递推法求一元n次实系数多项式函数的完全等价n次Bezier参数曲线

用递推方法论证了至少存在一条n次Bezier参数曲线与一元n次实数多项式函数完全等价。同时给出了将一元n次实纱多项式转换为完全等价的n次Bezier参数曲线的方法。     

A relation for the covariances of order statistics from n independent and non-identically distributed random variables

We derive a simple relation satisfied by the covariances of order statistics in the i.i.d. case and then generalize it to the case when the variables are independent and non-identically distributed. This relation could be employed successfully either to check the calculations or to reduce the amount of direct computations involved in evaluating the covariances of order statistics from an outlier model.     

On characterizing the normal and poisson distributions

Multivariate normal, correlated multivariate Poisson and multiple Poisson distributions are characterized, in the class of exponential-type distributions, by the properties of the linear combinations of the variables, the properties of their cumulants and the recurance relation between the cumulants.     

Association between long-term erectile dysfunction and biochemical recurrence after permanent seed I125 implant brachytherapy for prostate cancer. A longitudinal study of a single-institution

We aimed to investigate the predictive factor of erectile dysfunction (ED) in prostate cancer (PCa) patients who underwent low-dose permanent I¹²⁵ seed implant brachytherapy and to investigate if ED could represent a patient’s reported outcome measures (PROMs) of efficacy of BT and indirectly associated with biochemical recurrence free survival (BRFS). From 2000 to 2012, 176 consecutive patients with low-risk PCa underwent BT. ED was evaluated with the International Index of Erectile Function (IIEF-5). Cox regression analysis was performed to assess significant predictors of mild-to-severe ED and BRFS after BT, including covariates. The 10-year actuarial rate of ED was 66%. Subjects with severe ED had higher values of D90 (183.0 versus 177.0; p?p?p?p?=?0.20), while D90?≤?180?Gy independently predicted BCR (HR: 4.65; [95%CI: 1.25–17.34]; p?125 implant, but it is not associated with better BRFS.     

简论郑板桥的天道循环观

郑板桥的史论较多,他对历史的评价与他的喜怒哀乐是联系在一起的。但其历史观是相对稳定的。郑板桥历史评价的基点是他的天道循环观,他认为社会与人生都是一场大戏,世事总是翻来又复去的;同时在天道循环观的基础上郑板桥又出现了一种历史虚无主义的倾向,他认为人一切奋斗的结果都会因天道循环而走向缥缈;当然,他也认为,虽然天道循环是不可抗拒的,但人的因素不可忽视,只要人发挥积极的作用,人与社会就可以延缓这种循环的进程。     

Recurrence relations for moments of different orders of extremes from gamma distribution

Certain recurrence relations for the moments of different orders of the largest order statistic from a gamma distribution with shape parameter p are obtained. By using this it is shown that for obtaining the moment of any order of each order statistic of a sample of size n from the gamma distribution, one has to evaluate at most n-2 single integrals.     

A Measure of partial association between disease and genotype for the two-parent problem

The two-parent disease-genotype association problem is studied from the point of view of a coefficient of association between the disease phenotype of the child and the disease phenotypes of the parents, in the presence of some genotypic information about the parents. This coefficient of partial association is derived, and certain tests of hypotheses are constructed. The results are shown to be useful in estimation of recurrence risks, and in understanding the nature of the association between child and parental disease phenotypes.     

Order statistics from non-identical right-truncated Lomax random variables with applications

In this paper, we derive some recurrence relations for the single and the product moments of order statistics from n independent and non-identically distributed Lomax and right-truncated Lomax random variables. These recurrence relations are simple in nature and could be used systematically in order to compute all the single and product moments of all order statistics in a simple recursive manner. The results for order statistics from the multiple-outlier model (with a slippage of p observations) are deduced as special cases. We then apply these results by examining the robustness of censored BLUE's to the presence of multiple outliers. Received: November 30, 1998; revised version: March 8, 2000     

Generalized polya eggenberger family of distributions and its relation to lagrangian katz family

Janardan (1973) introduced the generalized Polya Eggenberger family of distributions (GPED) as a limiting distribution of the generalized Markov-Polya distribution (GMPD). Janardan and Rao (1982) gave a number of characterizing properties of the generalized Markov-Polya and generalized Polya Eggenberger distributions. Here, the GPED family characterized by four parameters, is formally defined and studied. The probability generating function, its moments, and certain recurrence relations with the moments are provided. The Lagrangian Katz family of distributions (Consul and Famoye (1996)) is shown to be a sub-class of the family of GPED (or GPED ₁ ) as it is called in this paper). A generalized Polya Eggenberger distribution of the second kind (GPED ₂ ) is also introduced and some of it's properties are given. Recurrence relations for the probabilities of GPED ₁ and GPED ₂ are given. A number of other structural and characteristic properties of the GPED ₁ are provided, from which the properties of Lagrangian Katz family follow. The parameters of GMPD ₁ are estimated by the method of moments and the maximum likelihood method. An application is provided.     

Maximum likelihood estimation for the generalized poisson distribution

The generalized Poisson distribution;containing two

parameters and studied by many researchers; describes the distribution of busy periods under a queueing system and has very interesting properties; The probabilities for successive classes depend upon the previous occurrences; The problem of admissible maximum likelihood estimators for for the parameters Is discussed and a necessary and sufficient condition is derived for which unique admissible maximum likelihood estimators exist; The first; order terms in the biases; variances and the covariance of these maximum likelihood estimators are obtained.