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Biomarkers are measured repeatedly in clinical studies until a pre-defined endpoint, such as death from certain causes, is reached. Such repeated measurements may present a dynamic process for understanding when to expect the study’s endpoint. Joint modelling is often employed to handle such a model. Typically, shared random effects are assumed to be common to both the longitudinal component and the study’s endpoint. These shared random effects usually assume homogeneous and follow a normal distribution. However, identifying homogeneous subgroups is important when the underlying population is heterogeneous. This issue has received little attention in the literature, particularly for multi-phase longitudinal responses. In this paper, we propose a joint modelling approach for longitudinal and survival models using a bent-cable mixed model for longitudinal measurements and a Weibull distribution for the survival component. We also incorporate a finite mixture of normal distribution assumptions to account for the unobserved heterogeneity in the shared random effects model. A Bayesian MCMC is developed for parameter estimation and inferences. The proposed method is evaluated using simulation studies and the Tehran Lipid and Glucose Study dataset. [ABSTRACT FROM AUTHOR]

Wind energy production has been a relevant topic of research for several years. Specifically, the estimation of wind energy potential has received important attention in different regions of the world. One of the main considerations for these estimations is based on the modeling of wind speed data based on probability density functions (PDF), given that once the best distribution for wind speed data is determined, the wind energy potential can be estimated. The objective of this paper is to investigate the wind speed and wind energy potential in Ciudad Juárez, México. To achieve this, three meteorological stations were installed in strategic open sites at a height of 10 meters within and on the edges of the city. Speed data were recorded for each meteorological station every ten minutes over a one-year period. The wind speed data were studied to define the best-fitting distribution, and different commercial wind turbines were considered to estimate the power curves for each location. With the characterized power curves, it was possible to estimate the potential energy production. In addition, wind shear was considered to estimate the energy production with wind turbines that have greater heights. The results show the importance of selecting the best distribution to estimate the wind energy potential of certain regions where measurements can be obtained from different locations. [ABSTRACT FROM AUTHOR]

Abstract.In the realm of mixed models, this article explores the estimation method for incorporating a mixture of distributions and addressing controlled heteroscedasticity. By relaxing the assumptions of normality and homoscedasticity, we introduce a more flexible approach to analyzing data. The article presents estimation techniques for variance components, estimable vectors, and cumulants, while also developing prediction intervals and prediction ellipsoids for future observations. A numerical example is employed to illustrate the method and compare it with traditional ANOVA and Bayesian estimation methods. The results demonstrate the superior flexibility and broader applicability of the proposed methods in diverse contexts. By extending the analysis beyond conventional assumptions, these approaches enhance the accuracy and robustness of statistical inference in mixed models. [ABSTRACT FROM AUTHOR]

AbstractRecently, considerable interest has been in deriving explicit expressions for moment of different truncated multivariate distributions. This is due to their usefulness in developing efficient EM-algorithm for the maximum likelihood estimation of the corresponding distributional parameters. One rich family of distributions is the multivariate normal mean-mixture distribution as it includes a number of important multivariate distributions as special cases. In this article, we derive exact expressions for the first two moments of doubly truncated multivariate normal mean-mixture distributions, from which results for various special cases are then deduced. [ABSTRACT FROM AUTHOR]

Abstract–Mixture models are widely employed in the analysis of heterogeneous data. However, existing approaches are based on the assumption that the observations in each component are normally distributed. The main objective of this article is to propose mixture models with Yeo-Johnson transformation to handle general heterogeneous data. Bayesian methods are developed for estimation and model comparison. The empirical performance of the proposed methodology is assessed through simulation studies. A real analysis of a data set derived from the National Longitudinal Survey of Youth 1997 is presented for illustration. [ABSTRACT FROM AUTHOR]

We introduce a mixture of mixtures of bounded asymmetric generalized Gaussian and uniform distributions. Based on this framework, we propose model-based classification and model-based clustering algorithms. We develop an objective function for the minimum message length (MML) model selection criterion to discover the optimal number of clusters for the unsupervised approach of our proposed model. Given the crucial attention received by Explainable AI (XAI) in recent years, we introduce a method to interpret the predictions obtained from the proposed model in both learning settings by defining their boundaries in terms of the crucial features. Integrating Explainability within our proposed algorithm increases the credibility of the algorithm's predictions since it would be explainable to the user's perspective through simple If-Then statements using a small binary decision tree. In this paper, the proposed algorithm proves its reliability and superiority to several state-of-the-art machine learning algorithms within the following real-world applications: fault detection and diagnosis (FDD) in chillers, occupancy estimation and categorization of residential energy consumers. [ABSTRACT FROM AUTHOR]

