacy levels. The investigation delves into the influence of indeterminacy on random numbers, revealing a significant impact across various degrees of freedom. Notably, the analysis of random variate tables demonstrates a consistent decrease in neutrosophic random variates as the degree of indeterminacy escalates across all degrees of freedom values. These findings underscore the pronounced effect of uncertainty on chi-square data generation. The proposed algorithm offers a valuable tool for generating data under conditions of uncertainty, particularly in scenarios where capturing real data proves challenging. Furthermore, the data generated through this approach holds utility in goodness-of-fit tests and assessments of variance homogeneity.

Information theory explains how systems encode and transmit information. This article examines the neuronal system, which processes information via neurons that react to stimuli and transmit electrical signals. Specifically, we focus on transfer entropy to measure the flow of information between sequences and explore its use in determining effective neuronal connectivity. We analyze the causal relationships between two discrete time series, X : = X t : t ∈ Z and Y : = Y t : t ∈ Z , which take values in binary alphabets. When the bivariate process (X , Y) is a jointly stationary ergodic variable-length Markov chain with memory no larger than k, we demonstrate that the null hypothesis of the test—no causal influence—requires a zero transfer entropy rate. The plug-in estimator for this function is identified with the test statistic of the log-likelihood ratios. Since under the null hypothesis, this estimator follows an asymptotic chi-squared distribution, it facilitates the calculation of p-values when applied to empirical data. The efficacy of the hypothesis test is illustrated with data simulated from a neuronal network model, characterized by stochastic neurons with variable-length memory. The test results identify biologically relevant information, validating the underlying theory and highlighting the applicability of the method in understanding effective connectivity between neurons. [ABSTRACT FROM AUTHOR]

This paper presents a novel methodology aimed at generating chi-square variates within the framework of neutrosophic statistics. It introduces algorithms designed for the generation of neutrosophic random chi-square variates and illustrates the distribution of these variates across a spectrum of indeterminacy levels. The investigation delves into the influence of indeterminacy on random numbers, revealing a significant impact across various degrees of freedom. Notably, the analysis of random variate tables demonstrates a consistent decrease in neutrosophic random variates as the degree of indeterminacy escalates across all degrees of freedom values. These findings underscore the pronounced effect of uncertainty on chi-square data generation. The proposed algorithm offers a valuable tool for generating data under conditions of uncertainty, particularly in scenarios where capturing real data proves challenging. Furthermore, the data generated through this approach holds utility in goodness-of-fit tests and assessments of variance homogeneity. [ABSTRACT FROM AUTHOR]

Lithium-ion batteries are currently used as a key energy source in various industrial facilities, electronics, and automotive industries. However, due to the frequent charging and discharging of batteries, overcharging and overdischarging can occur, leading to fire and safety accidents as well as additional financial damages due to equipment failure. Therefore, accurately estimating the battery state of charge (SOC) is very important. In this paper, the robustness of estimation models was analyzed in relation to data collected amidst sensor failures. This analysis was especially pertinent during the battery SOC estimation process, when voltage and current sensors were prone to failure. The impact of these sensor failures on the accuracy and reliability of the SOC estimation models was rigorously scrutinized. Normal data was trained as training data, and Gaussian distribution, Laplace and chi-square combined distribution, Add bias distribution were employed as the test data. Herein, multilayer neural network, long short-term memory, gated recurrent unit, gradient boosting machine (GBM) were used as neural networks, the failure signal processing performance of each estimation algorithm was compared and analyzed, and the failure diagnosis was performed using support vector machine and GBM. [ABSTRACT FROM AUTHOR]

Consider k independent random samples from p-dimensional multivariate normal distributions. We are interested in the limiting distribution of the log-likelihood ratio test statistics for testing for the equality of k covariance matrices. It is well known from classical multivariate statistics that the limit is a chi-square distribution when k and p are fixed integers. Jiang and Qi (Scand J Stat 42:988–1009, 2015) and Jiang and Yang (Ann Stat 41(4):2029–2074, 2013) have obtained the central limit theorem for the log-likelihood ratio test statistics when the dimensionality p goes to infinity with the sample sizes. In this paper, we derive the central limit theorem when either p or k goes to infinity. We also propose adjusted test statistics which can be well approximated by chi-squared distributions regardless of values for p and k. Furthermore, we present numerical simulation results to evaluate the performance of our adjusted test statistics and the log-likelihood ratio statistics based on classical chi-square approximation and the normal approximation. [ABSTRACT FROM AUTHOR]

