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]

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]

• 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]

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]

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]

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]

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.

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]

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]

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]

Studies of occluded oxygen-bearing compounds inside kerogen are scarce, although such studies are important in understanding early-stage transformation of organic matter. A relatively low-maturity kerogen from the late Permian mudstone of the Lucaogou Formation of the Santanghu Basin, northwestern China, was successively extracted with n -hexane, acetone and dichloromethane to release the adsorbed components, and the extracted kerogen was treated with a mild oxidation reagent H 2 O 2 to release the occluded components. Gas chromatography–mass spectrometry analysis of the adsorbed and occluded components revealed a suite of oxygen-bearing compounds, including n -alkan-2-ones, n -aldehydes and fatty acid methyl esters. The n -alkan-2-ones were mainly detected in the adsorbed fraction and n -aldehydes in the occluded component. Comparison of the long-chain oxygen-bearing compound distributions and their individual stable carbon isotope characteristics both suggest that the oxygen-bearing compounds released by H 2 O 2 treatment were occluded in the kerogen. The shorter-chain (C 15 to C 19 ) occluded n -aldehydes reflected similar isotopic distribution trends to the adsorbed n -alkan-2-ones, and the δ 13 C values of the mid-length (C 21 to C 25 ) occluded n -aldehydes were much closer to the adsorbed n -alkanes. Bacterially mediated methylation and decarbonylation of the n -aldehydes during kerogen formation may be important source(s) of n -alkan-2-ones and n -alkanes, respectively. The mid-chain ketones mainly originated from hydrothermal alteration of n -alkanes after kerogen formation. Uplift of the Lucaogou Formation in the Yuejingou section allowed surface-enhanced aerobic reactions. [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]

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]

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.

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]

The problem of discrepancy between certain statements of the Guide to the Expression of Uncertainty in Measurement and the State System for the Assurance of the Uniformity of Measurements is considered. Possible variants in the agreement between the statements of these documents as a function of the objective of the particular measurement problems solved are presented. [ABSTRACT FROM AUTHOR]

We introduce a class of systems, including Ledrappier’s example, which do not have multiple mixing. A classification of such systems for 2D lattice actions is constructed. [ABSTRACT FROM AUTHOR]

Background: Body Mass Index (BMI), like most human phenotypes, is substantially heritable. However, BMI is not normally distributed; the skew appears to be structural, and increases as a function of age. Moreover, twin correlations for BMI commonly violate the assumptions of the most common variety of the classical twin model, with the MZ twin correlation greater than twice the DZ correlation. This study aimed to decompose twin correlations for BMI using more general skew-t distributions. Methods: Same sex MZ and DZ twin pairs (N = 7,086) from the community-based Washington State Twin Registry were included. We used latent profile analysis (LPA) to decompose twin correlations for BMI into multiple mixture distributions. LPA was performed using the default normal mixture distribution and the skew-t mixture distribution. Similar analyses were performed for height as a comparison. Our analyses are then replicated in an independent dataset. Results: A two-class solution under the skew-t mixture distribution fits the BMI distribution for both genders. The first class consists of a relatively normally distributed, highly heritable BMI with a mean in the normal range. The second class is a positively skewed BMI in the overweight and obese range, with lower twin correlations. In contrast, height is normally distributed, highly heritable, and is well-fit by a single latent class. Results in the replication dataset were highly similar. Conclusions: Our findings suggest that two distinct processes underlie the skew of the BMI distribution. The contrast between height and weight is in accord with subjective psychological experience: both are under obvious genetic influence, but BMI is also subject to behavioral control, whereas height is not. [ABSTRACT FROM AUTHOR]