Most empirical studies of complex networks return rich but noisy data, as they measure the network structure repeatedly but with substantial errors due to indirect measurements. In this article, we propose a novel framework, called the group-based binary mixture (GBM) modeling approach, to simultaneously conduct network reconstruction and community detection from such rich but noisy data. A generalized expectation-maximization (EM) algorithm is developed for computing the maximum likelihood estimates, and an information criterion is introduced to consistently select the number of communities. The strong consistency properties of the network reconstruction and community detection are established under some assumption on the Kullback-Leibler (KL) divergence, and in particular, we do not impose assumptions on the true network structure. It is shown that joint reconstruction with community detection has a synergistic effect, whereby actually detecting communities can improve the accuracy of the reconstruction. Finally, we illustrate the performance of the approach with numerical simulations and two real examples. for this article are available online. [ABSTRACT FROM AUTHOR]

Abstract Feature selection is a difficult but highly important preliminary step for bearings remaining useful life (RUL) estimation. To avoid the weights setting problem in hybrid metric, this work devotes to conduct feature selection by using a single metric. Due to noise and outliers, an existing feature selection metric, called monotonicity, used for estimating bearings RUL, requires data smoothing processing before adequate implementation. Such a smoothing process may remove significant part of meaningful information from data. To overcome this issue, a mixture distribution analysis-based feature selection metric is proposed. Moreover, based on this new metric, a feature selection approach for bearings RUL estimation is proposed. Numerical experiments benchmarking the proposed method and the existing metric monotonicity method on available real datasets highlight its effectiveness.

The receiver operating characteristics (ROC) analysis is commonly used in clinical settings to check the performance of a single threshold for distinguishing population-wise bimodal-distributed test results. However, for population-wise three-modal distributed test results, a single threshold ROC (stROC) analysis showed poor discriminative performance. The purpose of this study is to use a double-threshold ROC analysis for the three-modal distributed test results to provide better discriminative performance than the stROC analysis. A double-threshold receiver operating characteristic plot (dtROC) is constructed by replacing the single threshold with a double threshold. The sensitivity and specificity coordinates are chosen to maximize sensitivity for a given specificity value. Besides a simulation study assuming a mixture of lognormal, Poisson, and Weibull distributions, a clinical application is examined by a secondary data analysis of palpation test results of the C7 spinous process using the modified thorax–rib static technique. For the assumed mixture models, the discrimination performance of dtROC analysis outperforms the stROC analysis (area under ROC (AUROC) increased from 0.436 to 0.983 for lognormal distributed test results, 0.676 to 0.752 for the Poisson distribution, and 0.674 to 0.804 for Weibull distribution). [ABSTRACT FROM AUTHOR]

This paper introduces a novel approach that utilizes the weighted harmonic mean in combination with multiple univariate cumulative distribution functions to create a fresh univariate cumulative distribution. In addition to an innovative expression, it exhibits direct ordering properties involving traditional mixtures of univariate cumulative distribution functions. After establishing the theoretical foundation, we leverage these findings to develop new families of trigonometric distributions. We highlight a special case that extends the exponentiated distribution's scope and demonstrates its superior performance in data fitting compared to fair competitors like the exponential, gamma, exponentiated exponential, and sine exponential distributions. In summary, our methodology offers a versatile framework for modeling and understanding a wide array of statistical phenomena. [ABSTRACT FROM AUTHOR]

Feature selection is a difficult but highly important preliminary step for bearings remaining useful life (RUL) estimation. To avoid the weights setting problem in hybrid metric, this work devotes to conduct feature selection by using a single metric. Due to noise and outliers, an existing feature selection metric, called monotonicity, used for estimating bearings RUL, requires data smoothing processing before adequate implementation. Such a smoothing process may remove significant part of meaningful information from data. To overcome this issue, a mixture distribution analysis-based feature selection metric is proposed. Moreover, based on this new metric, a feature selection approach for bearings RUL estimation is proposed. Numerical experiments benchmarking the proposed method and the existing metric monotonicity method on available real datasets highlight its effectiveness.Article Highlights: A feature selection method for bearings remaining useful life estimation Retrieval the underlying trend of vibration signal Address the drawbacks of smoothing methods that remove meaningful information from data [ABSTRACT FROM AUTHOR]

