论文标题
您看到的以及看不到的内容：概率分布的隐藏时刻
What You See and What You Don't See: The Hidden Moments of a Probability Distribution
论文作者
论文摘要
经验分布将其最大值作为自然审查。我们查看“隐藏的尾巴”，即分布的一部分，超过最大值，样本量为$ n $。使用极值理论，我们检查了隐藏尾巴的属性，并计算其订单$ p $的力矩。该方法对于显示一个给定的$ n $的偏差在可见的样本中的平均值与真实统计平均值（或更高的矩（或更高的矩）之间的偏见非常有用，对于$α$来说是相当大的，对于$α$来说是相当大的。除其他属性外，我们注意到“隐藏的”瞬间$ 0 $ 0，即$ 0 $，也就是说，$ 0，即$ 0，即$} $} $} $} $。不论尺度和尾部指数的参数化。
Empirical distributions have their in-sample maxima as natural censoring. We look at the "hidden tail", that is, the part of the distribution in excess of the maximum for a sample size of $n$. Using extreme value theory, we examine the properties of the hidden tail and calculate its moments of order $p$. The method is useful in showing how large a bias one can expect, for a given $n$, between the visible in-sample mean and the true statistical mean (or higher moments), which is considerable for $α$ close to 1. Among other properties, we note that the "hidden" moment of order $0$, that is, the exceedance probability for power law distributions, follows an exponential distribution and has for expectation $\frac{1}{n}$ regardless of the parametrization of the scale and tail index.