We consider a random walk with zero mean and finite variance whose steps are arithmetic. The arcsine law for the time the walk reaches its maximum is well known. In this paper, we consider the distribution of the moment of reaching the maximum under the assumption that the maximum value itself is fixed. We show that, in the case of a moderate deviation of the maximum, the distribution of the moment of the maximum with appropriate normalization converges to the chi-square distribution with one degree of freedom. Similar results are obtained in the nonlattice case. [ABSTRACT FROM AUTHOR]

Objective: To evaluate the association and risk of hypercholesterolemia among adult patients with prediabetes treated at a medical center in the district of Villa El Salvador in Lima, Peru. Materials and methods: An analytical, prospective and cross-sectional study conducted with data from medical consultation records of 749 patients treated at a polyclinic in the district of Villa El Salvador in Lima, Peru. Asymptomatic adult patients who had routine and preventive checkups were included in the research. Patients with endocrine and metabolic disorders or being treated with hypoglycemic drugs were excluded. The study variables were sex, hypercholesterolemia and prediabetes. The association analysis was performed using the chi-square test and the risk was evaluated by means of the odds ratio. In addition, the multivariate analysis was conducted through a binary logistic regression, and an alpha value of 0.05 and a confidence level of 95 % were considered as the cut-off point to determine the statistical significance. Results: There was a statistically significant association between prediabetes and hypercholesterolemia. Females with prediabetes were 1.66 times more likely to develop hypercholesterolemia than females with normal baseline glucose levels, while males with prediabetes were 2.37 times more likely to have high cholesterol than males with normal baseline blood glucose levels. Conclusions: Prediabetes is associated with hypercholesterolemia, thus increasing its risk. It is justifiable to carry out the joint measurement of fasting total cholesterol and baseline glucose in disease prevention and health promotion campaigns,regular checkups and follow-up of patients with risk factors for diabetes, prediabetes and hypercholesterolemia. This helps reduce the hemodynamic and cardiovascular consequences of high cholesterol levels and the worsening of the joint morbidity and mortality of chronic hyperglycemia. [ABSTRACT FROM AUTHOR]

Context. The problem of determining the object-oriented design (OOD) complexity of the open-source software, including Web apps created using the PHP frameworks, is important because nowadays open-source software is growing in popularity and using the PHP frameworks making app development faster. The object of the study is the process of determining the OOD complexity of the open-source Web apps created using the PHP frameworks. The subject of the study is the mathematical models to determine the OOD complexity due to the identification of classes of the open-source Web apps created using the PHP frameworks. Objective. The goal of the work is the build a mathematical model for determining the OOD complexity due to the identification of classes of the open-source Web apps created using the PHP frameworks based on the three-variate Box-Cox normalizing transformation to increase confidence in determining the OOD complexity of these apps. Method. The mathematical model for determining the OOD complexity due to the identification of classes of the open-source Web apps created using the PHP frameworks is constructed in the form of the prediction ellipsoid equation for normalized metrics WMC, DIT, and NOC at the app level. We apply the three-variate Box-Cox transformation for normalizing the above metrics. The maximum likelihood method is used to compute the parameter estimates of the three-variate Box-Cox transformation. Results. A comparison of the constructed model based on the F distribution quantile with the prediction ellipsoid equation based on the Chi-Square distribution quantile has been performed. Conclusions. The mathematical model in the form of the prediction ellipsoid equation for the normalized WMC, DIT, and NOC metrics at the app level to determine the OOD complexity due to the identification of classes of the open-source Web apps created using the PHP frameworks is firstly built based on the three-variate Box-Cox transformation. This model takes into account the correlation between the WMC, DIT, and NOC metrics at the app level. The prospects for further research may include the use of other data sets to confirm or change the prediction ellipsoid equation for determining the OOD complexity due to the identification of classes of the open-source Web apps created using the PHP frameworks. [ABSTRACT FROM AUTHOR]

