Search

The Burr XII and Nakagami distributions hold significant importance in both lifetime distribution and wealth distribution analyses. The Burr XII distribution serves as a valuable tool for understanding the distribution of wealth and wages within specific societies, while the Nakagami distribution finds its application in the realm of communication engineering. The incorporation of finite mixture distributions, aimed at accounting for unobserved variations, has gained substantial traction, particularly in the estimation of dynamic discrete choice models. This research delves into the fundamental characteristics of the mixture Burr XII and Nakagami distributions. The study introduces parameter estimation techniques and explores various aspects, including the cumulative distribution function, hazard rate, failure rate, inverse hazard function, odd function, cumulative hazard function, r th moment, moment generating function, characteristic function, moments, mean and variance, Renyi and Beta entropies, mean deviation from mean, and mean time between failures (MTBF). The paper also addresses the estimation of the mixing parameter through a Bayesian approach. To illustrate the effectiveness of the proposed model, two real-life datasets are examined. [ABSTRACT FROM AUTHOR]

In this paper we introduce the Exponential-Pareto mixture distribution. This distribution is associated as mixture of light and heavy-tailed data which arise in a wide class applications including risk analysis. Characteristic function, failure rate function, mean excess, conditional excess distribution are derived. It is proved that the limiting distribution of maxima among n values of rv’s with Exponential-Pareto distribution has Frechet-type form. The maximal likelihood estimation of parameters is discussed. The upper bound of uniform distance between Exponential-Pareto mixture and Pareto distributions is derived. [ABSTRACT FROM AUTHOR]

The xgamma distribution is vital in reliability/survival analysis and biomedical research. In this article, different estimation methods are proposed for the parameter of this distribution. The distribution is a unique finite mixture of exponential distribution and gamma distribution. Some further properties of the distribution that are not available in the earlier literature are studied. We consider the maximum likelihood estimator, least squares estimator, weighted least squares estimator, percentile estimator, the maximum product spacing estimator, the minimum spacing absolute distance estimator, the minimum spacing absolute log-distance estimator, Crame´r von Mises estimator, Anderson Darling estimator, right-tailed Anderson Darling estimator, and compare them using a comprehensive simulation study. For comparison purposes, the estimators’ bias and mean squared error are considered. A real data example is also a part of this work. Some model selection techniques are used to choose the best fitting of the distribution to the data. [ABSTRACT FROM AUTHOR]

In a number of real-world situations, one encounters count data with over-dispersion such that the typical Poisson distribution does not suit the data. In the current situation, it is appropriate to employ a combination of mixed Poisson and Poisson-Sujatha (PS) distributions. The PS distribution has been investigated for count data, which is of primary interest to a number of disciplines, including biology, medicine, demography, and agriculture. However, no research has been conducted regarding generating bootstrap confidence intervals for its parameter. The coverage probabilities and average lengths of bootstrap confidence intervals derived from the percentile, basic, and biasedcorrected and accelerated bootstrap methods were compared using Monte Carlo simulation. The results indicated that it was impossible to achieve the nominal confidence level using bootstrap confidence intervals for tiny sample sizes, regardless of the other settings. Furthermore, when the sample size was large, there was not much of a difference in the performance of the several bootstrap confidence intervals. The biascorrected and accelerated bootstrap confidence interval demonstrated superior performance compared to the other methods in all of the cases examined. Moreover, the effectiveness of the bootstrap confidence intervals was proven through their application to agricultural data sets. The calculations offer significant evidence in favor of the suggested bootstrap confidence intervals. [ABSTRACT FROM AUTHOR]

The bivariate and multivariate probability distributions are useful in joint modeling of several random variables. The development of bivariate and multivariate distributions is relatively tedious as compared with the development of univariate distributions. In this paper we have proposed a new method of developing bivariate and multivariate families of distributions from the univariate marginals. The properties of the proposed families of distributions have been studies. These properties include marginal and conditional distributions; product, ratio and conditional moments; joint reliability function and dependence measures. Statistical inference about the proposed families of distributions has also been done. The proposed bivariate family of distributions has been studied for Weibull baseline distribution giving rise to a new bivariate Weibull distribution. The properties of the proposed bivariate Weibull distribution have been studied alongside maximum likelihood estimation of the unknown parameters. The proposed bivariate Weibull distribution has been used for modeling of real bivariate data sets and we have found that the proposed bivariate Weibull distribution has been a suitable choice for the modeling of data used. [ABSTRACT FROM AUTHOR]

