论文标题
具有有限和无限支持的新的非负分布
A new non-negative distribution with both finite and infinite support
论文作者
论文摘要
Tukey-$λ$分布具有有趣的属性，包括（i）对于某些参数值，它具有有限的支持，而对于其他参数值，并且（ii）可以模仿其他几个分布，例如Tukey Distribution的参数估计是一种识别适当的分布以模拟一组数据的方法。 Tukey- $λ$是对称的。在这里，我们定义了一个新类{\ em非负}分布，具有与Tukey-$λ$分布相似的属性。与tukey-c $λ$分布一样，我们的分布是根据其分位数函数定义的，在这种情况下，该函数由Polyrogarithm函数给出。我们显示分布的支持为Riemann Zeta函数（有限时），并为期望提供了封闭形式，提供了简单的手段来计算CDF和PDF，并表明它与统一，指数，逆β和极值分布有关系。
The Tukey-$λ$ distribution has interesting properties including (i) for some parameters values it has finite support, and for others infinite support, and (ii) it can mimic several other distributions such that parameter estimation for the Tukey distribution is a method for identifying an appropriate class of distribution to model a set of data. The Tukey-$λ$ is, however, symmetric. Here we define a new class of {\em non-negative} distribution with similar properties to the Tukey-$λ$ distribution. As with the Tukey-$λ$ distribution, our distribution is defined in terms of its quantile function, which in this case is given by the polylogarithm function. We show the support of the distribution to be the Riemann zeta function (when finite), and we provide a closed form for the expectation, provide simple means to calculate the CDF and PDF, and show that it has relationships to the uniform, exponential, inverse beta and extreme-value distributions.