How much genome differences between species reflect neutral or adaptive evolution is a central question in evolutionary genomics. In humans and other mammals, the presence of adaptive versus neutral genomic evolution has proven particularly difficult to quantify. The difficulty notably stems from the highly heterogeneous organization of mammalian genomes at multiple levels (functional sequence density, recombination, etc.) which complicates the interpretation and distinction of adaptive versus neutral evolution signals. In this study, we introduce mixture density regressions (MDRs) for the study of the determinants of recent adaptation in the human genome. MDRs provide a flexible regression model based on multiple Gaussian distributions. We use MDRs to model the association between recent selection signals and multiple genomic factors likely to affect the occurrence/detection of positive selection, if the latter was present in the first place to generate these associations. We find that an MDR model with two Gaussian distributions provides an excellent fit to the genome-wide distribution of a common sweep summary statistic (integrated haplotype score), with one of the two distributions likely enriched in positive selection. We further find several factors associated with signals of recent adaptation, including the recombination rate, the density of regulatory elements in immune cells, GC content, gene expression in immune cells, the density of mammal-wide conserved elements, and the distance to the nearest virus-interacting gene. These results support the presence of strong positive selection in recent human evolution and highlight MDRs as a powerful tool to make sense of signals of recent genomic adaptation. [ABSTRACT FROM AUTHOR]

Abstract Background The problem of dealing with misreported data is very common in a wide range of contexts for different reasons. The current situation caused by the Covid-19 worldwide pandemic is a clear example, where the data provided by official sources were not always reliable due to data collection issues and to the high proportion of asymptomatic cases. In this work, a flexible framework is proposed, with the objective of quantifying the severity of misreporting in a time series and reconstructing the most likely evolution of the process. Methods The performance of Bayesian Synthetic Likelihood to estimate the parameters of a model based on AutoRegressive Conditional Heteroskedastic time series capable of dealing with misreported information and to reconstruct the most likely evolution of the phenomenon is assessed through a comprehensive simulation study and illustrated by reconstructing the weekly Covid-19 incidence in each Spanish Autonomous Community. Results Only around 51% of the Covid-19 cases in the period 2020/02/23–2022/02/27 were reported in Spain, showing relevant differences in the severity of underreporting across the regions. Conclusions The proposed methodology provides public health decision-makers with a valuable tool in order to improve the assessment of a disease evolution under different scenarios.

We estimate the distribution of COVID-19 mortality (measured as daily deaths) from the start of the pandemic until July 31st, 2022, for six European countries and the USA. We use the Pareto, the stretched exponential, the log-normal and the log-logistic distributions as well as mixtures of the log-normal and log-logistic distributions. The main results are that the Pareto does not describe well the data and that mixture distributions tend to offer a very good fit to the data. We also compute Value-at-Risk measures as well as mortality probabilities with our estimates. We also discuss the implications of our results and findings from the point of view of public health planning and modelling.

In this paper, we present a two-component Weibull mixture model. An important property is that this new model accommodates bimodality, which can appear in data representing phenomena in some heterogeneous populations. We provide statistical properties, such as the quantile function and moments. Additionally, the expectation-maximization (EM) algorithm is used to find maximum-likelihood estimates of the model parameters. Further, a Monte Carlo study is carried out to evaluate the performance of the estimators on finite samples. The new model's relevance is shown with an application referring to the vote proportion for the Brazilian presidential elections runoff in 2018. The proportion of votes is an important measure in analyzing electoral data. Since it is a variable limited to the unitary interval, unit distributions should be considered to analyze its probabilistic behavior. Thus, the introduced model is suitable for describing the characteristics detected in these data, such as the asymmetric behavior, bimodality, and the unit interval as support. In the application, the superiority of the proposed model is verified when comparing the fit with the two-component beta mixture models. [ABSTRACT FROM AUTHOR]

There currently exist a variety of statistical methods for modeling bivariate extremes. However, when the dependence between variables is driven by more than one latent process, these methods are likely to fail to give reliable inferences. We consider situations in which the observed dependence at extreme levels is a mixture of a possibly unknown number of much simpler bivariate distributions. For such structures, we demonstrate the limitations of existing methods and propose two new methods: an extension of the Heffernan–Tawn conditional extreme value model to allow for mixtures and an extremal quantile-regression approach. The two methods are examined in a simulation study and then applied to oceanographic data. Finally, we discuss extensions including a subasymptotic version of the proposed model, which has the potential to give more efficient results by incorporating data that are less extreme. Both new methods outperform existing approaches when mixtures are present. [ABSTRACT FROM AUTHOR]