A new two-parameter negative binomial mixture distribution named as negative binomial-Akash distribution is introduced in this paper. The proposed distribution is attained by compounding the negative binomial distribution with the Akash distribution. Some of its special characteristics are also derived, including factorial moments, mean, variance, index of dispersion etc. Furthermore, the behaviour of mean, variance and index of dispersion are discussed. The parameters of the proposed distribution are estimated using the maximum likelihood estimation method. This distribution can be used for modeling overdispersed count data. The usefulness and application of the proposed distribution are illustrated using two actual count data sets. [ABSTRACT FROM AUTHOR]

Branden Fitelson and Alan Hájek have suggested that it is finally time for a "revolution" in which we jettison Kolmogorov's axiomatization of probability, and move to an alternative like Popper's. According to these authors, not only did Kolmogorov fail to give an adequate analysis of conditional probability, he also failed to give an adequate account of another central notion in probability theory: probabilistic independence. This paper defends Kolmogorov, with a focus on this independence charge. I show that Kolmogorov's sophisticated theory of conditional distributions, advocated by authors such as Kenny Easwaran but often overlooked by philosophers, has the resources to define the notion of independence Fitelson and Hájek seek. I then argue that Kolmogorov's original definition of independence, once suitably reinterpreted as capturing a slight logical weakening of this notion, is not so problematic after all. Indeed, rather than discarding Kolmogorov's definition, we should make room for two distinct notions of probabilistic independence, one stronger and one weaker, which play different theoretical roles. [ABSTRACT FROM AUTHOR]

In spite of widespread use as well as theoretical properties of the multivariate scale mixture of normal distributions, practical studies show a lack of stability and robustness against asymmetric features such as asymmetry and heavy tails. In this paper, we develop a new multivariate model by assuming the Birnbaum-Saunders distribution for the mixing variable in the scale mixture of the restricted skew-normal distribution. An analytically simple and efficient EM-type algorithm is adopted for iteratively computing maximum likelihood estimate of model parameters. To account standard errors, the observed information matrix is derived analytically by offering an information-based approach. Results obtained from real and simulated datasets are reported to illustrate the practical utility of the proposed methodology. [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]

In an unprecedented experimental investigation, a ternary and a four component hydrocarbon mixture at high pressure have been studied in a nearly convection free environment to understand the thermodiffusion process. A binary mixture has also been investigated in this environment. Experimental investigations of the three mixtures have been conducted in space onboard the spacecraft FOTON-M3 thereby isolating the gravity-induced convection that otherwise interferes with thermodiffusion experiments on Earth. The experimental results have also been used to test a thermodiffusion model that has been calibrated based on the results of previous experimental investigations. It was found that with an increase in the number of components in the mixtures, the performance of the thermodiffusion model deteriorated. Computational analysis was also made to estimate the possible sources of errors. Simulations showed that the vibrations of the spacecraft could influence the estimates of thermodiffusion factors. It was also found that they are sensitive to slight variations in the temperature of the mixture. [ABSTRACT FROM AUTHOR]

In this work we compare lattice and continuum versions of the same theory, as derived in the previous paper (Paper I), to predict the behavior of simple alkane mixtures. In the course of doing this we use characteristic parameters obtained for the pure alkane fluids; no fits of mixture properties are involved. Our two sets of predictions are tested against experimental data and against new Monte Carlo simulation results. The experimental properties of interest include mixed pressure-volume-temperature surfaces, as well as a variety of coexistence diagrams characterizing mixed system liquid-vapor equilibria. We contrast the performance of the lattice and continuum approaches and discuss the results in the context of underlying model approximations as derived in Paper I. [ABSTRACT FROM AUTHOR]

We study the demixing transition of mixtures of equal size hard spheres and dipolar hard spheres using computer simulation and integral equation theories. Calculations are carried out at constant pressure, and it is found that there is a strong correlation between the total density and the composition. The critical temperature and the critical total density are found to increase with pressure. The critical mole fraction of the dipolar component on the contrary decreases as pressure is augmented. These qualitative trends are reproduced by the theoretical approaches that on the other hand overestimate by far the value of the critical temperature. Interestingly, the critical parameters for the liquid-vapor equilibrium extrapolated from the mixture results in the limit of vanishing neutral hard sphere concentration agree rather well with recent estimates based on the extrapolation of charged hard dumbbell phase equilibria when dumbbell elongation shrinks to zero [G. Ganzenmüller and P. J. Camp, J. Chem. Phys. 126, 191104 (2007)]. [ABSTRACT FROM AUTHOR]