Ballon d'Or is the most important individual award in football, and is a significant measure of excellence. From our knowledge, this is the first study that explored the relative age effect (RAE) throughout the history of the Ballon d'Or. A total of 1899 football players nominated for the award from the first edition in 1956 to the most recent edition (2023) were analyzed. To assess the RAE, the birthdate distributions were categorized into four trimesters. The comparison involved correcting for the uniform distribution using chi-square analysis, with Cramer's V serving as a measure of effect size. Standardized residuals were computed to identify quarters that exhibited significant deviation from the expected values. Odds Ratio and 95% confidence intervals were used to identify discrepancies between trimesters. The results indicated a pronounced presence of an RAE at the global level. However, the longitudinal analysis revealed variations in the behavior of the RAE over time. In the initial decades, there is an overrepresentation of players born in the last months of the year. Subsequently, there is no discernible RAE. In the most recent decades, there has been a clear resurgence of RAE, with an overrepresentation of players born in the first quarters of the year. [ABSTRACT FROM AUTHOR]

When the response variable is discrete as a number (count) and there is a violation of the assumption of equidispersion, namely overdispersion or underdispersion then one of the appropriate alternative models used is Negative Binomial Regression (NBR). Moreover, if there are two correlated response variables and have an equidispersion violation, the Bivariate Negative Binomial Regression (BNBR) model is the solution. However, the BNBR model is considered inappropriate if the data contains spatial and temporal heterogeneity derived from panel data with the unit of observation in the form of a region. Therefore, a model is offered which is known as Geographically and Temporally Weighted Bivariate Negative Binomial Regression (GTWBNBR) which accommodates spatial and temporal effects. This study aims to conduct parameter estimates and test statistics for the GTWBNBR model. Estimated parameters use Maximum Likelihood Estimation (MLE) with BHHH numerical iteration because the MLE estimates are not closed-form. When the sample size is large, the Maximum Likelihood Ratio Test (MLRT) is used for simultaneous parameter testing while the test statistic for partial parameter testing approaches the Chi-Square distribution so that it can be tested using the Z-Test. [ABSTRACT FROM AUTHOR]

This study aims to introduce a bivariate Log-Normal regression model and to develop a technique for parameter estimation and hypothesis testing. We term the model Bivariate Log-Normal Regression (BLNR). The estimation procedure is conducted by the standard Maximum Likelihood Estimation (MLE) employing the Newton-Raphson method. To perform hypothesis testing, we adapt the Maximum Likelihood Ratio Test (MLRT) for simultaneous testing with test statistics which, for large n, follows Chi-Square distribution with degrees of freedom p. In addition, the partial testing is derived from a central limit theorem which results in a Z-test statistic. [ABSTRACT FROM AUTHOR]

This paper discusses the approximate distributions of eigenvalues of a singular Wishart matrix. We give the approximate joint density of eigenvalues by Laplace approximation for the hypergeometric functions of matrix arguments. Furthermore, we show that the distribution of each eigenvalue can be approximated by the chi-square distribution with varying degrees of freedom when the population eigenvalues are infinitely dispersed. The derived result is applied to testing the equality of eigenvalues in two populations. [ABSTRACT FROM AUTHOR]

Based on the definition of the γ-order generalized normal, the γ-order generalized standard normal is obtained, and applications are referred. We proceed on the definition of the γ-order generalized chi-square, [Formula: see text] and the probability density function (pdf) is evaluated. Moreover, the moment generating function (mgf) of the [Formula: see text] is evaluated and in the case of γ = 2 the mgf of the well known [Formula: see text] is obtained. The same procedure is followed for the moments of the [Formula: see text] One step forward is the evaluation of the convolution of two [Formula: see text] and therefore [Formula: see text] is obtained eventually and the corresponding pdf is evaluated. Finally examples and applications of [Formula: see text] are discussed.

