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Abstract Biologists routinely fit novel and complex statistical models to push the limits of our understanding. Examples include, but are not limited to, flexible Bayesian approaches (e.g. BUGS, stan), frequentist and likelihood‐based approaches (e.g. packages lme4) and machine learning methods. These software and programs afford the user greater control and flexibility in tailoring complex hierarchical models. However, this level of control and flexibility places a higher degree of responsibility on the user to evaluate the robustness of their statistical inference. To determine how often biologists are running model diagnostics on hierarchical models, we reviewed 50 recently published papers in 2021 in the journal Nature Ecology & Evolution, and we found that the majority of published papers did not report any validation of their hierarchical models, making it difficult for the reader to assess the robustness of their inference. This lack of reporting likely stems from a lack of standardized guidance for best practices and standard methods. Here, we provide a guide to understanding and validating complex models using data simulations. To determine how often biologists use data simulation techniques, we also reviewed 50 recently published papers in 2021 in the journal Methods Ecology & Evolution. We found that 78% of the papers that proposed a new estimation technique, package or model used simulations or generated data in some capacity (18 of 23 papers); but very few of those papers (5 of 23 papers) included either a demonstration that the code could recover realistic estimates for a dataset with known parameters or a demonstration of the statistical properties of the approach. To distil the variety of simulations techniques and their uses, we provide a taxonomy of simulation studies based on the intended inference. We also encourage authors to include a basic validation study whenever novel statistical models are used, which in general, is easy to implement. Simulating data helps a researcher gain a deeper understanding of the models and their assumptions and establish the reliability of their estimation approaches. Wider adoption of data simulations by biologists can improve statistical inference, reliability and open science practices.

Purpose – Time headway (THW) is an essential parameter in traffic safety and is used as a typical control variable by many vehicle control algorithms, especially in safety-critical ADAS and automated driving systems. However, due to the randomness of human drivers, THW cannot be accurately represented, affecting scholars’ more profound research. Design/methodology/approach – In this work, two data sets are used as the experimental data to calculate the goodness-of-fit of 18 commonly used distribution models of THW to select the best distribution model. Subsequently, the characteristic parameters of traffic flow are extracted from the data set, and three variables with higher importance are extracted using the random forest model. Combining the best distribution model parameters of the data set, this study obtained a distribution model with adaptive parameters, and its performance and applicability are verified. Findings – In this work, two data sets are used as the experimental data to calculate the goodness-of-fit of 18 commonly used distribution models of THW to select the best distribution model. Subsequently, the characteristic parameters of traffic flow are extracted from the data set, and three variables with higher importance are extracted using the random forest model. Combining the best distribution model parameters of the data set, this study obtained a distribution model with adaptive parameters, and its performance and applicability are verified. Originality/value – The results show that the proposed model has a 62.7% performance improvement over the distribution model with fixed parameters. Moreover, the parameter function of the distribution model can be regarded as a quantitative analysis of the degree of influence of the traffic flow state on THW.

In this article, we propose new semiparametric and bootstrap tests based on the ratio of two variances under a density ratio model and compare them with existing tests for testing the equality of two variances from two independent populations. We showed that the ratio of two independent variances follows an asymptotic log-normal distribution. Also presented in this article are large sample asymptotic results of the semiparametric estimator of the ratio of the two sample variances. We also present a theoretical comparison of our semiparametric test on the ratio of two variances with the existing non parametric test using Pitman's relative efficiency. Numerical comparisons of the performance of various tests are performed via simulation studies. We also use two numerical examples to illustrate the implementation of new tests. [ABSTRACT FROM AUTHOR]

Pearson's chi-squared test is widely used to test the goodness of fit between categorical data and a given discrete distribution function. When the number of sets of the categorical data, say k, is a fixed integer, Pearson's chi-squared test statistic converges in distribution to a chi-squared distribution with k−1 degrees of freedom when the sample size n goes to infinity. In real applications, the number k often changes with n and may be even much larger than n. By using the martingale techniques, we prove that Pearson's chi-squared test statistic converges to the normal under quite general conditions. We also propose a new test statistic which is more powerful than chi-squared test statistic based on our simulation study. A real application to lottery data is provided to illustrate our methodology. [ABSTRACT FROM AUTHOR]

