论文标题
计算具有已知概率函数的连续单变量分布的最高密度区域
Computing highest density regions for continuous univariate distributions with known probability functions
论文作者
论文摘要
我们在计算环境中检查了计算最高密度区域（HDR）的问题，在该环境中，用户可以访问分布的密度函数和分位功能（例如，在统计语言r中）。我们根据密度函数的形状检查了几个常见的连续单变量分布。这包括单调密度，准孔孔和准凸密度以及一般的多模式密度。在每种情况下，我们都会显示用户如何通过将问题作为非线性优化问题来计算来自分位数和密度功能的HDR。我们在R中实施这些方法以获得一般功能，以计算分布类别的HDR，以及常用的分布族。我们将我们的方法与计算HDRS的现有R软件包进行了比较，我们表明我们的方法在准确性和平均速度方面都表现出色。
We examine the problem of computing the highest density region (HDR) in a computational context where the user has access to a density function and quantile function for the distribution (e.g., in the statistical language R). We examine several common classes of continuous univariate distributions based on the shape of the density function; this includes monotone densities, quasi-concave and quasi-convex densities, and general multimodal densities. In each case we show how the user can compute the HDR from the quantile and density functions by framing the problem as a nonlinear optimisation problem. We implement these methods in R to obtain general functions to compute HDRs for classes of distributions, and for commonly used families of distributions. We compare our method to existing R packages for computing HDRs and we show that our method performs favourably in terms of both accuracy and average speed.