Particle dynamics simulations reveal parallels between granular mixtures and chemical solutions. Thermodynamic solution theory provides a connection between the interaction strength of the molecules, the concentration of each species in the solution, and bulk solution behavior. Particle dynamics simulations demonstrate a similar relationship between the interparticle forces, the composition of the granular mixture, and bulk flow behavior. The analogy holds true over different particle interaction types (friction or adhesion) and over different bulk properties (the angle of repose in a rotating drum and the viscosity of particles sheared between parallel plates). A solution theory for granular mixtures would provide a framework to study the properties of granular mixtures. [ABSTRACT FROM AUTHOR]

The aim of this work is to investigate to what extent the structural properties of a short-range square-well (SW) fluid of range λ at a given packing fraction η and reduced temperature T*=kBT/ε can be represented by those of a sticky-hard-sphere (SHS) fluid at the same packing fraction and an effective stickiness parameter τ(T*,λ). Such an equivalence cannot hold for the radial distribution function g(r) since this function has a delta singularity at contact (r=σ) in the SHS case, while it has a jump discontinuity at r=λσ in the SW case. Therefore, the equivalence is explored with the cavity function y(r), i.e., we assume that ySW(r|η,T*;λ)≈ySHS(r|η,τ(T*,λ)). Optimization of the agreement between ySW and ySHS to first order in density suggests the choice τ(T*,λ)=[12(e1/T*-1)(λ-1)]-1. We have performed Monte Carlo (MC) simulations of the SW fluid for λ=1.05, 1.02, and 1.01 at several densities and temperatures T* such that τ(T*,λ)=0.13, 0.2, and 0.5. The resulting cavity functions have been compared with MC data of SHS fluids obtained by Miller and Frenkel[J. Phys.: Condens. Matter 16, S4901 (2004)]. Although, at given values of η and τ, some local discrepancies between ySW and ySHS exist (especially for λ=1.05), the SW data converge smoothly toward the SHS values as λ-1 decreases. In fact, precursors of the singularities of ySHS at certain distances due to geometrical arrangements are clearly observed in ySW. The approximate mapping ySW→ySHS is exploited to estimate the internal energy and structure factor of the SW fluid from those of the SHS fluid. Taking for ySHS the solution of the Percus-Yevick equation as well as the rational-function approximation, the radial distribution function g(r) of the SW fluid is theoretically estimated and a good agreement with our MC simulations is found. Finally, a similar study is carried out for short-range SW fluid mixtures. [ABSTRACT FROM AUTHOR]

A mean–variance heterogeneous tails mixture distribution is proposed for modeling financial asset returns. It captures, along with the obligatory leptokurtosis, different tail behavior among the assets. Its construction allows for joint maximum likelihood estimation of all model parameters via an expectation–maximization algorithm and thus is applicable in high dimensions. A useful and unique feature of the model is that the tail behavior of the individual assets is driven by asset-specific news effects. In the bivariate iid case, the model corresponds to the standard CAPM model, but enriched with a filter for capturing the news impact associated with both the market and asset excess returns. An empirical application using a portfolio of highly tail-heterogeneous cryptocurrencies and realistic transaction costs shows superior out-of-sample portfolio performance compared to numerous competing models. A model extension to capture asset-specific asymmetry is also discussed. [ABSTRACT FROM AUTHOR]

Plotting is among the most effective ways to quickly and accurately describe a probability distribution. It makes often complex information accessible, enabling intuition for respective outcomes at a glance. Matters complicate, however, for mixed-type distributions. Mixed-type distributions contain both continuous and discrete components, and accurately portraying those on a single axis can prove difficult—misleading intuition as a consequence of pulling two otherwise disjoint components into focus together. This article examines the challenges of maintaining the simple, concise, and accurate format of traditional probability distribution plots for mixed-type distributions. We illustrate issues arising within this plot classification paradigm, and why a secondary axis is uniquely suited to improve its communication. An algorithm is devised to consistently scale such plots so that they better coincide with intuition. National Football League football starting field position, meteorological data, and financial instruments provide examples demonstrating effectiveness of this plot technique. [ABSTRACT FROM AUTHOR]

Highlights • A Bayesian method to estimate parameters of a cylindrical mixture distribution. • Application of cylindrical distributions to a new dataset with time-of-day as circular variable. • Estimation uncertainty is directly inferred in the proposed method without extra calculations. Abstract This paper proposes a Metropolis–Hastings algorithm based on Markov chain Monte Carlo sampling, to estimate the parameters of the Abe–Ley distribution, which is a recently proposed Weibull-Sine-Skewed-von Mises mixture model, for bivariate circular-linear data. Current literature estimates the parameters of these mixture models using the expectation-maximization method, but we will show that this exhibits a few shortcomings for the considered mixture model. First, standard expectation-maximization does not guarantee convergence to a global optimum, because the likelihood is multi-modal, which results from the high dimensionality of the mixture's likelihood. Second, given that expectation-maximization provides point estimates of the parameters only, the uncertainties of the estimates (e.g., confidence intervals) are not directly available in these methods. Hence, extra calculations are needed to quantify such uncertainty. We propose a Metropolis–Hastings based algorithm that avoids both shortcomings of expectation-maximization. Indeed, Metropolis–Hastings provides an approximation to the complete (posterior) distribution, given that it samples from the joint posterior of the mixture parameters. This facilitates direct inference (e.g., about uncertainty, multi-modality) from the estimation. In developing the algorithm, we tackle various challenges including convergence speed, label switching and selecting the optimum number of mixture components. We then (i) verify the effectiveness of the proposed algorithm on sample datasets with known true parameters, and further (ii) validate our methodology on an environmental dataset (a traditional application domain of Abe–Ley mixtures where measurements are function of direction). Finally, we (iii) demonstrate the usefulness of our approach in an application domain where the circular measurement is periodic in time. [ABSTRACT FROM AUTHOR]

This paper presents the Bayes Fisher information measures, defined by the expected Fisher information under a distribution for the parameter, for the arithmetic, geometric, and generalized mixtures of two probability density functions. The Fisher information of the arithmetic mixture about the mixing parameter is related to chi-square divergence, Shannon entropy, and the Jensen–Shannon divergence. The Bayes Fisher measures of the three mixture models are related to the Kullback–Leibler, Jeffreys, Jensen–Shannon, Rényi, and Tsallis divergences. These measures indicate that the farther away are the components from each other, the more informative are data about the mixing parameter. We also unify three different relative entropy derivations of the geometric mixture scattered in statistics and physics literatures. Extensions of two of the formulations to the minimization of Tsallis divergence give the generalized mixture as the solution. [ABSTRACT FROM AUTHOR]

Highlights • Bhattacharyya distance is proposed as a novel UQ metric in stochastic model updating. • The proposed likelihood is a capable connection between UQ metrics and updating tool. • Both Bhattacharyya and Euclidian distances are utilized in the updating framework. • Bhattacharyya distance is more comprehensive than Euclidian distance as a UQ metric. • Calculation is significantly reduced thanks to the approximate Bayesian computation. Abstract The Bhattacharyya distance is a stochastic measurement between two samples and taking into account their probability distributions. The objective of this work is to further generalize the application of the Bhattacharyya distance as a novel uncertainty quantification metric by developing an approximate Bayesian computation model updating framework, in which the Bhattacharyya distance is fully embedded. The Bhattacharyya distance between sample sets is evaluated via a binning algorithm. And then the approximate likelihood function built upon the concept of the distance is developed in a two-step Bayesian updating framework, where the Euclidian and Bhattacharyya distances are utilized in the first and second steps, respectively. The performance of the proposed procedure is demonstrated with two exemplary applications, a simulated mass-spring example and a quite challenging benchmark problem for uncertainty treatment. These examples demonstrate a gain in quality of the stochastic updating by utilizing the superior features of the Bhattacharyya distance, representing a convenient, efficient, and capable metric for stochastic model updating and uncertainty characterization. [ABSTRACT FROM AUTHOR]

