A note on the statistical properties of animal locations

A statistical model of the successive locations of an animal in the plane induces a statistical model of the relative positions of successive locations. A common locational model is that the Cartesian coordinates of successive locations in the plane are independent bivariate normal random variables. This note gives the statistical properties of the direction and length of the vector joining successive locations.     

Using a Normal Approximation to Test for the Binomial Distribution

The commonly used method to test for the binomial distribution is the x²-test. In this paper, we introduce an alternative method to test for the binomial distribution. Suppose N is the number of sample groups with n individuals each, x_ij is the jth sample in ith group, a Bernoulli variable with parameter and VVI=s²/[m(1 - m)/n]. Then it is well know that the asymptotic distribution of the statistic (N - 1) VVI is x²(N - 1) under the hypothesis p₁ = p₂ = … = p_N. Here we find that VVI has an asymptotic normal distribution N(1, 2(1 - 1/n)/(N - 1)). Unlike the x²-statistic, the variance of the normal test statistic is a function of n. This method is convenient in detecting spatial patterns and dispersion in the study of diseased organisms (e.g., plants) in field samples.     

南亚热带森林群落种-多度的对数正态分布模型研究

通过对地处南亚热带的广东省黑石顶自然保护区森林群落的定点研究结果的分析表明：当用１,２,３,…分组每种个体数ｒ时,５个不同类型的群落样地的种一多度分布的直方图都呈明显的倒Ｊ－形;经Ｐｒｅｓｔｏｎ“倍程（ｏｃｔａｖｅｓ）”法分组ｒ后,其种－多度都服从对数正态分布。由种－多度模型可以推出另一新的模型一个体一多度分布模型,即Ｉ（Ｒ）＝２R0ＳＯＥＸＰ［［１ｎ２）２／４ａ２〕ＥＸＰ｛－ａ２（Ｒ－（ＲＯ＋１ｎ２／２ａ２）］２｝,它也符合对数正态分布。另外,还运用积分方法推导出估计总体（整个群落）中总种数Ｓ*和总个体数Ｉ*理论值的公式,用此公式估计的结果较为合理。     

On Parametric Confidence Intervals for the Cost‐Effectiveness Ratio

When comparing two competing interventions, confidence intervals for cost‐effectiveness ratios (CERs) provide information on the uncertainty in their point estimates. Techniques for constructing these confidence intervals are much debated. We provide a formal comparison of the Fieller, symmetric and Bonferroni methods for constructing confidence intervals for the CER using only the joint asymptotic distribution of the incremental cost and incremental effectiveness of the two interventions being compared. We prove the existence of a finite interval under the Fieller method when the incremental effectiveness is statistically significant. When this difference is not significant the Fieller method yields an unbounded confidence interval. The Fieller interval is always wider than the symmetric interval, but the latter is an approximation to the Fieller interval when the incremental effectiveness is highly significant. The Bonferroni method is shown to produce the widest interval. Because it accounts for the likely correlation between cost and effectiveness measures, and the intuitively appealing relationship between the existence of a bounded interval and the significance of the incremental effectiveness, the Fieller interval is to be preferred in reporting a confidence interval for the CER.     

北京市三个功能区空气微生物中值直径及粒径分布特征

空气中微生物对人类健康的危害除了与微生物的种类和浓度有关外,还与微生物粒子的大小密切相关,并且不同粒径的空气微生物对人们健康影响的作用机理不同。通过定点试验调查,运用国产安德森生物粒子取样器着重研究北京市3个功能区(文教区-中国科学院生态环境研究中心所在区域、交通干线-西直门和公园绿地-北京植物园)空气微生物的中值直径和粒径分布。结果表明,不同功能区空气微生物的粒径分布相同,空气细菌,真菌与放线菌的粒径分布各不相同。空气细菌粒径呈偏态分布,空气真菌呈对数正态分布,空气放线菌的分布特征与空气真菌相反,主要分布在>8.2μm和<2.0μm级中。不同属真菌的粒径分布也不相同,枝孢属、青霉属和曲霉属呈对数正态分布,链格孢属和无孢菌为偏态分布。空气细菌的中值直径明显大于空气真菌和放线菌。交通干线和公园绿地空气细菌和真菌粒子中值直径明显大于文教区,放线菌粒子中值直径交通干线明显高于文教区和公园绿地。空气微生物中值直径在一年各月中没有明显的变化规律。     

Robustness of Sequential Tests for Means

Three sequential tests of the null hypothesis, μ = μ₀, versus an alternative of the form (μ ? μ₀)²= =σ²d² are compared for different forms of violation of the underlying normal assumption. 10000 samples were simulated for d=0.6; 1.0 and 1.6 (σ² = 1), four (α, β)-combinations and seven alternative distributions. The results show that for small d-values one test is robust for α and another for β. For large d all tests can be used.     

Further Study on the Statistical Test to Detect Spatial Pattern

In the study of spatial patterns, the statistic I' = (n — 1)s²/x was commonly used. In this paper, we found that x — s² has an approximated normal distribution with zero mean if the x_i's (i = 1 to n) are independent identically distributed Poisson variables. Based on this conclusion, the hypothesis that a point pattern is completely random can be tested directly. And a method for the test of spatial patterns was proposed which can be sued as an alternative to the Chi-square based dispersion index test.     

Symmetrically dependent models arising in visual assessment data

Given data from bilateral visual assessments on N subjects at k occasions, we consider inference for contralateral correlations (C) between fellow eyes and lateral correlations (L) among p different assessments of the same eye. Under permutation symmetric dependence structure between observations from fellow eyes and among observations from the same eye, we obtain maximum likelihood estimates of L, C, and L-C. Based on the large-sample estimates of the corresponding covariance structures, we test the hypothesis that the association between fellow eyes is constant across time and the hypothesis that lateral and contralateral associations between any two occasions are the same.