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突变理论在生物科学统计建模中的应用AI 解读

Although catastrophe theory has been applied with mixed success to many problems in the biosciences, very few of these applications have used any form of statistical modeling. We present examples of the applications of statistical catastrophe theory in the analysis of experimental data. These include examples of hysteresis effects, bifurcation effects, and the full cusp catastrophe model. The methods of statistical catastrophe theory draw upon the theories of parameter…

指数族多峰分布的估计与矩递推关系AI 解读

Multimodal generalizations of the normal, gamma, inverse gamma, and beta distributions are introduced within a unified framework. These multimodal distributions, belonging to the exponential family, require fewer parameters than corresponding mixture densities and have unique maximum likelihood estimators. Simple moment recursion relations, which make maximum likelihood estimation feasible, also yield easily computed estimators that themselves are shown to be consistent and…