Highlights • Spatiotemporal modeling of the clear-sky index. • Markov-chain mixture distribution modeling. • Model output is comparable to state of the art. Abstract This study presents a spatiotemporal Markov-chain mixture distribution model of the clear-sky index for an arbitrary number of locations, and is particularly suited for simulations of small-scale spatial networks with a span of 10 km or less. The model is statistical, but in practice data-driven and based on clear-sky index input from an arbitrary number of locations to generate synthetic time-series for the same locations. When trained on clear-sky index data based on the NREL Hawaii network radiometer solar irradiance data, dispersed within 1 km × 1.2 km, the model is shown to have high goodness-of-fit compared with test data from the network in terms of probability distributions, autocorrelations, location pair-correlations and k -lag correlations between locations. It is also shown to perform comparably to state of the art temporal, spatial and spatiotemporal clear-sky index generators. All measures of model goodness-of-fit are shown to improve with increased number of bins, up to a certain limit of N > 4 , where the performance improvements reaches a plateau. The results are also shown to be insensitive with respect to choice of training and test data sets as well as number of output time-steps. [ABSTRACT FROM AUTHOR]

Abstract A preponderance of research evidence shows that normal distributions cannot capture the behaviour of stock returns. In some empirical experiments, alternatives to normal distributions have been applied to stock data on a case-by-case basis, but no simple and practical general solutions exist to capture stock behaviour. As a simple methodology, the normal mixture model is a linear combination of normal distributions that can be directly used to approximate the characteristics of stock returns. In this paper, we recommend usage of the normal mixture model as a general method to understand stock behaviour. We also compare the performance of different normal mixture models with kernel density estimations for ten major stock market indexes and two individual stocks from the years 2000 to 2016. Empirical results show that the normal mixture model with three components better represents the behaviour of stock returns, both statistically and economically, than models based on normal distributions and kernel density estimations. Highlights • The normal distribution is not suitable for modelling distributions of stock returns. • Normal mixture models with k = 3 better represent the behaviour of stock returns both statistically and economically. • A normal mixture method is more suitable for capturing the characteristics of joint distribution of intermarket. [ABSTRACT FROM AUTHOR]

The Widom–Rowlinson mixture is a two component fluid where like species do not interact and unlike species interact via a hard core repulsion. As the density is increased this fluid phase separates. Using semigrand ensemble simulations and finite size scaling we accurately locate the critical density at ρσ3=0.762±0.016 where ρ is the total number density and σ is the hard sphere diameter. This density is much higher than previous estimates for this model. We implement several integral equation theories, none of which are accurate for the critical point or coexistence curve. © 1996 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Examines the effects of nonequilibrium velocity distribution associated with a single reaction in binary gaseous mixture. Assumption on the mechanical properties of the molecules; Description of typical reaction schemes; Calculation of corrections to the distribution functions.

Develops the near-resonant four-wave mixing technique for the sensitive detection of nitric oxide. Basis of the four-wave mixing technique; Demonstration of four-wave mixing in low pressure cell and air/acetylene flame; Effects of seeder field on signal regime and intensity.

Using data on 560 firm-commitment initial public offerings of common stock for the 1982-1983 period, we find that the cross-sectional distribution of one-day returns is modeled better as a mixture of two distributions, with the parameter estimates of one distribution being consistent with underpricing and the other with price stabilization. Further, the evidence that early IPO returns are drawn from a mixture distribution persists for at least four weeks. The implications of these results for the analysis of IPO returns are illustrated by examining the influence of a measure of ex ante price uncertainty on IPO pricing. [ABSTRACT FROM AUTHOR]

This paper presents new tests of the mixture of distributions hypothesis. Previous tests examined security prices and volume measured only at daily intervals. Here, differential implications of the hypothesis for transaction data are derived and tested. The new predictions emanate from the assumption that prices and volume evolve at uniform rates in transaction time. The results support this assumption and the mixture of distributions hypothesis in general. In addition, the tests suggest that the daily transaction-count may be a useful instrumental variable for estimating unobserved realizations of stochastic price variances. [ABSTRACT FROM AUTHOR]

The authors use finite mixture distribution theory to develop a segmentation model for targeting potential consumer durable buyers. The model enables them to identify simultaneously durable replacer segments on the basis of household characteristics and product ages and determine which of the household characteristics are significant predictors of segment membership. Using household data for five borne appliances, the authors present an empirical application of the model. They also discuss managerial implications and uses of this approach. [ABSTRACT FROM AUTHOR]