Background: Liver cancer incidence increased in the US from 1975 through 2015 with heterogeneous rates across subpopulations. Upstream or distal area-level factors impact liver cancer risks. Objective: The aim of this study was to examine the association between area-level deprivation and hepatocellular carcinoma (HCC) incidence and survival. We also explored the association between area deprivation and treatment modalities. Methods: Louisiana Tumor Registry identified 4,151 adult patients diagnosed with malignant HCC from 2011 to 2020 and linked residential address to census tract (CT)-level Area Deprivation Index (ADI) categorized into quartiles (Q1 = least deprived). ANOVA examined the association between ADI quartile and CT age-adjusted incidence rate (AAIR) per 100,000. Chi-square tested the distribution of demographic and clinical characteristics across ADI quartiles. Kaplan-Meier and proportional hazard models evaluated survival by deprivation quartile. Results: Among the 1,084 CTs with incident HCC, the average (SD) AAIR was 8.02 (7.05) HCC cases per 100,000 population. ADI was observed to be associated with incidence, and the mean (SD) AAIR increased from 5.80 (4.75) in Q1 to 9.26 (7.88) in Q4. ADI was also associated with receipt of surgery (p < 0.01) and radiation (p < 0.01) but not chemotherapy (p = 0.15). However, among those who received chemotherapy, people living in the least deprived areas began treatment approximately 10 days sooner than those living in other quartiles. Q4 patients experienced the worst survival with a median of 247 (95% CI 211-290) days vs. Q1 patients with a median of 474 (95% CI 407-547) days (p < 0.0001). Q4 had marginally poorer survival (HR 1.20, 1.05-1.37) than Q1 but the association became non-significant (HR 1.12, 0.96-1.30) when adjusted for rurality, liquor store density, sex, race/ethnicity, age, insurance, BMI, stage, hepatitis diagnosis, and comorbidities. Conclusion: Increasing neighborhood (CT) deprivation (ADI) was observed to be associated with increased HCC incidence and poorer HCC survival. However, the association with poorer survival becomes attenuated after adjusting for putative confounders. [ABSTRACT FROM AUTHOR]

In this paper, the statistical inference of the partially linear varying coefficient quantile regression model is studied under random missing responses. A two-stage estimation procedure is developed to estimate the parametric and nonparametric components involved in the model. Furthermore, the asymptotic properties of the estimators obtained are established under some mild regularity conditions. In addition, the empirical log-likelihood ratio statistic based on imputation is proposed, and it is proven that this statistic obeys the standard Chi-square distribution; thus, the empirical likelihood confidence interval of the parameter component of the model is constructed. Finally, simulation results show that the proposed estimation method is feasible and effective. [ABSTRACT FROM AUTHOR]

Several major theorems pertaining to necessary and sufficient conditions under which quadratic forms in normal random vectors are chi-square distributed (both central and non central) are revisited and illuminated. Some of these results date back to the early 1950's and are scattered among journals that are not all easily accessible. Moreover, some of these presentations are very terse, reflecting the tendency to reduce the amount of technical typesetting. Most of these results are not available in their entirety in current graduate level statistics texts. Accordingly, the purpose here is to collect these in one place and to offer complete detailed and clear proofs with some new perspectives. The general case in which the variance matrix of the normal random vector can be positive semidefinite is emphasized, since those results will subsume the positive definite case with appropriate reductions of conditions. [ABSTRACT FROM AUTHOR]

This paper addresses certain distributional aspects of a scale-free scatter matrix denoted by R that is stemming from a matrix-variate gamma distribution having a positive definite scale parameter matrix B. Under the assumption that B is a diagonal matrix, a structural representation of the determinant of R is derived; the exact density functions of products and ratios of determinants of matrices possessing such a structure are obtained; a closed form expression is given for the density function of R. Moreover, a novel procedure is utilized to establish that certain functions of the determinant of the sample scatter matrix are asymptotically distributed as chi-square or normal random variables. Then, representations of the density function of R that respectively involve multiple integrals, multiple series and Gauss' hypergeometric function are provided for the general case of a positive definite scale parameter matrix, and an illustrative numerical example is presented. Cutting-edge mathematical techniques have been employed to derive the results. Naturally, they also apply to the conventional sample correlation matrix which is encountered in various multivariate inference contexts. [ABSTRACT FROM AUTHOR]

