On a property of the exponential distribution

If t is an independent exponentially distributed random variable, the distribution p = [t - x] is a modified geometric distribution, similar to the result of HAWKINS and KOTZ (1976), x is uniform.     

Some Tests for k£2 Upper Outliers in an Exponential Sample

The sequential procedure for testing up to k upper outliers proposed by Kimber (1982) for one-parameter exponential distribution is modified to a two-parameter exponential distribution. Further null distributions of some test statistics for an upper outlier-pair in a complete or censored sample from a two-parameter exponential distribution are given. Percentage points of the statistic T₁ are tabulated.     

Estimation of Exponential Parameters in the Presence of Outliers

In the present paper we discuss the estimation of the parameter and survival function of an exponential population. It is assumed that the sample based on which the estimation is done, contains k outliers that are also exponentially distributed with parameter, a constant multiple of that of the original distribution.     

时滞传染病模型的指数稳定性

利用分析技巧研究了一类SEIRS传染病模型的动力学行为.结论表明如果再生数小于1,则带变时滞的传染病模型的无病平衡点是全局指数渐近稳定的,如果再生数大于1,得到传染病平衡点局部指数稳定的充分条件,同时给出了例子说明结论的有效性.     

Randomized Blocks Analysis for the Exponential Distribution

A procedure for analyzing randomized blocks experiments for uncensored exponential random variables is presented. Its small sample behavior is studied in several simulations. Sample size requirements are given.     

Selfing rates in natural populations of Echium vulgare: a combined empirical and model approach

1. We quantified geitonogamous selfing in Echium vulgare , a self-compatible, bumble-bee pollinated plant. A maximum estimate of selfing was determined using a paternity analysis with RAPDs. In the first experiment, bumble-bees visited a sequence of virgin flowers. The percentage selfing increased rapidly from 12% in the first flower visited, up to 50% in the 15th flower visited in the sequence. In the second experiment, when bees visited plants in a natural population, the average selfing of plants increased with the number of open flowers from 0% to maximally 33%.
2. The results obtained in both experiments are consistently lower than predicted by our model on pollen dynamics ( Rademaker, de Jong & Klinkhamer 1997 ). We modified the model on pollen dynamics to link it more to the field situation with observations on flower stage, flower opening and bumble-bee preference, so that the bumble-bees encounter a variable number of pollen grains per flower. We also adjusted the parameters. If less pollen adheres to the bee (25% instead of 50%) after removal from the anthers, or if bees arrive at a plant with more pollen grains (6000 instead of 4448), the predictions of the model in regard to selfing could be improved but were still high compared with the observed selfing rates measured with RAPDs.
3. We suggest that the model is consistent with pollen dynamics in the field. However, post-pollination processes like selective abortion could play a role in E. vulgare .     

The Relationship Between Two Statistical Tests for the Comparison of Two Exponential Distributions

To compare two exponential distributions with or without censoring, two different statistics are often used; one is the F test proposed by COX (1953) and the other is based on the efficient score procedure. In this paper, the relationship between these tests is investigated and it is shown that the efficient score test is a large-sample approximation of the F test.     

北美CHIHUAHUAN荒漠啮齿动物群落动态III．变量的频次分布和预测

本文用х²方和柯尔莫哥洛夫检验分析了北美Chihuahuan荒漠啮齿动物群落6个生态学变量的频次分布,并用移动平均和指数平滑方法拟合了这些变量的动态变化。结果显示：1)结合种群密度、生物量、物种均匀性和生物量均匀性服从正态分布;2)物种数和物种多样性的频次为向右偏斜的分布,无法用常见的理论分布来近似表示;3)单移动平均和双移动平均分别较好地描述了物种多样性和物种均匀性;4)其余4个变量可用单指数平滑来较好的描述．     

突变率计算中细菌群体生长不同步系数的修正

遗传和变异是生物学最根本的问题之一, 而突变率估算有助于比较不同基因、不同生物个体、以及不同生长环境下突变率的差异。细菌因其生长繁殖快速和群体庞大而成为突变率估算的最方便的模式生物。突变率的定义为：每个细胞每一世代发生突变的概率。通常表示为。其中, 为突变数, 为细菌分裂的世代数。国内外的微生物学及遗传学教科书和专著中, 在计算细菌突变率时, 有些引入了ln2作为群体中细菌分裂不同步的校正系数, 有些则没有。那么, 在突变率估算中, 究竟是否应该对非同步生长群体进行校正？如果需要校正, 仅仅引入ln2作为     

Tree-Structured Exponential Regression Modeling

A method for fitting piecewise exponential regression models to censored survival data is described. Stratification is performed recursively, using a combination of statistical tests and residual analysis. The splitting criterion employed in cross-validation is the average squared error of the residuals. The bootstrap is employed to keep the probability of a type I error (the error of discovering two or more strata when there is only one) of the method close to a predetermined value. The proposed method can thus also serve as a formal goodness-of-fit test for the exponential regression model. Real and simulated data are used for illustration.     

变时滞SIS流行病模型的稳定性分析

研究了一类时滞SIS流行病模型,分析了该模型无病平衡点和地方平衡点的存在性,得到了无病平衡点全局指数渐近稳定和地方病平衡点局部指数渐近稳定的充分条件,同时给出了地方病平衡点吸引区域的估计。