On the convergence for PNQD sequences with general moment conditions

Let fX;Xn;n≥1g be a sequence of identically distributed pairwise negative quadrant dependent(PNQD)random variables and fan;n1g be a sequence of positive constants with an=f(n)and f(θ^k)=f(θ^k-1)for all large positive integers k,where 1<θ≤βand f(x)>0(x≥1)is a non-decreasing function on[b;+1)for some b≥1:In this paper,we obtain the strong law of large numbers and complete convergence for the sequence fX;Xn;n≥1g,which are equivalent to the general moment conditionΣ∞n=1P(|X|>an)<1.Our results extend and improve the related known works in Baum and Katz[1],Chen at al.[3],and Sung[14].

Bivariate Beta–Inverse Weibull Distribution:Theory and Applications

Probability distributions have been in use for modeling of random phenomenon in various areas of life.Generalization of probability distributions has been the area of interest of several authors in the recent years.Several situations arise where joint modeling of two random phenomenon is required.In such cases the bivariate distributions are needed.Development of the bivariate distributions necessitates certain conditions,in a field where few work has been performed.This paper deals with a bivariate beta-inverse Weibull distribution.The marginal and conditional distributions from the proposed distribution have been obtained.Expansions for the joint and conditional density functions for the proposed distribution have been obtained.The properties,including product,marginal and conditional moments,joint moment generating function and joint hazard rate function of the proposed bivariate distribution have been studied.Numerical study for the dependence function has been implemented to see the effect of various parameters on the dependence of variables.Estimation of the parameters of the proposed bivariate distribution has been done by using the maximum likelihood method of estimation.Simulation and real data application of the distribution are presented.

Likelihood Inference under Generalized Hybrid Censoring Scheme with Comp eting Risks

Statistical inference is developed for the analysis of generalized type-Ⅱ hybrid censoring data under exponential competing risks model. In order to solve the problem that approximate methods make unsatisfactory performances in the case of small sample size,we establish the exact conditional distributions of estimators for parameters by conditional moment generating function(CMGF). Furthermore, confidence intervals(CIs) are constructed by exact distributions, approximate distributions as well as bootstrap method respectively,and their performances are evaluated by Monte Carlo simulations. And finally, a real data set is analyzed to illustrate all the methods developed here.

Power Hamza Distribution with Application to Lifetime Data

In this paper, a three-parameter lifetime distribution named power Hamza distribution (PH) is proposed. The PH distribution is a useful generalization of the Hamza distribution which accommodates heavy-tailed, upside-down bathtub and J-shaped hazard rates making it more flexible than the Hamza distribution for modelling various kinds of lifetime data. A comprehensive account of the properties of this distribution is presented. The maximum likelihood estimators of the unknown model parameters are discussed. Finally, a real-life data is analyzed for illustrative purpose proving that the PH outperforms the Hamza distribution and several other lifetime distributions.

Complete Convergence Properties of the Sums for -mixing Sequences of Random Variables

This paper discusses complete convergence properties of the sums of -mixing random sequences.As a result,we improve the corresponding results of Wu Qunying(2001). And extended the Baum and Katz complete convergence to the case of -mixing random sequences by moment inequality and truncating without necessarily adding any extra conditions.

An Invariance Principle for ρ^--Mixing Random Sequences

In this paper,we establish an invariance principle for ρ^--mixing random sequences under some moment condition.The result improve and extend the relevant result of Wu（2003）.

Redundancy of Moment Conditions in Restricted GMM Estimation

Using a novel approach to calculating the rank of the difference of two asymptotic variance matrices, The author derives the necessary and sufficient conditions for an extra set of moment conditions to be redundant given a set of moment conditions in GMM estimation with general nonlinear restrictions. The necessary and sufficient conditions derived in this paper include as a special case the redundancy of moment conditions for GMM estimation without restrictions that was first derived by Breusch et al. （1999）. Therefore this paper advances the research on redundancy of moment conditions from unrestricted GMM estimation to a larger class of GMM estimation. To show their usefulness, the main results of the current paper are applied to instrumental variables estimation of linear regression models and the efficient estimation of seemingly unrelated regressions models, subject to restrictions.

Efficient GMM estimation with singular system of moment conditions

Standard generalised method of moments(GMM)estimation was developed for nonsingular system of moment conditions.However,many important economic models are characterised by singular system of moment conditions.This paper shows that efficient GMM estimation of such models can be achieved by using the reflexive generalised inverses,in particular the Moore–Penrose generalised inverse,of the variance matrix of the sample moment conditions as the weighting matrix.We provide a consistent estimator of the optimal weighting matrix and establish its consistency.Potential issues of using generalised inverse and some remedies are also discussed.