Partially linear models find extensive application in biometrics, econometrics, social sciences, and various other fields due to their versatility in accommodating both parametric and nonparametric elements. This study aims to establish statistical inference for the parametric component effects within these models, employing a nonparametric empirical likelihood approach. The proposed method involves a projection step to eliminate the nuisance nonparametric component and utilizes an empirical-likelihood-based technique, along with the Bartlett correction, to enhance the coverage probability of the confidence interval for the parameter of interest. This method demonstrates robustness in handling normally and non-normally distributed errors. The proposed empirical likelihood ratio statistic converges to a limiting chi-square distribution under certain regulations. Simulation studies demonstrate that this method provides better inference in terms of coverage probabilities compared to the conventional normal-approximation-based method. The proposed method is illustrated by analyzing the Boston housing data from a real study. [ABSTRACT FROM AUTHOR]

In many psychometric applications, the relationship between the mean of an outcome and a quantitative covariate is too complex to be described by simple parametric functions; instead, flexible nonlinear relationships can be incorporated using penalized splines. Penalized splines can be conveniently represented as a linear mixed effects model (LMM), where the coefficients of the spline basis functions are random effects. The LMM representation of penalized splines makes the extension to multivariate outcomes relatively straightforward. In the LMM, no effect of the quantitative covariate on the outcome corresponds to the null hypothesis that a fixed effect and a variance component are both zero. Under the null, the usual asymptotic chi-square distribution of the likelihood ratio test for the variance component does not hold. Therefore, we propose three permutation tests for the likelihood ratio test statistic: one based on permuting the quantitative covariate, the other two based on permuting residuals. We compare via simulation the Type I error rate and power of the three permutation tests obtained from joint models for multiple outcomes, as well as a commonly used parametric test. The tests are illustrated using data from a stimulant use disorder psychosocial clinical trial. [ABSTRACT FROM AUTHOR]

Top-k graph similarity search on probabilistic graphs is widely used in various scenarios, such as symptom–disease diagnostics, community discovery, visual pattern recognition, and communication networks. The state-of-the-art method uses the chi-square statistics to speed up the process. The effectiveness of the chi-square statistics solution depends on the effectiveness of the sample observation and expectation. The existing method assumes that the labels in the data graphs are subject to uniform distribution and calculate the chi-square value based on this. In fact, however, the actual distribution of the labels does not meet the requirement of uniform distribution, resulting in a low quality of the returned results. To solve this problem, we propose a top-k similar subgraph search algorithm ChiSSA based on chi-square statistics. We propose two ways to calculate the expectation vector according to the actual distribution of labels in the graph, including the local expectation calculation method based on the vertex neighbors and the global expectation calculation method based on the label distribution of the whole graph. Furthermore, we propose two optimization strategies to improve the accuracy of query results and the efficiency of our algorithm. We conduct rich experiments on real datasets. The experimental results on real datasets show that our algorithm improves the quality and accuracy by an average of 1.66× and 1.68× in terms of time overhead, it improves by an average of 3.41×. [ABSTRACT FROM AUTHOR]

Summary: The Anderson‐Rubin (AR) test is an important method that allows for reliable inference in the instrumental variable model when the instruments are weak. Yet, the robustness properties of this test have not been formally studied. As it turns out that the AR test is not robust to outliers, we show how to construct an outlier robust alternative—the robust AR test. We investigate the robustness properties of the robust AR test and show that the robust AR statistic asymptotically follows a chi‐square distribution. The theoretical results are illustrated by a simulation study. Finally, we apply the robust AR test to three different case studies that are affected by different types of outliers. [ABSTRACT FROM AUTHOR]

