Robust Frequency Estimation Under Additive Symmetric α-Stable Gaussian Mixture Noise

Here the estimating problem of a single sinusoidal signal in the additive symmetricα-stable Gaussian(ASαSG)noise is investigated.The ASαSG noise here is expressed as the additive of a Gaussian noise and a symmetricα-stable distributed variable.As the probability density function(PDF)of the ASαSG is complicated,traditional estimators cannot provide optimum estimates.Based on the Metropolis-Hastings(M-H)sampling scheme,a robust frequency estimator is proposed for ASαSG noise.Moreover,to accelerate the convergence rate of the developed algorithm,a new criterion of reconstructing the proposal covar-iance is derived,whose main idea is updating the proposal variance using several previous samples drawn in each iteration.The approximation PDF of the ASαSG noise,which is referred to the weighted sum of a Voigt function and a Gaussian PDF,is also employed to reduce the computational complexity.The computer simulations show that the performance of our method is better than the maximum likelihood and the lp-norm estimators.

Estimating the Components of a Mixture of Extremal Distributions under Strong Dependence

In this paper, we provide a method based on quantiles to estimate the parameters of a finite mixture of Fréchet distributions, for a large sample of strongly dependent data. This is a situation that appears when dealing with environmental data and there was a real need of such method. We validate our approach by means of estimation and goodness-of-fit testing over simulated data, showing an accurate performance.

Variable Selection for Robust Mixture Regression Model with Skew Scale Mixtures of Normal Distributions

In this paper, we propose a robust mixture regression model based on the skew scale mixtures of normal distributions (RMR-SSMN) which can accommodate asymmetric, heavy-tailed and contaminated data better. For the variable selection problem, the penalized likelihood approach with a new combined penalty function which balances the SCAD and l2 penalty is proposed. The adjusted EM algorithm is presented to get parameter estimates of RMR-SSMN models at a faster convergence rate. As simulations show, our mixture models are more robust than general FMR models and the new combined penalty function outperforms SCAD for variable selection. Finally, the proposed methodology and algorithm are applied to a real data set and achieve reasonable results.

A NEW CORRENTROPY BASED TDE METHOD UNDER α-STABLE DISTRIBUTION NOISE ENVIRONMENT

This paper presents a robust time delay estimation algorithm for the α-Stable noise based on correntropy. Many time delay estimation algorithms derived for impulsive stable noise are based on the theory of Fractional Lower Order Statistics (FLOS). Unlike previously introduced FLOS-type algorithms, the new algorithm is proposed to estimate the time delay by maximizing the generalized correlation function of two observed signals needing neither prior information nor estimation of the numerical value of the stable noise's characteristic exponent. An interval for kernel selection is found for a wide range of characteristic exponent values of α-Stable distribution. Simulations show the proposed algorithm offers superior performance over the existing covariation time delay estimation, least mean p-norm time delay estimation and achieves slightly improved performance than fractional lower order covariance time delay estimation at lower signal to noise ratio when the noise is highly impulsive.

Effect of Particle Size Distribution on Radiative Heat Transfer in High-Temperature Homogeneous Gas-Particle Mixtures

The weighted-sum-of-gray-gas(WSGG)model and Mie theory are applied to study the influents of particle size on the radiative transfer in high temperature homogeneous gas-particle mixtures,such as the flame in aero-engine combustor.The radiative transfer equation is solved by the finite volume method.The particle size is assumed to obey uniform distribution and logarithmic normal(L-N)distribution,respectively.Results reveal that when particle size obeys uniform distribution,increasing particle size with total particle volume fraction fvunchanged will result in the decreasing of the absolute value of radiative heat transfer properties,and the effect of ignoring particle scattering will also be weakened.Opposite conclusions can be obtained when total particle number concentration N0 is unchanged.Moreover,if particle size obeys L-N distribution,increasing the narrowness indexσor decreasing the characteristic diameter Dˉwith the total particle volume fraction fvunchanged will increase the absolute value of radiative heat transfer properties.With total particle number concentration N0 unchanged,opposite conclusions for radiative heat source and incident radiation terms can be obtained except for radiative heat flux term.As a whole,the effects of particle size on the radiative heat transfer in the high-temperature homogeneous gas-particle mixtures are complicated,and the particle scattering cannot be ignoring just according to the particle size.