On the Condition of Operator-valued Moment Problem

In Ref. [1] it is discussed that the sequence {A_n} of operators on the Hilbertspace can be expressed in the formA_n=integral from n=R to (λ~nB(λ)dλ), (1)where B(λ) is the integrable operator-valued function with compact support. Asufficient and necessary condition is that there is another sequence {A′_m}such

Analysis of Turbulence and Surface Growth Models on the Estimation of Soot Level in Ethylene Non-Premixed Flames

Soot prediction in a combustion system has become a subject of attention, as many factors influence its accuracy. An accurate temperature prediction will likely yield better soot predictions, since the inception, growth and de- struction of the soot are affected by the temperature. This paper reported the study on the influences of turbulence closure and surface growth models on the prediction of soot levels in turbulent flames. The results demonstrated that a substantial distinction was observed in terms of temperature predictions derived using the k-c and the Rey- nolds stress models, for the two ethylene flames studied here amongst the four types of surface growth rate model investigated, the assumption of the soot surface growth rate proportional to the particle number density, but inde- pendent on the surface area of soot particles,f（As） = pNs, yields in closest agreement with the radial data. Without any adjustment to the constants in the surface growth term, other approaches where the surface growth directly proportional to the surface area and square root of surface area, f （As） = As and f （A,） = √As, result in an un- der-prediction of soot volume fraction. These results suggest that predictions of soot volume fraction are sensitive to the modelling of surface growth.

Investigation of Detailed Kinetic Scheme Performance on Modelling of Turbulent Non-Premixed Sooting Flames

This paper presents the results of an application of a first-order conditional moment closure （CMC） approach coupled with a semi-empirical soot model to investigate the effect of various detailed combustion chemistry schemes on soot formation and destruction in turbulent non-premixed flames. A two-equation soot model repre- senting soot particle nucleation, growth, coagulation and oxidation, was incorporated into the CMC model. The turbulent flow-field of both flames is described using the Favre-averaged fluid-flow equations, applying a stan- dard k-c turbulence model. A number of five reaction kinetic mechanisms having 50 - 100 species and 200 - 1000 elementary reactions called ABF, Miller-Bowman, GRI-Mech3.0, Warnatz, and Qin were employed to study the effect of combustion chemistry schemes on soot predictions. The results showed that of various kinetic schemes being studied, each yields similar accuracy in temperature prediction when compared with experimental data. With respect to soot prediction, the kinetic scheme containing benzene elementary reactions tends to result in a better prediction on soot concentrations in comparison to those contain no benzene elementary reactions. Among five kinetic mechanisms being studied, the Qin combustion scheme mechanism turned to yield the best prediction on both flame temperature and soot levels.

Importance measure system of fuzzy and random input variables and its solution by point estimates

For structure system with fuzzy input variables as well as random ones, a new importance measure system is presented for evaluating the effects of the two kinds of input variables on the output response. Based on the fact that the fuzziness of the output response is determined by that of the input variable, the presented measure system defines the importance measures which evaluate the effect of the fuzzy input variable. And for the random input variable, the importance measure system analyzes its effect from two aspects, i.e. its effect on the central distribution position and that on the fuzzy degree of the membership function of the output response. Taking the effects of the two kinds of input variables on the first moment and second one of the output response into account, the definitions of the importance measures of the input variables are given and their engineering significations are demonstrated. Combining with the advantages of the point estimates of Zhao and Ono, a solution of the proposed importance measures is provided. Several examples show that the proposed measure system is comprehensive and reasonable, and the proposed solution can improve computational efficiency considerably with acceptable precision.

FURTHER STUDY STRONG CONSISTENCY OF M ESTIMATOR IN LINEAR MODEL FOR ρ-MIXING RANDOM SAMPLES

The strong consistency of M estimators of the regression parameters in linear models for ρ-mixing random errors under some mild conditions is established, which is an essential improvement over the relevant results in the literature on the moment conditions and mixing errors. Especially, Theorem of Wu （2005） is improved essentially on the moment conditions.

Some Properties for the Estimators in Linear Mixed Models

Linear mixed models （LMMs） have become an important statistical method for analyzing cluster or longitudinal data. In most cases, it is assumed that the distributions of the random effects and the errors are normal. This paper removes this restrictions and replace them by the moment conditions. We show that the least square estimators of fixed effects are consistent and asymptotically normal in general LMMs. A closed-form estimator of the covariance matrix for the random effect is constructed and its consistent is shown. Based on this, the consistent estimate for the error variance is also obtained. A simulation study and a real data analysis show that the procedure is effective.

Burnett Order Stress and Spatially-Dependent Boundary Conditions for the Lattice Boltzmann Method

Stress boundary conditions for the lattice Boltzmann equation that are consistent to Burnett order are proposed and imposed using a moment-based method.The accuracy of the method with complicated spatially-dependent boundary conditions for stress and velocity is investigated using the regularized lid-driven cavity flow.The complete set of boundary conditions,which involve gradients evaluated at the boundaries,are implemented locally.A recently-derived collision operator with modified equilibria and velocity-dependent collision rates to reduce the defect in Galilean invariance is also investigated.Numerical results are in excellent agreement with existing benchmark data and exhibit second-order convergence.The lattice Boltzmann stress field is studied and shown to depart significantly from the Newtonian viscous stress when the ratio of Mach to Reynolds numbers is not negligibly small.