分布的偏度是指分布不对称的方向和程度，这种离散的偏差用偏度来衡量。根据偏度的正负可以分为正偏、负偏和无偏（对称）三种情况，对应三种偏度的示意图如下图所示。

 

Error creating node with http://docs.google.com/drawings/image?id=sN0sWyZWTcxFyhgEn1nGl3A&w=179&h=179&rev=23&ac=1. Unable to fetch: http://docs.google.com/drawings/image?id=sN0sWyZWTcxFyhgEn1nGl3A&w=179&h=179&rev=23&ac=1 --- Reason: Response code 404 (Not Found) --- Fetch details: { "attempt": 3, "method": "GET", "errorCode": "ERR_NON_2XX_3XX_RESPONSE", "responseStatusCode": 404, "responseStatusMessage": "Not Found", "requestHeaders": { "user-agent": "got (https://github.com/sindresorhus/got)", "accept-encoding": "gzip, deflate, br" }, "responseHeaders": { "content-type": "text/html; charset=utf-8", "cache-control": "no-cache, no-store, max-age=0, must-revalidate", "pragma": "no-cache", "expires": "Mon, 01 Jan 1990 00:00:00 GMT", "date": "Tue, 17 Sep 2024 08:27:38 GMT", "p3p": "CP=\"This is not a P3P policy! See g.co/p3phelp for more info.\"", "x-chromium-appcache-fallback-override": "disallow-fallback", "content-security-policy": "require-trusted-types-for 'script';report-uri https://csp.withgoogle.com/csp/docs-tt", "content-encoding": "gzip", "server": "ESF", "x-xss-protection": "0", "x-content-type-options": "nosniff", "set-cookie": [ "NID=517=2Px_wjM6ynw2jV5WWGZnXid1IiFUzbFUvNV1GY0HKvyX02Vyt_Z7Ol0k5l0I2FpOiHAmv_EQ8tZBHrJp4NEqIu9KUkCJ-TspZ9Ollv99CnklwMvNQxU7Wy79XYqGn1vRzB124ZPrKSQvzAjt6ybw0fej6ysffxFQea88kQBI7lbHYlWFkfY; expires=Wed, 19-Mar-2025 08:27:38 GMT; path=/; domain=.google.com; HttpOnly" ], "alt-svc": "h3=\":443\"; ma=2592000,h3-29=\":443\"; ma=2592000", "connection": "close", "transfer-encoding": "chunked" } } --- Error creating node with http://docs.google.com/drawings/image?id=sYU0a1CyLAHj-k95K_nesMw&w=179&h=179&rev=8&ac=1. Unable to fetch: http://docs.google.com/drawings/image?id=sYU0a1CyLAHj-k95K_nesMw&w=179&h=179&rev=8&ac=1 --- Reason: Response code 404 (Not Found) --- Fetch details: { "attempt": 3, "method": "GET", "errorCode": "ERR_NON_2XX_3XX_RESPONSE", "responseStatusCode": 404, "responseStatusMessage": "Not Found", "requestHeaders": { "user-agent": "got (https://github.com/sindresorhus/got)", "accept-encoding": "gzip, deflate, br" }, "responseHeaders": { "content-type": "text/html; charset=utf-8", "cache-control": "no-cache, no-store, max-age=0, must-revalidate", "pragma": "no-cache", "expires": "Mon, 01 Jan 1990 00:00:00 GMT", "date": "Tue, 17 Sep 2024 08:28:06 GMT", "x-chromium-appcache-fallback-override": "disallow-fallback", "p3p": "CP=\"This is not a P3P policy! See g.co/p3phelp for more info.\"", "content-security-policy": "require-trusted-types-for 'script';report-uri https://csp.withgoogle.com/csp/docs-tt", "content-encoding": "gzip", "server": "ESF", "x-xss-protection": "0", "x-content-type-options": "nosniff", "set-cookie": [ "NID=517=ZVftqE51nBBKp6lF2nfhSu2b-vqaAfkXEmHwirP6ghaNQsI44WV9sbE_qQCBIj3oWhuneE78XvgcToMt15efZnxqtBlyhmWZeY0c9AlDOa4j0kCBQ0c-NBC-8JTKnSscm275sr_D2Skrkt3W8OaSon0oikx69SKWrRw45V-GdNvddofDnA; expires=Wed, 19-Mar-2025 08:28:06 GMT; path=/; domain=.google.com; HttpOnly" ], "alt-svc": "h3=\":443\"; ma=2592000,h3-29=\":443\"; ma=2592000", "connection": "close", "transfer-encoding": "chunked" } } --- Error creating node with http://docs.google.com/drawings/image?id=sUvedI5EoB2xMw1JFvwNh7g&w=179&h=179&rev=13&ac=1. Unable to fetch: http://docs.google.com/drawings/image?id=sUvedI5EoB2xMw1JFvwNh7g&w=179&h=179&rev=13&ac=1 --- Reason: Response code 404 (Not Found) --- Fetch details: { "attempt": 3, "method": "GET", "errorCode": "ERR_NON_2XX_3XX_RESPONSE", "responseStatusCode": 404, "responseStatusMessage": "Not Found", "requestHeaders": { "user-agent": "got (https://github.com/sindresorhus/got)", "accept-encoding": "gzip, deflate, br" }, "responseHeaders": { "content-type": "text/html; charset=utf-8", "cache-control": "no-cache, no-store, max-age=0, must-revalidate", "pragma": "no-cache", "expires": "Mon, 01 Jan 1990 00:00:00 GMT", "date": "Tue, 17 Sep 2024 08:28:19 GMT", "x-chromium-appcache-fallback-override": "disallow-fallback", "p3p": "CP=\"This is not a P3P policy! See g.co/p3phelp for more info.\"", "content-security-policy": "require-trusted-types-for 'script';report-uri https://csp.withgoogle.com/csp/docs-tt", "content-encoding": "gzip", "server": "ESF", "x-xss-protection": "0", "x-content-type-options": "nosniff", "set-cookie": [ "NID=517=ofZAYCxbpAQfn6peN0VZ8iV8cTE0YJfyGSWTq9QnKfPsCJyudm9XVXigk7mAuSS1HFCWOSWf_9-PWKpY18CI3HI2p2IDk23ZhD7yjc0Ss-bQDSq621hyAoZF89_zEly686Utn1nYOiV-L_1PNGF4Os-S_hERxPek02c8QUGJHnXEaHdaTQ; expires=Wed, 19-Mar-2025 08:28:19 GMT; path=/; domain=.google.com; HttpOnly" ], "alt-svc": "h3=\":443\"; ma=2592000,h3-29=\":443\"; ma=2592000", "connection": "close", "transfer-encoding": "chunked" } } ---