Increasing awareness of the qualitative differences between television and magazine advertisements and the resulting inference that a response to a television ad is much different from a response to a magazine ad suggest the appropriateness of a model which jointly evaluates an advertising schedule including both television and magazines. The mixed-media Dirichlet multinomial distribution model proposed estimates the joint frequency distribution of exposure of such a mixed-media advertising schedule and evaluates response under a variety of alternative theoretical assumptions. An empirical test is performed to evaluate the accuracy of the model, and the model's performance is compared with that of models with different theoretical assumptions. The results have important implications for media planning, with a strong case being made for coordinated planning of the television and magazine advertising schedules. [ABSTRACT FROM AUTHOR]

In the May 1980 issue of JMR, Lawrence replaces the gamma distribution on the purchasing rate component of the negative binomial model with the lognormal distribution. In this response the author shows that Lawrence's modeling effort is incomplete and that his data analysis is inconsistent with his implied model. In addition it is argued that the gamma distribution per se has some major advantages with respect to the lognormal distribution proposed by Lawrence. [ABSTRACT FROM AUTHOR]

• A multi-objective confidence gap decision based robust optimal dispatch model of IES is established. • An entropy expectation maximization Gaussian mixture model is proposed. • An adaptive harmonic aliasing efficient non-dominated sorting compound differential evolution algorithm is developed. • The IES dispatch scheme with low operating cost and high exergy efficiency and strong robustness can be obtained. To cope with the uncertainty of renewable energy output and achieve robust optimal dispatch of the integrated energy system, the confidence gap decision theory with Gaussian mixed probability distribution is introduced into the dispatch model. The entropy expectation maximization Gaussian mixture model (GMM), which is developed by adding an entropy factor to the expectation maximization algorithm, is proposed to reduce the initial value sensitivity in the GMM hidden variables solution process. Considering the comprehensive optimization objectives of maximizing exergy efficiency and minimizing operating cost, a multi-objective robust optimal dispatch model based on the confidence gap decision is established. And the model is transformed into a deterministic model according to the uncertainty theory for the sake of convenient calculation. Further, an efficient non-dominated sorting mechanism is combined with an improved differential evolution algorithm to efficiently solve the model. Finally, the effectiveness and superiority of the proposed method are verified by example analysis. [ABSTRACT FROM AUTHOR]

Background: Establishing the relationship between microbiota and specific diseases is important but requires appropriate statistical methodology. A specialized feature of microbiome count data is the presence of a large number of zeros, which makes it difficult to analyze in case-control studies. Most existing approaches either add a small number called a pseudo-count or use probability models such as the multinomial and Dirichlet-multinomial distributions to explain the excess zero counts, which may produce unnecessary biases and impose a correlation structure taht is unsuitable for microbiome data. Results: The purpose of this article is to develop a new probabilistic model, called BERnoulli and MUltinomial Distribution-based latent Allocation (BERMUDA), to address these problems. BERMUDA enables us to describe the differences in bacteria composition and a certain disease among samples. We also provide a simple and efficient learning procedure for the proposed model using an annealing EM algorithm. Conclusion: We illustrate the performance of the proposed method both through both the simulation and real data analysis. BERMUDA is implemented with R and is available from GitHub (https://github.com/abikoushi/Bermuda). [ABSTRACT FROM AUTHOR]

This paper discusses the mixture distribution-based data-driven robust chance constrained problem. We construct a data-driven mixture distribution-based uncertainty set from the perspective of simultaneously estimating higher-order moments. Then, we derive a reformulation of the data-driven robust chance constrained problem. As the reformulation is not a convex programming problem, we propose new and tight convex approximations based on the piecewise linear approximation method. We establish the theoretical foundation for these approximations. Finally, numerical results show that the proposed approximations are practical and efficient. [ABSTRACT FROM AUTHOR]

