On multimodal distributions

As a sequel to khinchine's definition of unimodality a multimodal distribution function is defined. A characterization for such a distribution is given. The convolution of two such distributions is studied.     

A New Kuznetsian Dynamic: The Knowledge Economy and Income Inequality in the United States, 1917–2008

The rise of the knowledge economy resulted in higher levels of income inequality in the United States and forced many to question the Kuznets Inverted‐U hypothesis. However, this study argues that the establishment of a knowledge economy does not negate the importance of employment shifts for income inequality. Instead, the expansion of knowledge employment alters the major sectors that are responsible for the overall distribution of income. To this end, this article presents the key argument that the current service–knowledge transition impacts income inequality trends, of today, in a way that is similar to the agricultural–industrial transition, of the past. According to the autoregressive conditional heteroskedasticity regressions, the agricultural–industrial transition returns stronger associations with income inequality in the United States before 1950. The agricultural–industrial transition's impact diminishes thereafter as the service–knowledge transition shares a more robust association with income inequality after 1980.     

关于农村信用社模式改革的思考

农村信用社经过多年的改革许多省份都选择了省联社的模式，在这种模式下的农村信用社有许多缺点。为了避免这些缺点，许多人建议将农村信用社改组为农村商业银行。但如果再建立省级农村商业银行容易使农村地区更难得到贷款的支持，所以建议在农村信用社下一步的改革中设立两级的农村商业银行。     

倒立摆小车系统的数学模型和主要参数的确定

倒摆系统参数测定的精确与否对控制质量有较大影响。本文从整个小车系统出发推导了求取该系统主要参数(M_0、F_0、G_0)的公式。证明了该系统可等同于一个惯性环节与一个积分环节相串联的结构形式,并导出了该结构形式下系统参数β_1、β_2和小车拖动系统参数M_0、F_0的G_0的关系式。文中还介绍了测取β_1、β_2的一种实用方法。     

FINITE MIXTURE OF CERTAIN DISTRIBUTIONS

ABSTRACT

A two parameter extended form of standard gamma function is suggested which provide extra flexibility to the density function over positive range. A finite mixture of beta distribution is defined by using the suggested extended form. The shape of density function of extended gamma distribution and also that of finite mixture of beta distribution for various values of the parameters are shown. Inverted distribution of extended gamma and that of finite mixture of beta distribution are given.     

Designing and integrating composite networks for monitoring multivariate gaussian pollution fields

Networks of ambient monitoring stations are used to monitor environmental pollution fields such as those for acid rain and air pollution. Such stations provide regular measurements of pollutant concentrations. The networks are established for a variety of purposes at various times so often several stations measuring different subsets of pollutant concentrations can be found in compact geographical regions. The problem of statistically combining these disparate information sources into a single 'network' then arises. Capitalizing on the efficiencies so achieved can then lead to the secondary problem of extending this network. The subject of this paper is a set of 31 air pollution monitoring stations in southern Ontario. Each of these regularly measures a particular subset of ionic sulphate, sulphite, nitrite and ozone. However, this subset varies from station to station. For example only two stations measure all four. Some measure just one. We describe a Bayesian framework for integrating the measurements of these stations to yield a spatial predictive distribution for unmonitored sites and unmeasured concentrations at existing stations. Furthermore we show how this network can be extended by using an entropy maximization criterion. The methods assume that the multivariate response field being measured has a joint Gaussian distribution conditional on its mean and covariance function. A conjugate prior is used for these parameters, some of its hyperparameters being fitted empirically.     

A Note on the Arithmetic—Geometric—Harmonic Mean Inequalities

The familiar inequalities relating the arithmetic, geometric, and harmonic means are derived as corollaries to likelihood ratio tests.     

Truncated inverted generalized exponential distribution and its properties

The inverted generalized exponential distribution is defined as an alternative model for lifetime data. The existence of moments of this distribution is shown to hold under some restrictions. However, all the moments exist for the truncated inverted generalized exponential distribution and closed-form expressions for them are derived in this article. The distributional properties of this truncated distribution are studied. Maximum likelihood estimation method is discussed for the estimation of the parameters of the distribution both theoretically and empirically. In order to see the modeling performance of the distribution, two real datasets are analyzed.     

Bayesian multivariate normal analysis under the extended reflected normal loss function

This paper considers the Bayesian analysis of the multivariate normal distribution under a new and bounded loss function, based on a reflection of the multivariate normal density function. The Bayes estimators of the mean vector can be derived for an arbitrary prior distribution of [d]. When the covariance matrix has an inverted Wishart prior density, a Bayes estimator of[d] is obtained under a bounded loss function, based on the entropy loss. Finally the admissibility of all linear estimators c[d]+ d for the mean vector is considered     

a bayesian analysis of the multivariate mixed-linear model

The Bayesian analysis of the multivariate mixed linear model is considered. The exact posterior distribution for the fixed effects matrix and the error covariance matrix are obtained. The exact posterior means and variances of the Bayesian estimators for the covariance matrices of random effects are also derived. These posterior moments are computed without constrained optimization and numerical integration. The calculations are feasible for arbitrary models. Reasonable approximations for the posterior distributions for the covariance matrices associated with the random effects are obtained also. Results are illustrated with a numerical example.