We develop a Bayesian nonparametric framework for modeling ordinal regression relationships, which evolve in discrete time. The motivating application involves a key problem in fisheries research on estimating dynamically evolving relationships between age, length, and maturity, the latter recorded on an ordinal scale. The methodology builds from nonparametric mixture modeling for the joint stochastic mechanism of covariates and latent continuous responses. This approach yields highly flexible inference for ordinal regression functions while at the same time avoiding the computational challenges of parametric models that arise from estimation of cut-off points relating the latent continuous and ordinal responses. A novel-dependent Dirichlet process prior for time-dependent mixing distributions extends the model to the dynamic setting. The methodology is used for a detailed study of relationships between maturity, age, and length for Chilipepper rockfish, using data collected over 15 years along the coast of California. Supplementary materials for this article are available online. [ABSTRACT FROM AUTHOR]

We have proposed a new multivariate Weibull distribution as a compound distribution of univariate Weibull distributions. We have studied some properties of the proposed distribution. The multivariate distribution of records for proposed distribution has also been studied. Estimation of the parameters has been done alongside application to the real data set. [ABSTRACT FROM AUTHOR]

In this article, the effects of mixtures of two normal distributions on the fraction non-conforming are studied in the context of capability analysis. When the output from several processes is mixed, the quality characteristic variables of the resulting mix may result in a normal mixture distribution. This can happen in cases such as monitoring an output from several suppliers, several machines, or several workers. This study considered the independence case and autocorrelated processes for a mixture of two normal distributions, using an autoregressive model of order one, AR(1). It is shown that the true attained process fraction non-conforming (corresponding to specific values for some capability index) can be very different from what is expected when the data are independent normal random variables. [ABSTRACT FROM AUTHOR]

Summary: Mixture distributions have become a very flexible and common class of distributions, used in many different applications, but hardly any literature can be found on tests for assessing their goodness of fit. We propose two types of smooth tests of goodness of fit for mixture distributions. The first test is a genuine smooth test, and the second test makes explicit use of the mixture structure. In a simulation study the tests are compared to some traditional goodness of fit tests that, however, are not customised for mixture distributions. The first smooth test has overall good power and generally outperforms the other tests. The second smooth test is particularly suitable for assessing the fit of each component distribution separately. The tests are applicable to both continuous and discrete distributions and they are illustrated on three medical data sets. [ABSTRACT FROM AUTHOR]

Generalized skew-symmetric probability density functions are proposed to model asymmetric interfacial density distributions for the parameterization of any arbitrary density profiles in the `effective-density model'. The penetration of the densities into adjacent layers can be selectively controlled and parameterized. A continuous density profile is generated and discretized into many independent slices of very thin thickness with constant density values and sharp interfaces. The discretized profile can be used to calculate reflectivities via Parratt's recursive formula, or small-angle scattering via the concentric onion model that is also developed in this work. [ABSTRACT FROM AUTHOR]

A new algebraic method for extracting tori from a minimal point set, made of two oriented points and a simple point, is proposed. We prove a degree bound on the number of such tori; this bound is reached on examples, even when we restrict to smooth tori. Our method is based on pre-computed closed formulae well suited for numerical computations with approximate input data. [ABSTRACT FROM AUTHOR]

Modeling mixtures of distributions has rested on Gaussian distributions and/or a conditional independence hypothesis for a long time. Only recently have researchers begun to construct and study broader generic models without appealing to such hypotheses. Some of these extensions use copulas as a tool to build flexible models, as they permit modeling the dependence and the marginal distributions separately. But this approach also has drawbacks. First, the practitioner has to make more arbitrary choices, and second, marginal misspecification may loom on the horizon. This paper aims at overcoming these limitations by presenting a copulabased mixture model which is semiparametric. Thanks to a location-shift hypothesis, semiparametric estimation, also, is feasible, allowing for data adaptation without any modeling effort. [ABSTRACT FROM AUTHOR]

