关于图形中肥尾的判断

NO.PZ2018122701000024

问题如下：

Consider the following QQ plot:

Empirical Quantiles

Which is the most likely true statement about the QQ plot?

选项：

The empirical distribution is actually parametric.

The empirical distribution has positive skew.

The empirical distribution has leptokurtosis (excess kurtosis>0)

If we perform a linear transformation of location and scale, the distribution is approximately normal.

解释：

C is correct.

考点 $：$ Quantile-Quantile Plots

解析 $：$ Heavy tails: the steeper slope - i.e., greater than 1.0 - at the tails indicates the tails are heavier than the reference distribution

右侧的肥尾是怎么分析出来的？

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1 个答案

李坏_品职助教 · 2025年05月02日

嗨，爱思考的PZer你好：

横坐标表示正态分布的分位点，纵坐标表示实际的分布情况。

如果这个分布是严格服从正态分布，那么应该是一条45度向上倾斜的直线。

现在实际分布情况的斜率，要明显大于45度直线的斜率。

当正态分布还处于-3的分位点时，实际的分布已经处于-6；当正态分布处于3的分位点时，实际的分布早已处于6. 这说明无论是左侧尾部还是右侧尾部，实际的分布情况的极端值都迅速累积，说明尾部比正态分布更肥。

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