Highlights • Suitability of probability distributions to model wind speed in Quebec (Canada). • Two-component mixture distributions were fitted to the data. • The L-moment ratio diagram is used for assessment of one-component distributions. • Mixture distributions provide better fits than one-component distributions. Abstract The assessment of wind energy potential at sites of interest requires reliable estimates of the statistical characteristics of wind speed. A probability density function (pdf) is usually fitted to short-term observed local wind speed data. It is common for wind speed data to present bimodal distributions for which conventional one-component pdfs are not appropriate. Mixture distributions represent an appropriate alternative to model such wind speed data. Homogeneous mixture distributions remain rarely used in the field of wind energy assessment while heterogeneous mixture models have only been developed recently. The present work aims to investigate the potential of homogeneous and heterogeneous mixture distributions to model wind speed data in a northern environment. A total of ten two-component mixture models including mixtures of gamma, Weibull, Gumbel and truncated normal are evaluated in the present study. The estimation of the parameter of the mixture models are obtained with the least-squares (LS) and the maximum likelihood (ML) methods. The optimization of the objective functions related to these estimation methods is carried out with a genetic algorithm that is more adapted to mixture distributions. The case study of the province of Québec (Canada), a Northern region with an enormous potential for wind energy production, is investigated in the present work. A total of 83 stations with long data records and providing a good coverage of the territory of the province are selected. To identify the most appropriate one-component distribution for the selected stations, the newly proposed method of L-moment ratio diagram (MRD) is used. The advantages of this approach are that it is simple to apply and it allows an easy comparison of the fit of several pdfs for several stations on a single diagram. One-component distributions are compared with the selected mixture distributions based on model selection criteria. Results show that mixture distributions often provide better fit than conventional one-component distributions for the study area. It was also observed that the ML method outperforms the LS method and that the mixture model combining two Gumbel distributions using ML is the overall best model. [ABSTRACT FROM AUTHOR]

While mixtures of Gaussian distributions have been studied for more than a century, the construction of a reference Bayesian analysis of those models remains unsolved, with a general prohibition of improper priors due to the ill-posed nature of such statistical objects. This difficulty is usually bypassed by an empirical Bayes resolution. By creating a new parameterization centered on the mean and possibly the variance of the mixture distribution itself, we manage to develop here a weakly informative prior for a wide class of mixtures with an arbitrary number of components. We demonstrate that some posterior distributions associated with this prior and a minimal sample size are proper. We provide Markov chain Monte Carlo (MCMC) implementations that exhibit the expected exchangeability. We only study here the univariate case, the extension to multivariate location-scale mixtures being currently under study. An R package called Ultimixt is associated with this article. Supplementary material for this article is available online. [ABSTRACT FROM AUTHOR]

Due to the harsh working environment of the construction machinery, a simple distribution cannot be used to approximate the shape of the rainflow matrix. In this paper, the Weibull-normal (W-n) mixture distribution is used. The lowest Akaike information criterion (AIC) value is employed to determine the components number of the mixture. A parameter estimation method based on the idea of optimization is proposed. The method estimates parameters of the mixture by maximizing the log likelihood function (LLF) using an intelligent optimization algorithm (IOA), genetic algorithm (GA). To verify the performance of the proposed method, one of the already existing methods is applied in the simulation study and the practical case study. The fitting effects of the fitted distributions are compared by calculating the AIC and chi-square (χ2) value. It can be concluded that the proposed method is feasible and effective for parameter estimation of the mixture distribution. [ABSTRACT FROM AUTHOR]

We empirically question the commonly invoked assumption of normality of taste distribution in mixed logit models with continuous random parameters. We use a WTP-space random utility discrete choice model with flexible distributions on data from two choice experiments regarding beef with nested set of quality attributes. We specifically focus on distributional features such as asymmetry, multi-modality and range of variation, and find little support for normality. Our results are robust to attribute dimensionality in experimental design. Implications of our results for practitioners in the field are discussed. [ABSTRACT FROM AUTHOR]

Background: A robust method for Mendelian randomization does not require all genetic variants to be valid instruments to give consistent estimates of a causal parameter. Several such methods have been developed, including a mode-based estimation method giving consistent estimates if a plurality of genetic variants are valid instruments; i.e. there is no larger subset of invalid instruments estimating the same causal parameter than the subset of valid instruments.Methods: We here develop a model-averaging method that gives consistent estimates under the same 'plurality of valid instruments' assumption. The method considers a mixture distribution of estimates derived from each subset of genetic variants. The estimates are weighted such that subsets with more genetic variants receive more weight, unless variants in the subset have heterogeneous causal estimates, in which case that subset is severely down-weighted. The mode of this mixture distribution is the causal estimate. This heterogeneity-penalized model-averaging method has several technical advantages over the previously proposed mode-based estimation method.Results: The heterogeneity-penalized model-averaging method outperformed the mode-based estimation in terms of efficiency and outperformed other robust methods in terms of Type 1 error rate in an extensive simulation analysis. The proposed method suggests two distinct mechanisms by which inflammation affects coronary heart disease risk, with subsets of variants suggesting both positive and negative causal effects.Conclusions: The heterogeneity-penalized model-averaging method is an additional robust method for Mendelian randomization with excellent theoretical and practical properties, and can reveal features in the data such as the presence of multiple causal mechanisms. [ABSTRACT FROM AUTHOR]