A new probability distribution function (PDF) called hyper-Exponentially Modified Gaussian (hyper-EMG) is introduced for the analysis of high-resolution spectra from multiple-reflection time-of-flight mass spectrometers. The hyper-EMG consists of a central Gaussian distribution modified by multiple exponential tails with different strengths at one or both sides. The basic statistical properties of the new PDF are given and the analysis of mass spectra containing separated and overlapping peaks is presented. The main requirement is to accurately determine the positions and areas of the individual mass peaks. From the distances of positions the mass values can be determined, from the areas the population of different ground and isomeric states can be obtained. The hyper-EMG has been applied to high-resolution time and mass spectra characterized by mass resolving powers of 140,000 and 520,000 obtained with Cs + 133 and K + 39 ions, respectively. From the measured mass distribution of K + 39 ions, an overlapping distribution of two peaks with an area ratio of 1:10 and a mass difference of 2.6 ppm (parts-per-million) is generated and analyzed. The results reveal significant advantages of the new PDF for the evaluation of overlapping distributions for accurate mass and area determinations compared with commonly used PDFs which are more than one order of magnitude less accurate. It is obvious that the hyper-EMG can be favorably applied also to other fields. [ABSTRACT FROM AUTHOR]

The increasing complexity of radar devices, and the variety of naval and coastal scenarios in which they need to be deployed, motivates the need for the stochastic modelling of the sea clutter, which will contribute to the assessment of the system before the implementation. Specifically, when radars are placed on aircrafts or elevated locations, the statistical distribution of the background echoes gets modified and therefore differs from the one commonly assumed for low grazing angles. For the accurate representation of the sea clutter observed at medium and high grazing angles, the authors modelled in MATLAB the Weibull-Weibull and K-K mixed distributions, which are frequently used in the literature. The implemented functions provide an easy access to the handling of density, cumulative distribution and survival functions, as well as the generation of random variables and the estimation of central and algebraic moments of the addressed distributions. Besides, additional functions were included, enabling the validation of the code by comparison with the results provided by other investigations and through the interaction of the functions. The created code models distributions which are commonly ignore by most software for statistical simulation, due to their specific application in radar related studies. Therefore, the current research is expected to lead to the conception of enhanced detection solutions adapted to different operation scenarios, also contributing to the creation of a framework specialized in radar clutter. [ABSTRACT FROM AUTHOR]

We study the problem of demixing a pair of sparse signals from noisy, nonlinear observations of their superposition. Mathematically, we consider a nonlinear signal observation model, y_i = g(a_i^Tx) + e_i, \ i=1,\ldots,m, where x = \Phi w+\Psi z denotes the superposition signal, \Phi and \Psi, and w, z\in \mathbb {R}^n are sparse coefficient vectors of the constituent signals, and e_i represents the noise. Moreover, g represents a nonlinear link function, and a_i\in \mathbb {R}^n is the ith row of the measurement matrix A\in \mathbb R^m\times n. Problems of this nature arise in several applications ranging from astronomy, computer vision, and machine learning. In this paper, we make some concrete algorithmic progress for the above demixing problem. Specifically, we consider two scenarios: first, the case when the demixing procedure has no knowledge of the link function, and second is the case when the demixing algorithm has perfect knowledge of the link function. In both cases, we provide fast algorithms for recovery of the constituents w and $z$ from the observations. Moreover, we support these algorithms with a rigorous theoretical analysis and derive (nearly) tight upper bounds on the sample complexity of the proposed algorithms for achieving stable recovery of the component signals. We also provide a range of numerical simulations to illustrate the performance of the proposed algorithms on both real and synthetic signals and images. [ABSTRACT FROM PUBLISHER]

Although each statistical unit on which measurements are taken is unique, typically there is not enough information available to account totally for its uniqueness. Therefore, heterogeneity among units has to be limited by structural assumptions. One classical approach is to use random effects models, which assume that heterogeneity can be described by distributional assumptions. However, inference may depend on the assumed mixing distribution, and it is assumed that the random effects and the observed covariates are independent. An alternative considered here is fixed effect models, which let each unit has its own parameter. They are quite flexible but suffer from the large number of parameters. The structural assumption made here is that there are clusters of units that share the same effects. It is shown how clusters can be identified by tailored regularised estimators. Moreover, it is shown that the regularised estimates compete well with estimates for the random effects model, even if the latter is the data generating model. They dominate if clusters are present. [ABSTRACT FROM AUTHOR]