In testing hypotheses pertaining to Lorenz dominance (LD), researchers have examined second- and third-order stochastic dominance using empirical Lorenz processes and integrated stochastic processes with the aid of bootstrap analysis. Among these topics, analysis of third-order stochastic dominance (TSD) based on the notion of risk aversion has been examined using crossing (generalized) Lorenz curves. These facts motivated the present study to characterize distribution pairs displaying the TSD without second-order (generalized Lorenz) dominance. It further motivated the development of likelihood ratio (LR) goodness-of-fit tests for examining the respective hypotheses of the LD, crossing (generalized) Lorenz curves, and TSD through approximate Chi-squared distributions. The proposed LR tests were assessed using simulated distributions, and applied to examine the COVID-19 regional death counts of bivariate samples collected by the World Health Organization between March 2020 and February 2021. [ABSTRACT FROM AUTHOR]

Empirical likelihood enables a nonparametric, likelihood-driven style of inference without restrictive assumptions routinely made in parametric models. We develop a framework for applying empirical likelihood to the analysis of experimental designs, addressing issues that arise from blocking and multiple hypothesis testing. In addition to popular designs such as balanced incomplete block designs, our approach allows for highly unbalanced, incomplete block designs. We derive an asymptotic multivariate chi-square distribution for a set of empirical likelihood test statistics and propose two single-step multiple testing procedures: asymptotic Monte Carlo and nonparametric bootstrap. Both procedures asymptotically control the generalised family-wise error rate and efficiently construct simultaneous confidence intervals for comparisons of interest without explicitly considering the underlying covariance structure. A simulation study demonstrates that the performance of the procedures is robust to violations of standard assumptions of linear mixed models. We also present an application to experiments on a pesticide. [ABSTRACT FROM AUTHOR]

Two-sample hypothesis testing is a classical problem in statistics. Given i.i.d. samples X1, :::, Xm ~ P and Y1, :::, Yn ~ Q, the two-sample testing is to test whether P is significantly different from Q or not. Among the various statistical tests, the maximum mean discrepancy (MMD) has been proven to have excellent performance compared to traditional methods. In application of MMD, we are confronted with two challenges: (I) For large data set, MMD is computationally demanding with computational cost O((m + n)²); (II) The limiting distribution under the null hypothesis usually contains infinitely many unknown parameters. In this paper, we propose two testing methods that solve (I) and (II) respectively. To address (I), the data are independently and evenly divided into k groups, calculate the MMD on each group and then combine them by empirical likelihood to yield a test statistic Tk: It converges in distribution to the chi-square distribution with degree of freedom one (X1²) under the null hypothesis as k goes to infinity. To address (II), we propose to compute the two-sample jackknife pseudo-values on each group and combine them by empirical likelihood to get a new test statistic Rnm: Under the null hypothesis, Rnm converges in distribution to X1² if k = o(n): The simulation and real data application indicates that the proposed tests performs well. [ABSTRACT FROM AUTHOR]

Universal lipid screening (ULS) is recommended for all 9- to 11-year-old children. We investigated ULS outcomes and long-term pediatrician management of children with dyslipidemia using a retrospective chart review of well-child visits between 2014 and 2016. Descriptive statistics summarized demographics, ULS results, and follow-up visits/testing. Pearson χ2 test examined differences between those with and without an abnormal screen. A total of 1039 children aged 9 to 11 years were seen for a well-child visit; only 33.3% (343/1039) completed screening. Of children screened, 18.1% (62/343) had abnormal screen results and were more likely to have an elevated body mass index (P < .001), though 30.1% (19/62) had no risk factors. A total of 10.2% (35/343) had dyslipidemia. A total of 77.1% of children with dyslipidemia received nutrition/exercise counseling and 57.1% received dietitian referrals; only 68.6% had a follow-up visit and 31.4% had repeat lipid testing. Pediatricians would benefit from more practical strategies for universal testing such as point-of-care testing and long-term management to ensure ULS is an effective screening tool.

Alzheimer's Disease (AD) is a neurodegenerative disorder that is still not fully understood. Sex modifies AD vulnerability, but the reasons for this are largely unknown. We utilize two independent electronic medical record (EMR) systems across 44,288 patients to perform deep clinical phenotyping and network analysis to gain insight into clinical characteristics and sex-specific clinical associations in AD. Embeddings and network representation of patient diagnoses demonstrate greater comorbidity interactions in AD in comparison to matched controls. Enrichment analysis identifies multiple known and new diagnostic, medication, and lab result associations across the whole cohort and in a sex-stratified analysis. With this data-driven method of phenotyping, we can represent AD complexity and generate hypotheses of clinical factors that can be followed-up for further diagnostic and predictive analyses, mechanistic understanding, or drug repurposing and therapeutic approaches.

