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对于生物医学统计中的一类二次感染问题,提出了一种研究其简单差和危险率的区间估计几何方法.比较系统地研究了非线性多项分布模型参数置信域的几何理论,通过基于曲率的置信域和基于Score检验的置信域这2种方法得到了3个关于参数置信域的定理.抽象出二次感染问题为一个特殊的非线性多项分布(三项分布)模型,其概率密度为p(Y;π(θ))=n!∏3i=1(πyii(θ)/yi!),其中Y={y1,y2,y3}T,∑3i=1πi(θ)=1,∑3i=1yi=n,并进一步指出这些定理对于2×2表以及二次感染问题的应用.
For a class of secondary infection problems in biomedical statistics, a geometric method for interval estimation of the simple difference and hazard rate is proposed. The geometrical theory of the parameter confidence domain of the nonlinear multinomial distribution model is systematically studied. The two methods of the confidence domain of curvature and the confidence domain based on score test have obtained three theorems on the parameter confidence domain. Abstract the secondary infection problem is a special non-linear multinomial distribution (trinomial distribution) model, the probability of which The density is p(Y;π(θ))=n!∏3i=1(πyii(θ)/yi!), where Y={y1,y2,y3}T,∑3i=1πi(θ)=1, ∑3i=1yi=n, and further point out the application of these theorems for 2×2 tables and quadratic infection problems.