In this paper, a New Generalized Gamma-Weibull (NGGW) distribution is developed by compounding Weibull and generalized gamma distribution. Some mathematical properties such as moments, R°enyi entropy and order statistics are derived and discussed. The maximum likelihood estimation (MLE) method is used to estimate the model parameters. The proposed model is applied to two real-life datasets to illustrate its performance and flexibility as compared to some other competing distributions. The results obtained show that the new distribution fits each of the data better than the other competing distributions. [ABSTRACT FROM AUTHOR]

We provide a new extension of the exponential distribution with an emphasis on the practical elements of the model. Six different classical estimation methods were applied and compared. The main test was evaluated on complete data using four sets of data. Additionally, four applications and the derivation of the new Nikulin statistic test for the new probability model under the censored situation are described. Both tests were evaluated through simulation experiments on complete data and on artificial and censored data. In addition, a set of simulation experiments were presented, which were used and employed to evaluate the original statistical test and the new modified statistical test based on statistical controls in the evaluation processes. [ABSTRACT FROM AUTHOR]

Imperfect repair (IR) modelling has attracted a lot of attention during the last decades. To assess and predict repairable systems' reliability, analysts have to choose among a plethora of models: renewal processes, non‐homogeneous Poisson processes (NHPPs), Brown–Proschan, Kijima, ARA, ARI, Quasi‐Renewal (QR), Trend‐Renewal and so forth. Choosing an appropriate model for a given failures, dataset is an important practical issue. The fit of an IR model can be assessed using goodness‐of‐fit (GoF) tests but very few have been proposed and a good fit to past data does not guarantee good reliability predictions. This work proposes general GoF tests for IR models based on sequential (or on‐line) assessment of times‐to‐failures forecasts. The suggested predictive‐sequential (or prequential) GoF tests have a low computational complexity and a common test statistic for several IR models. These tests have been proved to be asymptotically distribution‐free (ADF) for renewal and power‐law processes (PLPs). Our numerical simulations and preliminary theoretical results highly suggest that this ADF property still holds for several other IR models. The prequential tests are much easier to use than the already known bootstrap tests, and a simulation study shows that they are also slightly more powerful. The simulations also show that the prequential tests are powerful to identify classes of similar appropriate models but are much less powerful to distinguish models belonging to the same class. A comparison of MTTF estimates show that models from the same class give close reliability predictions and that the tests are able to reject models which would yield to dramatic errors in reliability predictions. [ABSTRACT FROM AUTHOR]

We propose a class of goodness-of-fit test procedures for arbitrary parametric families of circular distributions with unknown parameters. The tests make use of the specific form of the characteristic function of the family being tested, and are shown to be consistent. We derive the asymptotic null distribution and suggest that the new method be implemented using a bootstrap resampling technique that approximates this distribution consistently. As an illustration, we then specialize this method to testing whether a given data set is from the von Mises distribution, a model that is commonly used and for which considerable theory has been developed. An extensive Monte Carlo study is carried out to compare the new tests with other existing omnibus tests for this model. An application involving five real data sets is provided in order to illustrate the new procedure.

Background: Data with ordinal categories occur in many diverse areas, but methodologies for modeling ordinal data lag severely behind equivalent methodologies for continuous data. There are advantages to using a model specifically developed for ordinal data, such as making fewer assumptions and having greater power for inference. Methods: The ordered stereotype model (OSM) is an ordinal regression model that is more flexible than the popular proportional odds ordinal model. The primary benefit of the OSM is that it uses numeric encoding of the ordinal response categories without assuming the categories are equally-spaced. Results: This article summarizes two recent advances in the OSM: (1) three novel tests to assess goodness-of-fit; (2) a new Generalized Estimating Equations approach to estimate the model for longitudinal studies. These methods use the new spacing of the ordinal categories indicated by the estimated score parameters of the OSM. Conclusions: The recent advances presented can be applied to several fields. We illustrate their use with the well-known arthritis clinical trial dataset. These advances fill a gap in methodologies available for ordinal responses and may be useful for practitioners in many applied fields.