In this paper, two residue number system (RNS) to binary converters for the moduli set {2n,2n-1-1,2n-1,2n+1-1} for (n even) are presented. One of them uses a two-level conversion, in which, in the first level, two pairs of moduli are considered to obtain two intermediate decoded numbers. A second-level converter obtains the final decoded number corresponding to these two intermediate decoded numbers. Both levels use mixed radix conversion. The second proposed RNS to binary converter uses the conventional MRC of the four-moduli set. The proposed converters are compared with previously reported conversion techniques for this moduli set and converters for other four, five and eight moduli sets for realizing similar dynamic ranges regarding hardware requirement and conversion time. The hardware resource requirement (A), conversion time (T), AT and AT2 trade-offs are discussed to bring out the relative advantages of various converters. The proposed converters have been shown to need less hardware or less conversion time than the other some of the reported converters for this moduli set. It has been shown by detailed comparison that converters using conjugate moduli and vertical extension generally exhibit better performance (lower hardware /lower conversion time) than those using no vertical extension, while needing differing word lengths of various moduli. These, however, need slightly complex multipliers/adders in the (2n+1) channel. Implementation results on FPGA of the proposed converters for few dynamic ranges also have been presented. [ABSTRACT FROM AUTHOR]

A review of the randomized response model introduced by Warner (1965) is given, then a randomized response model applicable to continuous data that considers a mixture of two normal distributions is considered. The target here is not to estimate any parameter, but rather to select the population with the best parameter value. This article provides a study on how to choose the best population between k distinct populations using an indifference-zone procedure. Also, this article includes tables for the required sample size needed in order to have a probability of correct selection higher than some specified value in the preference zone for the randomized response model considered. [ABSTRACT FROM AUTHOR]

This article aims at modeling unified S-N curves based on multifailure modes and stress ratios. Heterogeneous mixture distributions are used to describe life distribution of multifailure modes. Bayes clustering is applied to cluster failure data to avoid convergence to global optima. Derived from regression analysis, failure data are compensated by nonrandom error. The relationship between distribution parameters and stress is established, and the ultimately unified probabilistic S-N curve is modeled. Two assumptions are presented to modify an original S-N curve model with varied stress ratios. The first one is to take into account the effects of low-amplitude load "exercising," which we call results in the "pseudo-fatigue damage." The other one is to set up probability density function of fatigue limit considering uncertainty. Combined with material parameters modification, thus a new modified and unified S-N curves model is available for not only researchers, but engineers as well. [ABSTRACT FROM AUTHOR]

A block-diagonal preconditioner with the minimal residual method and an approximate block-factorization preconditioner with the generalized minimal residual method are developed for Hu-Zhang mixed finite element methods for linear elasticity. They are based on a new stability result for the saddle point system in mesh-dependent norms. The mesh-dependent norm for the stress corresponds to the mass matrix which is easy to invert while for the displacement it is spectral equivalent to the Schur complement. A fast auxiliary space preconditioner based on the H¹-conforming linear element of the linear elasticity problem is then designed for solving the Schur complement. For both diagonal and triangular preconditioners, it is proved that the conditioning numbers of the preconditioned systems are bounded above by a constant independent of both the crucial Lamé constant and the mesh size. Numerical examples are presented to support theoretical results. As byproducts, a new stabilized low order mixed finite element method is proposed and analyzed and superconvergence results for the Hu-Zhang element are obtained. [ABSTRACT FROM AUTHOR]

A new mortality model based on a mixture distribution function is proposed. We mix a half-normal distribution with a generalization of the skew-normal distribution. As a result, we get a six-parameter distribution function that has a good fit with a wide variety of mortality patterns. This mixture model is fitted to several mortality data schedules and compared with the Siler (five-parameter) and Heligman- Pollard (eight-parameter) models. Our proposal serves as a convenient compromise between the Heligman-Pollard model (which ensures a good fit with data but is often overparameterized) and the Siler model (which is more compact but fails to capture 'accident humps'). [ABSTRACT FROM AUTHOR]