On the convolution of normal and t random variables

The need for the convolution of normal and Student's t random variables arises in many areas. Since the 1930s, various authors have attempted to derive closed-form expressions for the probability density function (pdf) of the convolution, but with little success. Here, general closed-form expressions are derived for the pdf.     

Estimation of the parameters of a general student’s t distribution

We have observations for a t distribution with unknown mean, variance, and degrees of freedom, each of which we wish to estimate. The major problem lies in the estimate of the degrees of freedom. We show that a relatively efficient yet very simple estimator is a given function of the ratio of percentile estimates. We derive the appropriate estimator, provide equations for transformation and standard errors, contrast this with other estimators, and give examples.     

Tail Behavior of the General Error Distribution

An inequality on the tail behavior of the general error distribution and an asymptotic Mills-type ratio are established. Two applications are provided. The first application considers the asymptotic behavior of the ratio of probability densities and the ratio of the tails of the general error and normal distributions. The second application establishes the asymptotic distribution of the partial maximum of an independent and identically distributed sequence from the general error distribution.     

A linear algebraic algorithm for reducing the support size of t-designs and to generate a basis for trades

A simple linear algebraic algorithm to generate a basis of the null space of a given integral matrix is utilized to present a computer algorithm, which in general, is used to reduce the support size of a given design as in a theorem of FoodyHedayat (Theorem 4.1, 1977), and in particular, it is used to produce a basis for trades. The computations based on this algorithm is of order of a polynomial function.     

An algorithn for generating a basis of the trades on t-designs

For the purpose of constructing t-designs (a special family of incomplete block designs) from a given design, a trade off method has been introduced and studied [Hedayat and Li (1979)]. In this paper, we present a computer algorithm for generating a basis of the trades on t-designs utilizing the results of Graham, Li and Li (1980).     

Robustness of the two - sample t - test under violations of the homogeneity of variance assumption,part ii

In a previous paper, Posten, Yeh and Owen (1982), the robustness of the type I error for the two tailed two sample t - test was studied under departures from the assumption of equal variances. The level of robustness of this test was then quantified under the concept of regions of robustness. These results are extended here to the one - tailed test for the same problem. The high level of robustness for equal or nearly equal sample sizes observed in the previous study is again documented quantitatively.     

Bayesian forecasting with changing linear models

This investigation considers a general linear model which changes parameters exactly once during the observation period. Assuming all the parameters are unknown and a proper prior distribution, the Bayesian predictive distribution of the future observations is derived.

It is shown that the predictive distribution is a mixture of multivariate t distributions and that the mixing distribution is the marginal posterior mass function of the change point parameter.     

构建东亚区域合作架构的挑战

经过20年的经济发展,东亚在世界上的地位已经大大提高,已成为世界上一支重要的力量。在新的历史条件和背景下,东亚须更有目标地和战略性地组织起来,但东亚区域架构的构建面临诸多挑战。中美关系是世界上和影响东亚地区合作的最重要的关系,构建东亚区域合作架构应当乐于见到美国的参与。总之,关于东亚区域合作架构的安排的共识正在形成,包括四个要素：即10＋3、10＋6、东盟以及APEC。10＋3应当成为东亚区域合作和东亚共同体建设的主导,10＋6应当发展成为关于地区重要战略利益问题有效的领导人对话论坛,东盟则必须实现东盟共同体的建设,APEC则在于推动亚太国家间的尤其是经济的关系。     

A Retrievable Recipe for Inverse t

Although the percentage points of the Student-t distribution have been widely tabulated, a simple approximation is given and derived in this article. The approximation can be re-derived easily, since it is based on the percentage points from the Gaussian distribution, and can thus be used for applications requiring non-integer degrees of freedom (e.g., Welch's two-sample t test) and for arbitrary significance levels (e.g., for Bonferroni multiple comparison procedures). Comparisons between this approximation and others suggested in the literature indicate three-digit accuracy for even small degrees of freedom and tail areas.