Parametric techniques commonly rely on specific distributional assumptions. It is therefore fundamental to preliminarily identify the eventual violations of such assumptions. Therefore, appropriate testing procedures are required for this purpose to deal with a the goodness-of-fit (GoF) problem. This task can be quite challenging, especially with small sample sizes and multivariate data. Previous studiesshowed how a GoF problem can be easily represented through a traditional two-sample system of hypotheses. Following this idea, in this paper, we propose a multi-aspect permutation-based test to deal with the multivariate goodness-of-fit, taking advantage of the nonparametric combination (NPC) methodology. A simulation study is then conducted to evaluate the performance of our proposal and to identify the eventual critical scenarios. Finally, a real data application is considered.

A new and simple blockwise empirical likelihood moment-based procedure to test if a stationary autoregressive process is Gaussian has been proposed. The proposed test utilizes the skewness and kurtosis moment constraints to develop the test statistic. The test nonparametrically accommodates the dependence in the time series data whilst exhibiting some useful properties of empirical likelihood, such as the Wilks theorem with the test statistic having a chi-square limiting distribution. A Monte Carlo simulation study shows that our proposed test has good control of type I error. The finite sample performance of the proposed test is evaluated and compared to some selected competitor tests for different sample sizes and a variety of alternative applied distributions by means of a Monte Carlo study. The results reveal that our proposed test is on average superior under the log-normal and chi-square alternatives for small to large sample sizes. Some real data studies further revealed the applicability and robustness of our proposed test in practice. [ABSTRACT FROM AUTHOR]

The generalized linear model is an important method in the statistical toolkit. The isotonic single index model can be thought of as a further generalization whereby the link function is assumed to be monotone non-decreasing as opposed to known and fixed. Such a shape constraint is quite natural in many statistical problems, and is fulfilled by the usual generalized linear models. In this paper we consider inference in this model in the setting where repeated measurements of predictor values and associated responses are observed. This setting is encountered in medical studies and is very different from the one considered in the classical monotone single index model studied in the literature. Here, we use nonparametric maximum likelihood estimation to infer the unknown regression vector and link function. We present a detailed study of finite and asymptotic properties of this estimator and propose goodness-of-fit tests for the model. Through an extended simulation study, we show that the model has competitive predictive performance. We illustrate our estimation approach using a Leukemia data set. [ABSTRACT FROM AUTHOR]

In this paper, we propose a flexible and general family of distributions based on an original power-exponential transformation approach. We call it the modified generalized-G (MGG) family. The elegance and significance of this family lie in the ability to modify the standard distributions by changing their functional forms without adding new parameters, by compounding two distributions, or by adding one or two shape parameters. The aim of this modification is to provide flexible shapes for the corresponding probability functions. In particular, the distributions of the MGG family can possess increasing, constant, decreasing, "unimodal", or "bathtub-shaped" hazard rate functions, which are ideal for fitting several real data sets encountered in applied fields. Some members of the MGG family are proposed for special distributions. Following that, the uniform distribution is chosen as a baseline distribution to yield the modified uniform (MU) distribution with the goal of efficiently modeling measures with bounded values. Some useful key properties of the MU distribution are determined. The estimation of the unknown parameters of the MU model is discussed using seven methods, and then, a simulation study is carried out to explore the performance of the estimates. The flexibility of this model is illustrated by the analysis of two real-life data sets. When compared to fair and well-known competitor models in contemporary literature, better-fitting results are obtained for the new model. [ABSTRACT FROM AUTHOR]

This paper studies the goodness of fit test for the bivariate Hermite distribution. Specifically, we propose and study a Cramér–von Mises-type test based on the empirical probability generation function. The bootstrap can be used to consistently estimate the null distribution of the test statistics. A simulation study investigates the goodness of the bootstrap approach for finite sample sizes. [ABSTRACT FROM AUTHOR]