Prediction Based on Generalized Order Statistics from a Mixture of Rayleigh Distributions Using MCMC Algorithm

This article considers the problem in obtaining the maximum likelihood prediction (point and interval) and Bayesian prediction (point and interval) for a future observation from mixture of two Rayleigh (MTR) distributions based on generalized order statistics (GOS). We consider one-sample and two-sample prediction schemes using the Markov chain Monte Carlo (MCMC) algorithm. The conjugate prior is used to carry out the Bayesian analysis. The results are specialized to upper record values. Numerical example is presented in the methods proposed in this paper.

Evaluating Traffic Congestion Using the Traffic Occupancy and Speed Distribution Relationship: An Application of Bayesian Dirichlet Process Mixtures of Generalized Linear Model

Accurate classification and prediction of future traffic conditions are essential for developing effective strategies for congestion mitigation on the highway systems. Speed distribution is one of the traffic stream parameters, which has been used to quantify the traffic conditions. Previous studies have shown that multi-modal probability distribution of speeds gives excellent results when simultaneously evaluating congested and free-flow traffic conditions. However, most of these previous analytical studies do not incorporate the influencing factors in characterizing these conditions. This study evaluates the impact of traffic occupancy on the multi-state speed distribution using the Bayesian Dirichlet Process Mixtures of Generalized Linear Models (DPM-GLM). Further, the study estimates the speed cut-point values of traffic states, which separate them into homogeneous groups using Bayesian change-point detection (BCD) technique. The study used 2015 archived one-year traffic data collected on Florida’s Interstate 295 freeway corridor. Information criteria results revealed three traffic states, which were identified as free-flow, transitional flow condition (congestion onset/offset), and the congested condition. The findings of the DPM-GLM indicated that in all estimated states, the traffic speed decreases when traffic occupancy increases. Comparison of the influence of traffic occupancy between traffic states showed that traffic occupancy has more impact on the free-flow and the congested state than on the transitional flow condition. With respect to estimating the threshold speed value, the results of the BCD model revealed promising findings in characterizing levels of traffic congestion.

A Bayesian Mixture Model Approach to Disparity Testing

The topic of this article is one-sided hypothesis testing for disparity, i.e., the mean of one group is larger than that of another when there is uncertainty as to which group a datum is drawn. For each datum, the uncertainty is captured with a given discrete probability distribution over the groups. Such situations arise, for example, in the use of Bayesian imputation methods to assess race and ethnicity disparities with certain insurance, health, and financial data. A widely used method to implement this assessment is the Bayesian Improved Surname Geocoding (BISG) method which assigns a discrete probability over six race/ethnicity groups to an individual given the individual’s surname and address location. Using a Bayesian framework and Markov Chain Monte Carlo sampling from the joint posterior distribution of the group means, the probability of a disparity hypothesis is estimated. Four methods are developed and compared with an illustrative data set. Three of these methods are implemented in an R-code and one method in WinBUGS. These methods are programed for any number of groups between two and six inclusive. All the codes are provided in the appendices.

Inference and Properties of Mixture Two Extreme Lower Bound Distributions

In this paper, we discuss the mixture model of two extreme lower bound distributions. First, some properties we obtain of the model with hazard function are discussed. In addition, the estimates of the unknown parameters via the EM algorithm are obtained. The performance of the findings in the paper is showed by demonstrating some numerical illustrations through Monte Carlo simulation.

Inference on Constant-Partially Accelerated Life Tests for Mixture of Pareto Distributions under Progressive Type-II Censoring

The main purpose of this paper is to obtain the inference of parameters of heterogeneous population represented by finite mixture of two Pareto (MTP) distributions of the second kind. The constant-partially accelerated life tests are applied based on progressively type-II censored samples. The maximum likelihood estimates (MLEs) for the considered parameters are obtained by solving the likelihood equations of the model parameters numerically. The Bayes estimators are obtained by using Markov chain Monte Carlo algorithm under the balanced squared error loss function. Based on Monte Carlo simulation, Bayes estimators are compared with their corresponding maximum likelihood estimators. The two-sample prediction technique is considered to derive Bayesian prediction bounds for future order statistics based on progressively type-II censored informative samples obtained from constant-partially accelerated life testing models. The informative and future samples are assumed to be obtained from the same population. The coverage probabilities and the average interval lengths of the confidence intervals are computed via a Monte Carlo simulation to investigate the procedure of the prediction intervals. Analysis of a simulated data set has also been presented for illustrative purposes. Finally, comparisons are made between Bayesian and maximum likelihood estimators via a Monte Carlo simulation study.