In this paper, a new generalization of one parameter Lindely distribution is proposed. The new distribution is a mixture distribution of Gamma distributions with fixed scale parameter and variable shape parameter. The distribution is called 'GOLD Distribution' as it is a generalization for several distributions such as exponential, Lindely, Sujatha, Amarendra, Devya and Shambhu distributions. The probability density and cumulative density functions are derived. Also, the statistical properties of the GOLD distribution are discussed. Parameter estimation using the maximum likelihood and the method of moments are given. Moreover, an illustration of the usefulness of the GOLD distribution in survival data analysis is discussed based on a real lifetime data. [ABSTRACT FROM AUTHOR]

Background: The problem of dealing with misreported data is very common in a wide range of contexts for different reasons. The current situation caused by the Covid-19 worldwide pandemic is a clear example, where the data provided by official sources were not always reliable due to data collection issues and to the high proportion of asymptomatic cases. In this work, a flexible framework is proposed, with the objective of quantifying the severity of misreporting in a time series and reconstructing the most likely evolution of the process. Methods: The performance of Bayesian Synthetic Likelihood to estimate the parameters of a model based on AutoRegressive Conditional Heteroskedastic time series capable of dealing with misreported information and to reconstruct the most likely evolution of the phenomenon is assessed through a comprehensive simulation study and illustrated by reconstructing the weekly Covid-19 incidence in each Spanish Autonomous Community. Results: Only around 51% of the Covid-19 cases in the period 2020/02/23–2022/02/27 were reported in Spain, showing relevant differences in the severity of underreporting across the regions. Conclusions: The proposed methodology provides public health decision-makers with a valuable tool in order to improve the assessment of a disease evolution under different scenarios. [ABSTRACT FROM AUTHOR]

The Shanker distribution, a one-parameter lifetime distribution with an increasing hazard rate function, is recommended by Shanker for modelling lifespan data. In this study, we examine the theoretical and practical implications of 2-component mixture of Shanker model (2-CMSM). A significant feature of proposed model's hazard rate function is that it has rising, decreasing, and upside-down bathtub forms. We investigate the statistical characteristics of a mixed model, such as the probability-generating function, the factorial-moment-generating function, cumulants, the characteristic function, the Mills ratio, the mean residual life, and the mean time to failure. There is a graphic representation of density, mean, hazard rate functions, coefficient of variation, skewness, and kurtosis. Our final approach is to estimate the parameters of the mixture model using appropriate approaches such as maximum likelihood, least squares, and weighted least squares. Using a simulation analysis, we examined how the estimates behaved graphically. The simulation results demonstrated that, in the majority of cases, the maximum likelihood estimates have the smallest mean square errors among all other estimates. Finally, we observed that when the sample size rises, the precision measures decrease for all of the estimation techniques, indicating that all of the estimation approaches are consistent. Through two real data analyses, the suggested model's validity and adaptability are contrasted with those of other models, including the mixture of the exponential distributions and the Lindley distributions. [ABSTRACT FROM AUTHOR]

The fundamental assumption of flood frequency analysis is that flood samples are generated by the same flood generation mechanism (FGM). However, flood events are usually triggered by the interaction of meteorological factors and watershed properties, which results in different FMGs. To solve this problem, researchers have put forward traditional two-component mixture distributions (TCMD-T) without clearly linking each component distribution to an explicit FGM. In order to improve the physical meaning of mixture distributions in seasonal snow-covered areas, the ratio of rainfall to flood volume (referred to as rainfall–flood ratio, RF) method was used to classify distinct FGMs. Thus, the weighting coefficient of each component distribution was determined in advance in the rainfall–flood ratio based TCMD (TCMD-RF). TCMD-RF model was applied to 34 basins in Norway. The results showed that flood types can be clearly divided into rain-on-snow-induced flood, snowmelt-induced flood and rainfall-induced flood. Moreover, the design flood and associated uncertainties were also estimated. It is found that TCMD-RF model can reduce the uncertainties of design flood by 20% compared with TCMD-T. The superiority of TCMD-RF is attributed to its clear classification of FGMs, thus determining the weighting coefficients without optimization and simplifying the parameter estimation procedure of mixture distributions. [ABSTRACT FROM AUTHOR]