A lot of studies on the summary measures of predictive strength of categorical response models consider the likelihood ratio index (LRI), also known as the McFadden-R 2, a better option than many other measures. We propose a simple modification of the LRI that adjusts for the effect of the number of response categories on the measure and that also rescales its values, mimicking an underlying latent measure. The modified measure is applicable to both binary and ordinal response models fitted by maximum likelihood. Results from simulation studies and a real data example on the olfactory perception of boar taint show that the proposed measure outperforms most of the widely used goodness-of-fit measures for binary and ordinal models. The proposed R 2 interestingly proves quite invariant to an increasing number of response categories of an ordinal model. [ABSTRACT FROM AUTHOR]

Biologists routinely fit novel and complex statistical models to push the limits of our understanding. Examples include, but are not limited to, flexible Bayesian approaches (e.g. BUGS, stan), frequentist and likelihood‐based approaches (e.g. packages lme4) and machine learning methods.These software and programs afford the user greater control and flexibility in tailoring complex hierarchical models. However, this level of control and flexibility places a higher degree of responsibility on the user to evaluate the robustness of their statistical inference. To determine how often biologists are running model diagnostics on hierarchical models, we reviewed 50 recently published papers in 2021 in the journal Nature Ecology & Evolution, and we found that the majority of published papers did not report any validation of their hierarchical models, making it difficult for the reader to assess the robustness of their inference. This lack of reporting likely stems from a lack of standardized guidance for best practices and standard methods.Here, we provide a guide to understanding and validating complex models using data simulations. To determine how often biologists use data simulation techniques, we also reviewed 50 recently published papers in 2021 in the journal Methods Ecology & Evolution. We found that 78% of the papers that proposed a new estimation technique, package or model used simulations or generated data in some capacity (18 of 23 papers); but very few of those papers (5 of 23 papers) included either a demonstration that the code could recover realistic estimates for a dataset with known parameters or a demonstration of the statistical properties of the approach. To distil the variety of simulations techniques and their uses, we provide a taxonomy of simulation studies based on the intended inference. We also encourage authors to include a basic validation study whenever novel statistical models are used, which in general, is easy to implement.Simulating data helps a researcher gain a deeper understanding of the models and their assumptions and establish the reliability of their estimation approaches. Wider adoption of data simulations by biologists can improve statistical inference, reliability and open science practices. [ABSTRACT FROM AUTHOR]

In this paper, we revisit the classical goodness-of-fit problems for univariate distributions; we propose a new testing procedure based on a characterization of the uniform distribution. Asymptotic theory for the simple hypothesis case is provided in a Hilbert-Space setting, including the asymptotic null distribution as well as values for the first four cumulants of this distribution, which are used to fit a Pearson system of distributions as an approximation to the limit distribution. Numerical results indicate that the null distribution of the test converges quickly to its asymptotic distribution, making the critical values obtained using the Pearson system particularly useful. Consistency of the test is shown against any fixed alternative distribution and we derive the limiting behaviour under fixed alternatives with an application to power approximation. We demonstrate the applicability of the newly proposed test when testing composite hypotheses. A Monte Carlo power study compares the finite sample power performance of the newly proposed test to existing omnibus tests in both the simple and composite hypothesis settings. This power study includes results related to testing for the uniform, normal, Pareto and gamma distributions. The empirical results obtained indicate that the test is competitive. An application of the newly proposed test in financial modelling is also included. [ABSTRACT FROM AUTHOR]

In this article, we present a review of important results and statistical applications obtained or generalized by Canadian pioneers and their collaborators, for empirical processes of independent and identically distributed observations, pseudo‐observations, and time series. In particular, we consider weak convergence and strong approximations results, as well as tests for model adequacy such as tests of independence, tests of goodness‐of‐fit, tests of change point, and tests of serial dependence for time series. We also consider applications of empirical processes of interacting particle systems for the approximation of measure‐valued processes. [ABSTRACT FROM AUTHOR]

