Survival distributions arising from two families and generated by transformations

Two families of distributions are introduced and studied within the framework of parametric survival analysis. The families are derived from a general linear form by specifying a function of the survival function with certain restrictions. Distributions within each family are generated by transformations of the survival time variable subject to certain restrictions. Two specific transformations were selected and, thus, four distributions are identified for further study. The distributions have one scale and two shape parameters and include as special cases the exponential, Weibull, log-logistic and Gompertz distributions. One of the new distributions, the modified Weibull, is studied in some detail.

The distributions are developed with an emphasis on those features that data analysts find especially useful for survivorship studies, A wide variety of hazard shapes are available. The survival, density and hazard functions may be written in simple algebraic forms. Parameter estimation is demonstrated using the least squares and maximum likelihood methods. Graphical techniques to assess goodness of fit are demonstrated. The models may be extended to include concmitant information.     

Forecasting of some; transformed series

The delta method is proposed as a. retransformation approach for coramputing forecasts for a nonstationary process (Z$inf:t$einf t, = 1, 2, ...), A derived variance stabilizing transformation technique is also used to compute forecasts, The performance of the two methods is compared to other techniques. Numerical results show that forecasts based on the variance stabilizing transformation method (VSTM) can lead to forecasts with a lower mean square error (MSE) as compared to other transformation techniqnes.     

On inequalities for functionals of bivariate distributions with monotone failure rates

Estimates are obtained for functionals of convolutions of distributions functions with monotone failure rate.These estimates are expressed in terms of the corresponding functionals for convolutions of bivariate exponential distributions with dependent components.The obtained inequalities cannot be improved in a special sense in the class of all bivariate distributions with the monotone failure rate.The mentioned inequalities are used for the estimation of some characteristics of bivariate cumulative processes and to obtain conservative confidence bands.     

A set of independent sequential residuals for the multivariate regression model

In this paper a set of residuals for the multivariate linear regression model is introduced. These residuals are shown to be independent with known distributions which do not depend on the parameters of the model. Transformations of the mentioned residuals may be used to construct exact α goodness-of-fit tests for the multivariate regression model.     

A method for estimating age-specific reference intervals ('normal ranges') based on fractional polynomials and exponential transformation

The age-specific reference interval is an important screening tool in medicine. Put crudely, an individual whose value of a variable of interest lies outside certain extreme centiles may be suspected of abnormality. We propose a parametric method for constructing such intervals. It provides smooth centile curves and explicit formulae for the centile estimates and for standard deviation (SD) scores (age-standardized values). Each parameter of an exponential–normal or modulus–exponential–normal density is modelled as a fractional polynomial function of age. Estimation is by maximum likelihood. These three- and four-parameter models involve transformations of the data towards normality which remove non-normal skewness and/or kurtosis. Fractional polynomials provide more flexible curve shapes than do conventional polynomials. The method easily accommodates binary covariates facilitating, for example, parsimonious modelling of age- and sex-specific centile curves. A method of calculating precision profiles for centile estimates is proposed. Goodness of fit is assessed by using Q–Q -plots and Shapiro–Wilk W -tests of the SD scores, and likelihood ratio tests of the parameters of an enlarged model. Four substantial real data sets are used to illustrate the method. Comparisons are made with the semiparametric LMS method of Cole and Green.     

系统对应说与转化机制

夸克等人的系统对应说和张今的转化机制均属语法转换领域中的学说。这两个学说都不同程度地受到转换生成语法的影响 ,但它们不采用其理论系统 ,而是以一种非正式的方法来说明结构或句型之间的关系。本文旨在对二者进行比较研究 ,探讨其共性和差异     

Designing for a Response Transformation Parameter

We investigate D -optimum designs for experiments in which a linear model holds after an unknown power transformation of the univariate response variable. This is a departure from standard D -optimal design in which an appropriate scale for the response is assumed known before data collection. The design problem that we formulate is intrinsically non-linear, requiring characterization of likely parameter values. Several applications are presented to illustrate the importance of recognizing the role of response transformations at the design stage.     

Vec and vech operators for matrices,with some uses in jacobians and multivariate statistics

The vec of a matrix X stacks columns of X one under another in a single column; the vech of a square matrix X does the same thing but starting each column at its diagonal element. The Jacobian of a one-to-one transformation X → Y is then ∣∣?(vecX)/?(vecY) ∣∣ when X and Y each have functionally independent elements; it is ∣∣ ?(vechX)/?(vechY) ∣∣ when X and Y are symmetric; and there is a general form for when X and Y are other patterned matrices. Kronecker product properties of vec(ABC) permit easy evaluation of this determinant in many cases. The vec and vech operators are also very convenient in developing results in multivariate statistics.     

“三化论”视角下许渊冲诗词“意美”的英译策略研究

英译唐诗宋词时，能准确传达一字一词、一境一情是一项艰巨的任务。许渊冲先生用他的“三化论”开创了自己独特的翻译风格，既译词句，也译情感。选择“三化论”视角，通过举例赏析，主要探究“意美”传递与“等化、深化、浅化”的有机结合，分析许渊冲诗词英译中所采用的英译策略，旨在丰富翻译美学理论的具体实践，启迪译者灵活、准确地再现原诗词的美学内涵，也让译者体会只有细细琢磨和推敲才能得出较为理想的译诗，才能更深刻地感染读者，更好地传播中国传统诗词的韵味和美感。