The multiple stream process involves equipment with several modules producing the same items, but with respective random variables' subpopulations. This particularity demands specific control charts for the statistical processes monitoring. Among the initiatives proposed are the finite mixture control chart and T2-Hotelling control chart, but there are no comparative studies between them. This article aims to study and compare the proposed use of a finite mixture control chart with the T2-Hotelling control chart for monitoring the multiple stream process (MSP). The modeling and simulation were performed using actual data from the dietary sector to develop an illustrative case. The results show that the T2-Hotelling charts' performance was superior in detecting special causes and generating false alarms about the process and supplementary to having less mathematical difficulty in implementing. However, the finite mixture chart is a more recently used approach, considering the literature's occurrence, compared with the T2-Hotelling chart. Furthermore, the finite mixture chart considering all streams and the variability between them in just one control chart is more straightforward in terms of sampling, but more difficult in mathematical terms for its application. In conclusion, the finite mixture and T2-Hotelling charts are suitable for solving MSP, monitoring with no losing information on each stream variability, and not masking effects from special causes in the process. [ABSTRACT FROM AUTHOR]

We estimate the distribution of COVID-19 mortality (measured as daily deaths) from the start of the pandemic until July 31st, 2022, for six European countries and the USA. We use the Pareto, the stretched exponential, the log-normal and the log-logistic distributions as well as mixtures of the log-normal and log-logistic distributions. The main results are that the Pareto does not describe well the data and that mixture distributions tend to offer a very good fit to the data. We also compute Value-at-Risk measures as well as mortality probabilities with our estimates. We also discuss the implications of our results and findings from the point of view of public health planning and modelling. [ABSTRACT FROM AUTHOR]

We study some properties of the failure rate for a mixture of Erlang distributions. In particular, we discuss mixtures of Erlang distributions with the same scale parameter and we describe the behavior of the failure rate. Some remarks are also given for an infinite mixture of Erlangs, in particular with regard to stochastic order properties. [ABSTRACT FROM AUTHOR]

This paper studies the prediction problem of future order statistics based on a mixture of exponential distributions. We suggest different scenarios to construct predictive intervals and point predictions for the future observations in two cases. In the first case, we assume fixed sample size, while in the second case, the sample size is assumed to be positive integer–valued random variable independent of the observations. [ABSTRACT FROM AUTHOR]

In this paper, by using a new method, we derive the trapezoidal beta (TB) distribution and its properties. The TB distribution is a mixture model, generalizes both the beta and rectangular beta distributions, and allows one to describe bounded data with heavy right and/or left tails. In relation to the two-parameter beta distribution, we add two additional parameters which have an intuitive interpretation. The four TB parameters are estimated with the expectation-maximization algorithm. We conduct a simulation study to evaluate performance of the TB distribution. An application with real data is carried out, which includes a comparison among the beta, rectangular beta and TB distributions indicating that the TB one describes these data better.

In this paper, we present a two-component Weibull mixture model. An important property is that this new model accommodates bimodality, which can appear in data representing phenomena in some heterogeneous populations. We provide statistical properties, such as the quantile function and moments. Additionally, the expectation-maximization (EM) algorithm is used to find maximum-likelihood estimates of the model parameters. Further, a Monte Carlo study is carried out to evaluate the performance of the estimators on finite samples. The new model’s relevance is shown with an application referring to the vote proportion for the Brazilian presidential elections runoff in 2018. The proportion of votes is an important measure in analyzing electoral data. Since it is a variable limited to the unitary interval, unit distributions should be considered to analyze its probabilistic behavior. Thus, the introduced model is suitable for describing the characteristics detected in these data, such as the asymmetric behavior, bimodality, and the unit interval as support. In the application, the superiority of the proposed model is verified when comparing the fit with the two-component beta mixture models.

Motivated by the need for transportation infrastructure and incident management planning, we study traffic density under non-recurrent congestion. This paper provides an analytical solution approximating the stationary distribution of traffic density in roadways where deterioration of service occurs unpredictably. The proposed solution generalizes a queuing model discussed in the literature to long segments that are not space-homogeneous. We compare single and tandem queuing approaches to segments of different lengths and verify whether each model is appropriate. A single-queue approach works sufficiently well in segments with similar traffic behavior across space. In contrast, a tandem-queue approach more appropriately describes the density behavior for long segments with sections having distinct traffic characteristics. These models have a comparable fit to the ones generated using a lognormal distribution. However, they also have interpretable parameters, directly connecting the distribution of congestion to the dynamics of roadway behavior. The proposed models are general, adaptable, and tractable, thus being instrumental in infrastructure and incident management.