Fracture trace length distributions are often assumed to follow a power law, which implies that the distribution is scale-independent. The present study tests this assumption by evaluating the goodness-of-fit of three statistical models—the power law, piecewise power law, and lognormal distribution—upon a dataset of 57 trace maps that cover a range of fracture modes, host rock types, network scales, and topologies. The goodness-of-fit was assessed through the unbiased Kolmogorov-Smirnov (KS) test, which accounts for the fitting procedure and the degrees of freedom of each model. The results show that the power law provides a poor fit to trace length distributions, being rejected in 24 trace maps at a significance level of 0.05. In contrast, the piecewise power law and lognormal distribution demonstrated better fits across the fracture networks, with the piecewise power law performing the best overall. The poor fit of the power law can be attributed to mechanical and chemical controls on fracture growth, mainly fracture abutment, as well as stress shadowing and cementation, which affect growth rate at different length scales and result in scale-dependent trace length distributions. The consistent poor fit of the power law across various fracture networks suggests that these controls are prevalent in natural systems. While the power law remains a simple and effective model for trace length distribution, it should be recognized that it overlooks such controls that can influence the mechanical and hydraulic properties of fracture networks. Meanwhile, the fit of the piecewise power-law suggests the existence of a characteristic length where a transition in fracture growth occurs. • The power law, piecewise power law, and lognormal distribution were tested for modeling fracture trace length distributions. • The piecewise power law provided the best fit overall, while the power law was rejected in 42% of cases. • Scale-dependent length distributions are attributed to mechanical and chemical factors controlling fracture growth. [ABSTRACT FROM AUTHOR]

A 2-dimensional (2D) egg-shape equation can be used to construct a 3D egg geometry based on the hypothesis that an egg is a solid of revolution, which helps to calculate egg volume and surface area. The parameters in the 2D egg-shape equation are potentially valuable for providing a clue to the ecology and evolution of avian eggs. In this study, the 5-parameter Preston equation (PE), the 4-parameter Troscianko equation (TE), and another 2 egg-shape equations, were compared in describing real 2D egg-shape data of 300 Gallus gallus domesticus eggs and additional 50 eggs that represented the variation in avian egg geometries. Adjusted root-mean-square error was used to quantify each equation's prediction error. Given that the 4 equations are nonlinear, relative curvature measures of nonlinearity were used to assess the extent of nonlinearity in each equation. PE was found to be the best among the 4 equations in terms of adjusted root-mean-square error and minimizing nonlinearity. The empirically determined egg volumes using a graduated cylinder were compared with the predicted egg volumes using the formula for a solid of revolution based on 2D predictions from the 4 egg-shape equations. There were negligible differences in the predicted egg volumes and surface areas among the 4 equations, indicating that these equations are all valid in calculating egg volume and surface area. In addition, we proposed a 5-parameter TE and found that it outperformed the above 4 equations in describing the 2D egg shape of G. gallus , but was less general than PE for other egg shapes. This work provides statistical evidence to show which equation is the best for describing the geometry of avian eggs and nondestructively calculating their volume and surface area, helping to classify poultry eggs into different grades according to the morphological characteristics of the eggs. [ABSTRACT FROM AUTHOR]