Distribution performance of gas–liquid mixture in the shell side of spiral-wound heat exchangers

The non-uniformity of gas–liquid mixture is a critical issue which leads to the heat transfer deterioration of spiralwound heat exchangers(SWHEs).Two-phase mass flow rate and the content of gas are important parameters as well as structural parameters which have prominent influences on flow distribution uniformity of SWHE shell side.In order to investigate the influences of these parameters,an experimental test system was built using water and air as mediums and a novel distributor named"tubes distributor"was designed.The effects of mass flow rate and the content of gas on two-phase distribution performance were analyzed,where the mass flow rate ranged from 28.4 to 171.9 kg·h-1 and the content of gas changed from 0.2 to 0.8,respectively.The results showed that the mixture mass flow rate considerably influenced the liquid distribution than that of gas phase and the larger mass flow rate exhibited the better distribution uniformity of two-phase flow.It was also found that the tubes distributor had the better two-phase uniformity when the content of gas was around 0.4.Tube diameter played an important role in the distribution of gas phase and slit width was more significant for the uniformity of liquid phase.

EXPLICIT EXPRESSIONS FOR SOME DISTRIBUTIONS RELATED TO RUIN PROBLEMS

The classical risk process that is perturbed by diffusion is studied. The explicit expressions for the ruin probability and the surplus distribution of the risk process at the time of ruin are obtained when the claim amount distribution is a finite mixture of exponential distributions or a Gamma (2, α) distribution.

Statistical Analysis of the Asphalt Mixtures Volumetric Properties

Based on statistics principle,random error and systematic error were considered and the volumetric properties of the two mixtures types,namely A and B,were statistically analyzed using different distribution methods.Seventy-two samples of mixture A and fifty-two of mixture B were fabricated using the Marshall method.The probability distributions were compared on the basis of goodness of fit.Weibull model was found to be most appropriate model for describing the asphalt mixtures volumetric properties distribution.The two-parameter Weibull distribution function applied well to model the bulk specific gravity and voids filled with asphalt data,whereas,the three-parameter Weibull distribution appeared to be more appropriate in the discussing of air voids and voids in mineral aggregate.The experimetal results is revealed that compared with the mean value,the peak value of Weibull distribution was suggested as an alternative and more powerful parameter for describing the test data distribution characteristic.The analysis of test results also revealed that there were significant differences in the volumetric properties of the two tested mixtures for the same confidence level.The confidence interval decreased with the decreasing in reliability.

The Conditional Poisson Process and the Erlang and Negative Binomial Distributions

It is a well known fact that for the hierarchical model of a Poisson random variable Y?whose mean has an Erlang distribution, the unconditional distribution of Y is negative binomial. However, the proofs in the literature [1] [2] provide no intuitive understanding as to why this result should be true. It is the purpose of this manuscript to give a new proof of this result which provides such an understanding. The memoryless property of the exponential distribution allows one to conclude that the events in two independent Poisson processes may be regarded as Bernoulli trials, and this fact is used to achieve the research purpose. Another goal of this manuscript is to give another proof of this last fact which does not rely on the memoryless property.

Modified likelihood ratio test for homogeneity in normal mixtures with two samples

This paper investigates the modified likelihood ratio test（LRT） for homogeneity in normal mixtures of two samples with mixing proportions unknown. It is proved that the limit distribution of the modified likelihood ratio test is X^2（1）.