This work investigates aspects of the global sensitivity analysis of computer codes when alternative plausible distributions for the model inputs are available to the analyst. Analysts may decide to explore results under each distribution or to aggregate the distributions, assigning, for instance, a mixture. In the first case, we lose uniqueness of the sensitivity measures, and in the second case, we lose independence even if the model inputs are independent under each of the assigned distributions. Removing the unique distribution assumption impacts the mathematical properties at the basis of variance‐based sensitivity analysis and has consequences on result interpretation as well. We analyze in detail the technical aspects. From this investigation, we derive corresponding recommendations for the risk analyst. We show that an approach based on the generalized functional ANOVA expansion remains theoretically grounded in the presence of a mixture distribution. Numerically, we base the construction of the generalized function ANOVA effects on the diffeomorphic modulation under observable response preserving homotopy regression. Our application addresses the calculation of variance‐based sensitivity measures for the well‐known Nordhaus' DICE model, when its inputs are assigned a mixture distribution. A discussion of implications for the risk analyst and future research perspectives closes the work. [ABSTRACT FROM AUTHOR]

Eliciting information regarding available energy in the wind resource is intricately linked to the viability of a wind power project. The energy output of wind power plant is affected primarily by the wind speed characteristics. Probability distributions have proved to be useful for stochastic modeling of the wind resource and power potential estimation. This work fits ten most popular wind speed marginal distributions and four mixture distributions to 80 m mast measured 10-min averaged wind speed data in Odisha, India. The yearly mean wind speed is found to be 5.95 m/s with a coefficient of variation of 52% whereas the highest monthly mean wind speed of 9.14 m/s occurs in May. It is found that only generalized extreme value distribution could fit the yearly wind speed whereas a number of marginal and mixture distributions are found suitable for modeling monthly and seasonal wind speeds. The best fitted Weibull shape and scale parameters are 2.00 and 6.72 m/s, respectively. The annual wind power density (WPD) of 247 W/m2 with a very high summer WPD of 414 W/m2 confirms the feasibility of commercial wind power development. [ABSTRACT FROM AUTHOR]

The Korean Long-Term Care Insurance (K-LTCI) provides financial support for long-term care service to people who need various types of assistance with daily activities. As the number of elderly people in Korea is expected to increase in the future, the demand for long-term care insurance would also increase over time. Projection of future expenditure on K-LTCI depends on the number of beneficiaries within the grading system of K-LTCI based on the test scores of applicants. This study investigated the suitability of mixture distributions to the model K-LTCI score distribution using recent empirical data on K-LTCI, provided by the National Health Insurance Service (NHIS). Based on the developed mixture models, the number of beneficiaries in each grade and its variability under the current grading system were estimated by simulation. It was observed that a mixture model is suitable for K-LTCI score distribution and may prove useful in devising a funding plan for K-LTCI benefit payment and investigating the e ects of any possible revision in the K-LTCI grading system. [ABSTRACT FROM AUTHOR]

Grouped data are frequently used in several fields of study. In this work, we use the expectation-maximization (EM) algorithm for fitting the skew-normal (SN) mixture model to the grouped data. Implementing the EM algorithm requires computing the one-dimensional integrals for each group or class. Our simulation study and real data analyses reveal that the EM algorithm not only always converges but also can be implemented in just a few seconds even when the number of components is large, contrary to the Bayesian paradigm that is computationally expensive. The accuracy of the EM algorithm and superiority of the SN mixture model over the traditional normal mixture model in modelling grouped data are demonstrated through the simulation and three real data illustrations. For implementing the EM algorithm, we use the package called ForestFit developed for R environment available at . [ABSTRACT FROM AUTHOR]

This article aims to make use of moment-generating functions (mgfs) to derive the density of mixture distributions from hierarchical models. When the mgf of a mixture distribution doesn't exist, one can extend the approach to characteristic functions to derive the mixture density. This article uses a result given by E.R. Villa, L.A. Escobar, Am. Stat. 60 (2006), 75–80. The present work complements E.R. Villa, L.A. Escobar, Am. Stat. 60 (2006), 75–80 article with many new examples.

Abstract Matrix population models are a standard tool for studying stage‐structured populations, but they are not flexible in describing stage duration distributions. This study describes a method for modeling various such distributions in matrix models. The method uses a mixture of two negative binomial distributions (parametrized using a maximum likelihood method) to approximate a target (true) distribution. To examine the performance of the method, populations consisting of two life stages (juvenile and adult) were considered. The juvenile duration distribution followed a gamma distribution, lognormal distribution, or zero‐truncated (over‐dispersed) Poisson distribution, each of which represents a target distribution to be approximated by a mixture distribution. The true population growth rate based on a target distribution was obtained using an individual‐based model, and the extent to which matrix models can approximate the target dynamics was examined. The results show that the method generally works well for the examined target distributions, but is prone to biased predictions under some conditions. In addition, the method works uniformly better than an existing method whose performance was also examined for comparison. Other details regarding parameter estimation and model development are also discussed.