Neutral detergent fiber (NDF) and acid detergent fiber (ADF) composition have been shown to predict in vitro true digestibility (IVTD), in vitro NDF digestibility (IVNDFD), and in vitro ADF digestibility (IVADFD) in ruminants. This study’s objective was to estimate in vitro digestibility measures within the DaisyII incubator using equine fecal inoculum from feedstuff NDF and ADF composition. Analyzed feedstuffs included alfalfa hay (Medicago sativa), Coastal Bermudagrass hay, soybean meal, rice bran, hempseed meal, and Bluebonnet® Equilene® Pellets. Data were analyzed using Akaike’s information criterion (AIC) within the R Statistical Program©. The highest ranked model for IVTD was the interaction of NDF and ADF: 10003.32 – 0.2904 × NDF − 0.4220 × ADF − 0.0010 × NDF × ADF (Adjusted R2 = 0.959 and AICc = 474.97). Sample IVNDFD was moderately predicted by ADF: 855.15 – 1.5183 × ADF (Adjusted R2 = 0.749 and AICc = 560.82). Feedstuff ADF produced the highest ranked model for IVNDFD: 881.91 – 1.5952 × ADF (Adj. R2 = 0.835 and AICc = 541.33). These results indicate the effectiveness of using feedstuff NDF and ADF composition to predict IVTD, IVNDFD, and IVADFD within equine fecal inoculum. The findings of this study provide better understanding of feedstuff digestibility using equine fecal inoculum, but more research is warranted for validation of the models and the potential impact in vivo.

Solid-state drives represent the preferred backbone storage solution thanks to their low latency and high throughput capabilities compared to mechanical hard disk drives. The performance of a drive is intertwined with the reliability of the memories; hence, modeling their reliability is an important task to be performed as a support for storage system designers. In the literature, storage developers devise dedicated parametric statistical approaches to model the evolution of the memory’s error distribution through well-known statistical frameworks. Some of these well-founded reliability models have a deep connection with the 3D NAND flash technology. In fact, the more precise and accurate the model, the less the probability of incurring storage performance slowdowns. In this work, to avoid some limitations of the parametric methods, a non-parametric approach to test the model goodness-of-fit based on combined permutation tests is carried out. The results show that the electrical characterization of different memory blocks and pages tested provides an FBC feature that can be well-modeled using a multiple regression analysis.

Unnormalized statistical models play an important role in machine learning, statistics, and signal processing. In this paper, we derive a new hypothesis testing procedure for unnormalized models. Our approach is motivated by the success of score matching techniques that avoid the intensive computational costs of normalization constants in many high-dimensional settings. Our proposed test statistic is the difference between Hyvärinen scores corresponding to the null and alternative hypotheses. Under some reasonable conditions, we prove that the asymptotic distribution of this statistic is Chi-squared. We outline a bootstrap approach to learn the test critical values, particularly when the distribution under the null hypothesis cannot be expressed in a closed form, and provide consistency guarantees. Finally, we conduct extensive numerical experiments and demonstrate that our proposed approach outperforms goodness-of-fit benchmarks in various settings.

In this paper, we investigate the goodness-of-fit of the flexible four-parameter generalized Lambda Distribution (GLD) for high-frequency 5-min returns sampled from the DJI30 Index. Applying Moment Matching (MM) and Maximum Likelihood Estimation (MLE) techniques, we highlight the significance of the higher-order parameters of the GLD distribution to depict the asymmetric and fat-tailed behaviour observed in high-frequency returns data. We also show and explain why the MLE consistently outperforms the MM; especially in the presence of “outliers”. Finally, we use lambda-space scatterplots to introduce, clarify and discuss additional stylized facts of high-frequency index returns not found in the extant high-frequency literature.

We propose a spatiotemporal point process model that enhances the classical Epidemic‐Type Aftershock Sequence (ETAS) model. This is achieved with the introduction of a renewal main‐shock arrival process and we call this extension the renewal ETAS (RETAS) model. This modification is similar in spirit to the renewal Hawkes (RHawkes) process but the conditional intensity process supports a spatial component. It empowers the main‐shock intensity to reset upon the arrival of main‐shocks. This allows for heavier clustering of main‐shocks than the classical spatiotemporal ETAS model. We introduce a likelihood evaluation algorithm for parameter estimation and provide a novel procedure to evaluate the fitted model's goodness‐of‐fit (GOF) based on a sequential application of the Rosenblatt transformation. A simulation algorithm for the RETAS model is outlined and used to validate the numerical performance of the likelihood evaluation algorithm and GOF test procedure. We illustrate the proposed model and methods on various earthquake catalogues around the world each with distinctly different seismic activity. These catalogues demonstrate the RETAS model's additional flexibility in comparison to the classical spatiotemporal ETAS model and emphasizes the potential for superior modelling and forecasting of seismicity. [ABSTRACT FROM AUTHOR]