Evaluation of the Effectiveness of a 4-Months Continuous Injection of a Gas Mixture (CO₂and Inert Gases) on <i>Legionella</i>Contamination of a Hot Water Distribution System

Within the biofilm and scales Legionella is less far susceptible to the effects of the most frequently used biocides. The objective of this study was to evaluate the effect of a 4-months continuous injection of a gas mixture (CO2 and inert gas) in the hot water distribution system of a large hotel colonized by L. pneumophila sg3 on limiting biofilm formation and scales and in turn Legionella growth. Before the continuous injection of the gas mixture, out of the 15 sampling points examined every month 60% were colonized by Legionella (mean concentrations of 102 cfu/L in the boilers and the return loop, and 104 cfu/L in taps and showers). One week after the injection of the gas mixture and daily fluxing of the distal outlets, the level of colonization decreased (3 cfu/L). When it was decided to flux all the distal outlets only 1 day per week the mean concentration of Legionella increased again (>104 cfu/L) in all the sampling points. Thus, cleaning of the boilers was performed and distal outlets were again fluxed daily. One week after the level of contamination decreased again (2 cfu/L). Nonetheless, the colonization was not eliminated and when fluxing of the distal outlets was not performed every day the mean concentrations of Legionella raised up to >104 cfu/L. Results indicate that the gas mixture was able to reduce the level of colonization by Legionella only because associated to the fluxing of the distal outlets.

Adaptive Sparse Group Variable Selection for a Robust Mixture Regression Model Based on Laplace Distribution

The traditional estimation of Gaussian mixture model is sensitive to heavy-tailed errors;thus we propose a robust mixture regression model by assuming that the error terms follow a Laplace distribution in this article. And for the variable selection problem in our new robust mixture regression model, we introduce the adaptive sparse group Lasso penalty to achieve sparsity at both the group-level and within-group-level. As numerical experiments show, compared with other alternative methods, our method has better performances in variable selection and parameter estimation. Finally, we apply our proposed method to analyze NBA salary data during the period from 2018 to 2019.

A 2D numerical study on the condensation characteristics of three non-azeotropic binary hydrocarbon vapor mixtures on a vertical plate

To improve the transportation efficiency and reduce the supply cost,the liquefaction becomes an important technology to store and transport the natural gas.During the liquefaction,the various components(e.g.propane,ethane,methane etc.)undergo fractional condensation phenomenon due to their different boiling points.This means that when one component condenses,others play a role of non-condensable gas(NCG).In order to reveal the influence mechanism of NCG on this condensation process,a numerical method was employed in this paper to study the condensation characteristics of three non-azeotropic binary hydrocarbon vapor mixtures,namely the propane/methane(80%–95%),ethane/methane(65%–85%)and methane/nitrogen(2%–13%)mixtures,on a vertical plate.The model was proposed based on the diffusion layer model,and the finite volume method was used to solve the governing equations.A user defined function was developed by cell iterative method to obtain the source terms in the condensation process.The numerical results show that the gas phase boundary layer formed by the NCG becomes the main resistance to the reduction of heat transfer coefficient.And for the above three mixtures,there is a negative correlation between the NCG concentration and the heat transfer coefficient.Meanwhile,the results show a good agreement with the experimental data,meaning that the proposed model is reliable.Three mixtures within same non-condensable mole fraction of 20%were also investigated,indicating that the mixtures with a higher binary hydrocarbon molecular ratio have a lower heat transfer coefficient.As a result,the presence of the lighter NCG contributes to a thicker boundary layer.

Asymptotic Properties of Estimators for Ornstein-Uhlenbeck Processes with Small Symmetricα-Stable Motions

The asymptotic behaviors for estimators of the drift parameters in the Ornstein-Uhlenbeck process driven by small symmetricα-stable motion are studied in this paper.Based on the discrete observations,the conditional least squares estimators(CLSEs)of all the parameters involved in the Ornstein–Uhlenbeck process are proposed.We establish the consistency and the asymptotic distributions of our estimators asεgoes to 0 and n goes to∞simultaneously.

Gamma-Generalized Inverse Gaussian Class of Distributions

Gamma distribution nests exponential, chi-squared and Erlang distributions;while generalized Inverse Gaussian distribution nests quite a number of distributions. The aim of this paper is to construct a gamma mixture using Generalized inverse Gaussian mixing distribution. The rth moment of the mixture is obtained via the rth moment of the mixing distribution. Special cases and limiting cases of the mixture are deduced.