The stable symmetric family of distribution functions (cdf's) is a family that contains the reverse of every cdf that belongs to it. It is revealed that this family is capable of describing many types of statistical data. We show that the mixture of any baseline distribution and its reverse, after multiplying and dividing, respectively to them the same scale parameter, is stable. This method is applied to yield a new three-parameter extension of the normal cdf, which contains all the possible types of cdf's and possesses very wide range of the indices of skewness and kurtosis. Moreover, an application of this method yields a new two-parameter extension of the log-normal cdf. The support of this new cdf is the real line and it may be symmetric. To motivate the use of the new suggested families of distributions, we present three different successful examples of real data. [ABSTRACT FROM AUTHOR]

In this paper, we suggest a new efficient method, that yields two new point predictors, for predicting future order statistics, when the sample size remains fixed and when it is enlarged. The two suggested point predictors are constructed based on some characterization properties of order statistics via their distributions. A comprehensive simulation study is conducted on several distributions, among them is a mixture distribution, to evaluate the performance of the suggested predictors. Two examples of lifetime real data are analyzed in which several methods of the point predictions are compared. [ABSTRACT FROM AUTHOR]

The Kumaraswamy distribution has been a very studied tool in the analysis and modeling of limited-range continuous random variables. Several variants of this distribution have been studied, but they do not have the possibility of lifting the tails of this distribution. However, in many situations, scenarios where the data are bounded and tail-area events occur at one or both tails independently. In order to model these scenarios, we propose the trapezoidal Kumaraswamy distribution. This paper is centered on the trapezoidal Kumaraswamy distribution, which has two intuitive additional parameters with respect to the Kumaraswamy distribution and generalizes this. We study its probability density function and derive some fundamental properties, such as the moments, moment generating function, and characteristic function. Then, the trapezoidal Kumaraswamy distribution is rewritten conveniently as a finite mixture showing that its parameters can be easily estimated using the expectation-maximization algorithm. We report results of a simulation and an application to a real data set. Comparison with several competing distributions indicates that the trapezoidal Kumaraswamy distribution presents a better fit and so it can be quite useful in empirical applications. [ABSTRACT FROM AUTHOR]

Process capability indices are widely used to check quality standards both at the production level and for business activity. They consider the location and the deviation from specification limits and targets. The literature contains many contributions on this topic both in the univariate and the multivariate context. Motivated by a real semiconductor case study, we discuss the role of rational subgroups and the challenge they present in the computation of capability indices, especially when data refer to lots of products. In addition, our context involves a mix of problems: unilateral specification limit, nonsymmetric distribution of the data, evidence of data from a mixture of distributions, and the need to filter one component of the mixture. After solving the previous issues and because of the peculiar characteristics of semiconductor processes based on the so called "wafers," we contribute to the literature a proposal on how to compute capability indices in the case of heteroscedastic spatial processes. With a generalized additive model, we show that it is possible to estimate a capability surface that allows the identification of regions expected to not be fully compliant with the desired quality standards. [ABSTRACT FROM AUTHOR]

In this paper, we derive a new continuous-discrete mixture regression model which is useful for describing highly censored data. This mixture model employs the Birnbaum-Saunders distribution for the continuous response variable of interest, whereas the Bernoulli distribution is used for the point mass of the censoring observations. We estimate the corresponding parameters with the maximum likelihood method. Numerical evaluation of the model is performed by means of Monte Carlo simulations and of an illustration with real data. The results show the good performance of the proposed model, making it an addition to the tool-kit of biometricians, medical doctors, applied statisticians, and data scientists. [ABSTRACT FROM AUTHOR]