Multivariate behavioral research often focuses on latent constructs--such as motivation, self-concept, or wellbeing--that cannot be directly observed. Typically, these latent constructs are measured with items in standardized instruments. To test the factorial structure and multidimensionality of latent constructs in educational and psychological research, Morin et al. (2016a) proposed bifactor exploratory structural equation modeling (B-ESEM). This meta-analytic review (158 studies, k = 308, N = 778,624) aimed to estimate the extent to which B-ESEM model fit differs from other model representations, including confirmatory factor analysis (CFA), exploratory structural equation modeling (ESEM), hierarchical CFA, hierarchical ESEM, and bifactor-CFA. The study domains included learning and instruction, motivation and emotion, self and identity, depression and wellbeing, and interpersonal relations. The meta-analyzed fit indices were the X2/df ratio, the comparative fit index (CFI), the Tucker-Lewis index (TLI), the root mean square error of approximation (RMSEA), and the standardized root mean squared residual (SRMR). The findings of this meta-analytic review indicate that the B-ESEM model fit is superior to the fit of reference models. Furthermore, the results suggest that model fit is sensitive to sample size, item number, and the number of specific and general factors in a model. [ABSTRACT FROM AUTHOR]

Ocean is a huge basin of bacteria, storing about thousands of species of microbial organisms. Ocean ecosystems need microbes to prosper their resources. Ocean pollution harms the marine ecosystems by infesting the water not suitable for marine life; altering the chemical constituents of water; and distressing the size and species of the organisms as well as the aquatic animals. This paper explores the optimal range of the water quality parameters for a perpetual marine lifecycle. Study of the microorganisms such as fecal coliforms, enterococci and total coliforms has steered towards understanding the marine water quality. This paper investigated the open dataset of city of San Diego available under ocean monitoring program to examine the quality determinants of marine water in the presence of microbes such as enterococci, fecal coliform and total coliform and to estimate and predict the relationship between them using regression models. The assessment of the prediction models confirmed that the factors such as the high variability in data, seasonal and climatic variations have affected the predictions. [ABSTRACT FROM AUTHOR]

The financial market is a complex system with chaotic behavior that can lead to wild swings within the financial system. This can drive the system into a variety of interesting phenomenon such as phase transitions, bubbles, and crashes, and so on. Of interest in financial modelling is identifying the distribution and the stylized facts of a particular time series, as the distribution and stylized facts can determine if volatility is present, resulting in financial risk and contagion. Regression modelling has been used within this study as a methodology to identify the goodness-of-fit between the original and generated time series model, which serves as a criterion for model selection. Different time series modelling methods that include the common Box–Jenkins ARIMA, ARMA-GARCH type methods, the Geometric Brownian Motion type models and Tsallis entropy based models when data size permits, can use this methodology in model selection. Determining the time series distribution and stylized facts has utility, as the distribution allows for further modelling opportunities such as bivariate regression and copula modelling, apart from the usual forecasting. Determining the distribution and stylized facts also allows for the identification of the parameters that are used within a Geometric Brownian Motion forecasting model. This study has used the Carbon Emissions Futures price between the dates of 1 May 2012 and 1 May 2022, to highlight this application of regression modelling. [ABSTRACT FROM AUTHOR]

Traffic demand prediction is one of the major elements of traffic planning and modelling. Traffic surveys routinely estimate the profile of traffic demand on a certain road section, showing the expected evolution of the demand over a day or week. However, the actual demand fluctuates around this value on day-to-day basis and thus can exceed otherwise sufficient capacity and consequently cause congestion due to the capacity drop. This type of traffic demand variability has not yet been properly studied although it can play significant role in traffic modelling and engineering. The relevance of this variability is further increasing with the growing popularity of stochastic traffic models. This paper presents results of a statistical analysis of the demand variability in five-minute aggregation intervals. Normal, lognormal and gamma distributions all show reasonably well fit to the data for individual intervals and often do not differ on statistically significant level. Based on the count of the best fits, the lognormal distribution seems to be most suitable, while the gamma distribution is the most universal and with generally acceptable fit. There appears to be a pattern where certain distributions have better fit in different times of the day and week. The regularity and magnitude of demand probably both play a role in this, as well as the aggregation interval. Two simple models for modelling the variability are proposed for practical applications when there is not enough data to perform similar analysis. [ABSTRACT FROM AUTHOR]