 

很多方法可以把偏度数量化来衡量，常用的有偏斜度、矩偏度系数、四分位数偏度系数和Spearman偏度系数。

 

一、偏斜度

 

偏斜度能够反映以平均值为中心的分布的不对称程度，正偏斜度表示不对称部分的分布更趋向正值，负偏斜度表示不对称的分布更趋向负值。在Excel给出的函数中即采用偏斜度来衡量分布的偏度，对应统计函数库中的SKEW函数。

 

对应偏斜度的计算公式为

 

偏斜度 = Error creating node with https://www.google.com/chart?cht=tx&chf=bg,s,FFFFFF00&chco=000000&chl=%5Cfrac%7Bn%7D%7B(n-1)(n-2)%7D%5CSigma(%5Cfrac%7Bx_%7Bi%7D-%5Cbar%7Bx%7D%20%7D%7Bs%7D)%5E3. Unable to fetch: https://www.google.com/chart?cht=tx&chf=bg,s,FFFFFF00&chco=000000&chl=%5Cfrac%7Bn%7D%7B(n-1)(n-2)%7D%5CSigma(%5Cfrac%7Bx_%7Bi%7D-%5Cbar%7Bx%7D%20%7D%7Bs%7D)%5E3 --- Reason: Response code 404 (Not Found) --- Fetch details: { "attempt": 3, "method": "GET", "errorCode": "ERR_NON_2XX_3XX_RESPONSE", "responseStatusCode": 404, "responseStatusMessage": "Not Found", "requestHeaders": { "user-agent": "got (https://github.com/sindresorhus/got)", "accept-encoding": "gzip, deflate, br" }, "responseHeaders": { "content-type": "text/html; charset=UTF-8", "referrer-policy": "no-referrer", "content-length": "1566", "date": "Tue, 17 Sep 2024 08:28:23 GMT", "alt-svc": "h3=\":443\"; ma=2592000,h3-29=\":443\"; ma=2592000", "connection": "close" } } ---

 

例：运用 SKEW 求偏斜度

 

此例为某股票 18 个交易日的价格，试求股票价格的偏斜度。该示例文件可详见：偏斜度示例

 

如果通过以上链接无法在线查看，可以通过此链接下载Excel文件离线查看。

 

---

说明：SKEW，返回分布的偏斜度。

语法：SKEW(Number1, Number2, ...)，其中Number1, Number2, ...为需要计算偏斜度的1~30个参数。

应注意的是，如果数据点个数少于3个，或者样本标准偏差为零，函数SKEW返回错误值#DIV/0!。

可以看出，对应该股票价格的偏斜度为-0.9236。