Lower‐crustal seismicity is commonly observed in continental rift zones despite the crust at such depths being ductile enough to prohibit brittle failure. The source of such deep seismicity across the East African Rift remains an outstanding question. Here we present analysis of an isolated cluster of lower‐crustal earthquakes located on the eastern border faults of the Main Ethiopian Rift, near the Corbetti caldera. Lower‐crustal earthquakes have not previously been observed in this area. Phase arrival times were determined using an automated picking approach based on continuous wavelet transform and statistical changepoint detection methods. We overcome misinterpretations from large hypocenter depth errors by considering mixture distributions for all events and their associated uncertainties. These mixture distributions represent probability density functions of any event occurring at a given depth. The mixture distribution mode for a variety of different velocity models and error parameters remained stable at a depth of 28–32 km, with the vast majority of maximum likelihood estimates for individual hypocenters located at depths of 25–35 km. Most events occur over a 2 month period, with 90% of cumulative seismic moment occurring during March and April 2012. The ephemeral and localized nature of this seismicity, combined with low event magnitudes and regional hydrothermal/magmatic activity, suggests that these lower‐crustal events are likely related to fluid or magmatic processes. Plausible mechanisms include the movement of magma and/or exsolution of volatiles at depth causing transient high strain rates and pore fluid pressures that induce seismicity. Key Points: A sequence of lower‐crustal seismicity is identified 30 km east of Corbetti caldera on the eastern border faults of the Main Ethiopian RiftMixture distributions are used to overcome misinterpretations from large uncertainty in individual event locationsSpatial and temporal characteristics indicate that the source of this seismicity relates to fluid or magmatic processes [ABSTRACT FROM AUTHOR]

In recent years, modifications of the classical Lindley distribution have been considered by many authors. In this paper, we introduce a new generalization of the Lindley distribution based on a mixture of exponential and gamma distributions with different mixing proportions and compare its performance with its sub-models. The new distribution accommodates the classical Lindley, Quasi Lindley, Two-parameter Lindley, Shanker, Lindley distribution with location parameter, and Three-parameter Lindley distributions as special cases. Various structural properties of the new distribution are discussed and the size-biased and the lengthbiased are derived. A simulation study is conducted to examine the mean square error for the parameters by means of the method of maximum likelihood. Finally, simulation studies and some real-world data sets are used to illustrate its flexibility in terms of its location, scale and shape parameters. [ABSTRACT FROM AUTHOR]

Comparing populations on one or more variables is often of interest. These comparisons are typically made using the mean; however, it is well known that mean comparisons can lead to misinterpretation because of Simpson's paradox. Simpson's paradox occurs when there is a differential distribution of subpopulations across the populations being compared and the means of those subpopulations are different. This article develops the relative performance index (RPI) to ameliorate effects of Simpson's paradox. Data from the National Assessment of Educational Progress (NAEP) are used to illustrate use of the new index. The utility of RPI is compared to the population mean and a prior index, the balanced index. This article shows how RPI can be generalized to a variety of contexts with implications for decision making. [ABSTRACT FROM AUTHOR]

A conceptual study of iterative coupling (IC) is performed, providing a unified description and new research directions. IC chain growth rates and functional group choice are analyzed, guiding construction of efficient schemes. The concept of cycle efficiency is defined as a more complete metric of experimental implementations of IC, and then applied to the main linear and exponential IC processes. The mathematical relations between individual reactions, cycles, and the iterative process as a whole are studied. Finally, macromolecule IC is proposed as a strikingly complementary process to standard IC, with potential to reduce the dispersity of non‐uniform samples. Due to its connection with the central limit theorem of statistics, it provides an unusually robust, powerful, and general method for scalable production of polymer samples with narrow distribution. In all, this contribution assists development of improved IC processes targeting low dispersity linear oligomers and polymers. [ABSTRACT FROM AUTHOR]

Knowing whether a household behaves according to separability or non-separability is needed for the correct modeling of production decisions. We propose a superior test to those found in the literature on separability by using a mixture distribution approach to estimate the probability that a farm household behaves according to non-separability, and test that the determinants of consumption affect production decisions for households categorized as non-separable. With non-separability attributed to labor market constraints, the switcher equation shows that Peruvian farm households that are indigenous and young, with low levels of education, and lack of local employment opportunities are more likely to be constrained on the labor market.

Proteins are found in all living organisms and constitute a large group of macromolecules with many functions. Proteins achieve their operations by adopting distinct three-dimensional structures encoded within the sequence of the constituent amino acids in one or more polypeptides. New, more flexible distributions are proposed for the MCMC sampling method for predicting protein 3D structures by applying a Möbius transformation to the bivariate von Mises distribution. In addition to this, sine-skewed versions of the proposed models are introduced to meet the increasing demand for modelling asymmetric toroidal data. Interestingly, the marginals of the new models lead to new multimodal circular distributions. We analysed three big datasets consisting of bivariate information about protein domains to illustrate the efficiency and behaviour of the proposed models. These newly proposed models outperformed mixtures of well-known models for modelling toroidal data. A simulation study was carried out to find the best method for generating samples from the proposed models. Our results shed new light on proposal distributions in the MCMC sampling method for predicting the protein structure environment.