The multivariate skew-normal family of distributions is a flexible class of probability models that includes the multivariate normal distribution as a special case. Two procedures for testing that a multivariate random sample comes from the multivariate skew-normal distribution are proposed here based on the estimated canonical form. Canonical data are transformed into approximately multivariate normal observations and then a multivariate version of the Shapiro-Wilk test is used for testing multivariate normality. Critical values for the tests are approximated without using parametric bootstrap. Monte Carlo simulation results provide evidence that the nominal test level is preserved, in general, under the considered settings. The simulation results also indicate that these tests are in general more powerful than existing tests for the same problem versus the studied alternatives. [ABSTRACT FROM AUTHOR]

By applying a sinusoidal function (as a trigonometric model), this study aimed to introduce this function into ostrich weight development research, using ostrich growth data from the literature and comparing it with some routinely used growth models such as monomolecular, Bridges, Janoschek, logistic, Von Bertalanffy, Richards, Schumacher, Morgan, Chanter, and Weibull. During the fitting of nonlinear regression curves, model performance was evaluated and model behavior was examined. Body weight data of the domestic ostriches used in this study were reported in the Blue Mountain Ostrich Nutrition e-bulletin from three different studies (data sets 1 to 3). In all data sets, body weight was measured monthly from one to twelve months of age. The adjusted coefficient of determination, root mean square error, Akaike's information criterion, and Bayesian information criterion were used to evaluate each model's overall goodness-of-fit to different data profiles. Based on the goodness-of-fit criteria, the sinusoidal model was determined to be the most suitable function for fitting the growth curve of ostriches in data sets 1 and 2. However, both monomolecular and logistic models had the worst fit to the growth curve of ostriches in these data sets. For data set 3, the Weibull model provided the best fit of the growth curve of ostriches, but the sinusoidal function had the worst fit. Absolute growth rate (AGR), calculated using the first derivative of the best model with time showed that AGR values ​​increased with age until days 174, 90, and 68 for data sets 1 to 3, respectively, and then decreased. Overall, this study offers implications for advancing research on ostrich production systems and providing insightful information on the application of alternative nonlinear models in modeling ostrich growth., Competing Interests: Declaration of competing interest The author confirms that there are no known conflicts of interest associated with this manuscript which have influenced its outcome., (Copyright © 2024. Published by Elsevier Inc.)

Multivariate behavioral research often focuses on latent constructs—such as motivation, self-concept, or wellbeing—that cannot be directly observed. Typically, these latent constructs are measured with items in standardized instruments. To test the factorial structure and multidimensionality of latent constructs in educational and psychological research, Morin et al. (2016a) proposed bifactor exploratory structural equation modeling (B-ESEM). This meta-analytic review (158 studies, k = 308, N = 778,624) aimed to estimate the extent to which B-ESEM model fit differs from other model representations, including confirmatory factor analysis (CFA), exploratory structural equation modeling (ESEM), hierarchical CFA, hierarchical ESEM, and bifactor-CFA. The study domains included learning and instruction, motivation and emotion, self and identity, depression and wellbeing, and interpersonal relations. The meta-analyzed fit indices were the χ2/df ratio, the comparative fit index (CFI), the Tucker-Lewis index (TLI), the root mean square error of approximation (RMSEA), and the standardized root mean squared residual (SRMR). The findings of this meta-analytic review indicate that the B-ESEM model fit is superior to the fit of reference models. Furthermore, the results suggest that model fit is sensitive to sample size, item number, and the number of specific and general factors in a model.