BackgroundDipeptidyl peptidase 3 (DPP3) is a cytosolic enzyme involved in the degradation of various cardiovascular and endorphin mediators. High levels of circulating DPP3 (cDPP3) indicate a high risk of organ dysfunction and mortality in cardiogenic shock patients.MethodsThe aim was to assess relationships between cDPP3 during the initial intensive care unit (ICU) stay and short-term outcome in the AdrenOSS-1, a prospective observational multinational study in twenty-four ICU centers in five countries. AdrenOSS-1 included 585 patients admitted to the ICU with severe sepsis or septic shock. The primary outcome was 28-day mortality. Secondary outcomes included organ failure as defined by the Sequential Organ Failure Assessment (SOFA) score, organ support with focus on vasopressor/inotropic use and need for renal replacement therapy. cDPP3 levels were measured upon admission and 24 h later.ResultsMedian [IQR] cDPP3 concentration upon admission was 26.5 [16.2-40.4] ng/mL. Initial SOFA score was 7 [5-10], and 28-day mortality was 22%. We found marked associations between cDPP3 upon ICU admission and 28-day mortality (unadjusted standardized HR 1.8 [CI 1.6-2.1]; adjusted HR 1.5 [CI 1.3-1.8]) and between cDPP3 levels and change in renal and liver SOFA score (p = 0.0077 and 0.0009, respectively). The higher the initial cDPP3 was, the greater the need for organ support and vasopressors upon admission; the longer the need for vasopressor(s), mechanical ventilation or RRT and the higher the need for fluid load (all p  40.4 ng/mL upon admission, a decrease in cDPP3 below 40.4 ng/mL after 24 h was associated with an improvement of organ function at 48 h and better 28-day outcome. By contrast, persistently elevated cDPP3 at 24 h was associated with worsening organ function and high 28-day mortality.ConclusionsAdmission levels and rapid changes in cDPP3 predict outcome during sepsis. Trial Registration ClinicalTrials.gov, NCT02393781. Registered on March 19, 2015.

PurposeGermline testing (GT) for prostate cancer (PCA) is now central to treatment and hereditary cancer assessment. With rising demand for and shortage of genetic counseling (GC), tools to deliver pretest informed consent across practice settings are needed to improve access to GT and precision care. Here, we report on Evaluation and Management for Prostate Oncology, Wellness, and Risk (EMPOWER), a patient-choice study for pretest video-based genetic education (VBGE) versus GC to inform urgent practice needs.Patients and methodsMen with PCA or at risk for PCA (family history of PCA) were eligible and could choose pretest VBGE or GC. Outcomes included decisional conflict for GT, change in genetics knowledge, satisfaction, and intention to share results with family and/or providers. Descriptive statistics summarized results with counts and percentages for categorical variables and mean ± standard deviation for continuous variables. Data were compared with Fisher's exact, chi-squared, or Wilcoxon two-sample tests. Mean change in genetics knowledge was compared with t tests. The significance level was set a priori at .05.ResultsData on the first 127 participants were analyzed. Characteristics were White (85.8%), bachelor's degree (66.9%), and PCA diagnosis (90.6%). The majority chose VBGE (71%) versus GC (29%; P < .001). No differences were observed in decisional conflict for GT or satisfaction. Cancer genetics knowledge improved in both groups without significant difference (+0.9 VBGE, +1.8 GC, P = .056). Men who chose VBGE had higher intention to share GT results (96.4% VBGE v 86.4% GC, P = .02). Both groups had high rates of GT uptake (VBGE 94.4%, GC 92%).ConclusionA substantial proportion of men opted for pretest VBGE, with comparable patient-reported outcomes and uptake of GT. The results support the use of pretest video to address the critical GC shortage in the precision era.