Recent developments in the probabilistic and statistical analysis of probability density functions are reviewed. Density functions are treated as data objects for which suitable notions of the center of distribution and variability are discussed. Special attention is given to nonlinear methods that respect the constraints density functions must obey. Regression, time series and spatial models are discussed. The exposition is illustrated with data examples. A supplementary vignette contains expanded versions of data analyses with accompanying codes.

中文翻译：

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将概率密度函数建模为数据对象

回顾了概率密度函数的概率和统计分析的最新进展。密度函数被视为数据对象，讨论了分布中心和可变性的适当概念。特别注意尊重密度函数必须遵守的约束的非线性方法。讨论了回归、时间序列和空间模型。该说明通过数据示例进行说明。补充小插曲包含数据分析的扩展版本以及随附的代码。