Question

Scipy（迄今为止，版本0.19.1）Statistical Functions模块（又名scipy.stats）包含scipy.stats.skew和scipy.stats.kurtosis的函数来计算偏斜和峰度（分别为第3和第4统计矩）。此外，scipy.stats.describe会调用这些函数。

偏度和峰度的定义可能有所不同;因此，在文献中没有就它们达成共识。然后，在Scipy中使用哪些数学表达式来定义上述两个函数中的偏差和峰度及其默认设置？

Answer 1

scipy.stats.skew和scipy.stats.kurtosis都调用scipy.stats.moment的函数，该函数计算数据样本的第k个中心矩的以下内容：

<script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.0/MathJax.js?config=TeX-AMS_HTML-full"></script> <script type="text/x-mathjax-config"> MathJax.Hub.Config({"HTML-CSS": { preferredFont: "TeX", availableFonts:["STIX","TeX"], linebreaks: { automatic:true }, EqnChunk:(MathJax.Hub.Browser.isMobile ? 10 : 50) }, tex2jax: { inlineMath: [ ["$", "$"], ["\\\\(","\\\\)"] ], displayMath: [ ["$$","$$"], ["\\[", "\\]"] ], processEscapes: true, ignoreClass: "tex2jax_ignore|dno" }, TeX: { noUndefined: { attributes: { mathcolor: "red", mathbackground: "#FFEEEE", mathsize: "90%" } }, Macros: { href: "{}" } }, messageStyle: "none" });   </script>

$$m_k = \frac{1}{n} \sum_{i = 1}^n (x_i - \bar{x})^k$$

因此，scipy.stats.skew使用默认设置（例如bias=True）计算：

<script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.0/MathJax.js?config=TeX-AMS_HTML-full"></script> <script type="text/x-mathjax-config"> MathJax.Hub.Config({"HTML-CSS": { preferredFont: "TeX", availableFonts:["STIX","TeX"], linebreaks: { automatic:true }, EqnChunk:(MathJax.Hub.Browser.isMobile ? 10 : 50) }, tex2jax: { inlineMath: [ ["$", "$"], ["\\\\(","\\\\)"] ], displayMath: [ ["$$","$$"], ["\\[", "\\]"] ], processEscapes: true, ignoreClass: "tex2jax_ignore|dno" }, TeX: { noUndefined: { attributes: { mathcolor: "red", mathbackground: "#FFEEEE", mathsize: "90%" } }, Macros: { href: "{}" } }, messageStyle: "none" });   </script>

$$ S = \frac{m_3}{(m_2)^{1.5}} $$

scipy.stats.kurtosis使用默认设置：

<script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.0/MathJax.js?config=TeX-AMS_HTML-full"></script> <script type="text/x-mathjax-config"> MathJax.Hub.Config({"HTML-CSS": { preferredFont: "TeX", availableFonts:["STIX","TeX"], linebreaks: { automatic:true }, EqnChunk:(MathJax.Hub.Browser.isMobile ? 10 : 50) }, tex2jax: { inlineMath: [ ["$", "$"], ["\\\\(","\\\\)"] ], displayMath: [ ["$$","$$"], ["\\[", "\\]"] ], processEscapes: true, ignoreClass: "tex2jax_ignore|dno" }, TeX: { noUndefined: { attributes: { mathcolor: "red", mathbackground: "#FFEEEE", mathsize: "90%" } }, Macros: { href: "{}" } }, messageStyle: "none" });   </script>

$$ K = \frac{m_4}{(m_2)^{2}} $$

Scipy中使用的偏斜和峰度的默认表达式是什么？

1 个答案: