{"id":494,"date":"2018-08-04T20:17:08","date_gmt":"2018-08-04T11:17:08","guid":{"rendered":"https:\/\/best-biostatistics.com\/toukei-er\/entry\/how-to-calculate-skewness-and-kurtosis-in-r\/"},"modified":"2024-10-13T21:41:34","modified_gmt":"2024-10-13T12:41:34","slug":"how-to-calculate-skewness-and-kurtosis-in-r","status":"publish","type":"post","link":"https:\/\/best-biostatistics.com\/toukei-er\/entry\/how-to-calculate-skewness-and-kurtosis-in-r\/","title":{"rendered":"R \u3067 skewness \u3084 kurtosis \u3092\u8a08\u7b97\u3059\u308b\u65b9\u6cd5"},"content":{"rendered":"\n

R \u3067 skewness \u3084 kurtosis \u3092\u8a08\u7b97\u3059\u308b\u65b9\u6cd5\u3002<\/p>\n\n\n\n\n\n\n\n

\u5e73\u5747\u3068\u6a19\u6e96\u504f\u5dee<\/h2>\n\n\n\n

\u7d71\u8a08\u30bd\u30d5\u30c8R\u3067\u3001\u5e73\u5747\u5024\u306f\u3001mean()\u3067\u7b97\u51fa\u3059\u308b\u3002<\/p>\n\n\n\n

\u6a19\u6e96\u504f\u5dee\u306f\u3001sd()\u3067\u8a08\u7b97\u3059\u308b\u3002<\/p>\n\n\n\n

sd\u306fstandard deviation\u306e\u7565\u3002<\/p>\n\n\n\n

\u5e73\u5747\u5024\u3068\u6a19\u6e96\u504f\u5dee\u306e\u5024\u306e\u95a2\u4fc2\u3067\u3001\u30c7\u30fc\u30bf\u306e\u5206\u5e03\u3092\u5927\u307e\u304b\u306b\u63a8\u6e2c\u3067\u304d\u308b\u3002<\/p>\n\n\n\n

\u5e73\u5747\u5024\u304c\u6a19\u6e96\u504f\u5dee\u306e3\u500d\u3042\u308c\u3070\u3001\u3060\u3044\u3060\u3044\u6b63\u898f\u5206\u5e03\u3057\u3066\u3044\u308b\u3002<\/p>\n\n\n\n

\u6b63\u898f\u5206\u5e03\u3092\u3057\u3066\u3044\u308c\u3070\u3001\u5e73\u5747\u5024\u306b\u00b1\u6a19\u6e96\u504f\u5dee\u306e2\u500d\u306e\u7bc4\u56f2\u306b\u3001\u30c7\u30fc\u30bf\u306e\u7d0495\uff05\u304c\u53ce\u307e\u308b\u3002<\/p>\n\n\n\n

><\/span> mean<\/span>(<\/span>chickwts$<\/span>weight)<\/span>\n[<\/span>1<\/span>]<\/span> 261.3099<\/span>\n><\/span> sd<\/span>(<\/span>chickwts$<\/span>weight)<\/span>\n[<\/span>1<\/span>]<\/span> 78.0737<\/span>\n<\/code><\/pre>\n\n\n\n
\u5e73\u5747\u3092\u6a19\u6e96\u504f\u5dee\u3067\u5272\u3063\u3066\u307f\u308b\u3068\u7d043\u500d\u3002<\/p>\n\n\n\n
\u3060\u3044\u305f\u3044\u6b63\u898f\u5206\u5e03\u3057\u3066\u3044\u308b\u3068\u60f3\u50cf\u3059\u308b\u3002<\/p>\n\n\n\n
><\/span> 261.3099<\/span>\/<\/span>78.0787<\/span>\n[<\/span>1<\/span>]<\/span> 3.34675<\/span>\n<\/code><\/pre>\n\n\n\n
\u30d2\u30b9\u30c8\u30b0\u30e9\u30e0\u3092\u898b\u3066\u307f\u308b\u3002<\/p>\n\n\n\n
\u3060\u3044\u305f\u3044\u6b63\u898f\u5206\u5e03\u3068\u8a00\u3063\u3066\u3088\u3044\u3002<\/p>\n\n\n\n
\"\"<\/figure>\n\n\n\n
<\/span><\/p>\n\n\n\n
\u4e2d\u592e\u5024\uff08\u30e1\u30c7\u30a3\u30a2\u30f3\uff09<\/h2>\n\n\n\n
\u6b63\u898f\u5206\u5e03\u3057\u3066\u3044\u306a\u3044\u30c7\u30fc\u30bf\u306e\u5834\u5408\u3001\u4ee3\u8868\u5024\u3068\u3057\u3066\u306f\u3053\u3061\u3089\u306e\u307b\u3046\u304c\u671b\u307e\u3057\u3044\u3002<\/p>\n\n\n\n
chickwts\u30c7\u30fc\u30bf\u30d5\u30ec\u30fc\u30e0\u5185\u306eweight\u306e\u4e2d\u592e\u5024\u306f\u3001\u5e73\u5747\u5024\u3068\u307b\u307c\u540c\u3058\u3067\u3001\u307b\u307c\u6b63\u898f\u5206\u5e03\u306a\u306e\u3067\u3001\u5e73\u5747\u5024\u3068\u4e2d\u592e\u5024\u304c\u307b\u307c\u540c\u3058\u306b\u306a\u308b\u3002<\/p>\n\n\n\n
><\/span> median<\/span>(<\/span>chickwts$<\/span>weight)<\/span>\n[<\/span>1<\/span>]<\/span> 258<\/span>\n><\/span> mean<\/span>(<\/span>chickwts$<\/span>weight)<\/span>\n[<\/span>1<\/span>]<\/span> 261.3099<\/span>\n<\/code><\/pre>\n\n\n\n
\uff1e\uff1e\u3082\u3046\u7d71\u8a08\u3067\u60a9\u3080\u306e\u306f\u7d42\u308f\u308a\u306b\u3057\u307e\u305b\u3093\u304b\uff1f\u00a0<\/a><\/strong><\/span><\/p>\r\n\"\"<\/a>\r\n
\u21911\u4e07\u4eba\u4ee5\u4e0a\u306e\u533b\u7642\u5f93\u4e8b\u8005\u304c\u8cfc\u8aad\u4e2d<\/span><\/strong><\/span><\/p><\/div>
\u6b6a\u5ea6\uff08\u308f\u3044\u3069\uff09Skewness<\/h2>\n\n\n\n
\u5206\u5e03\u304c\u6b63\u898f\u5206\u5e03\u304b\u3089\u5916\u308c\u3066\u3086\u304c\u3093\u3067\u3044\u308b\u5ea6\u5408\u3044\u304c\u6b6a\u5ea6\u3060\u3002<\/p>\n\n\n\n
\u975e\u5bfe\u79f0\u6027\u3092\u8868\u3059\u6307\u6a19\u3002e1071\u30d1\u30c3\u30b1\u30fc\u30b8\u306b\u542b\u307e\u308c\u3066\u3044\u308b\u3002<\/p>\n\n\n\n
\u6700\u521d\u4e00\u56de\u3060\u3051\u3001e1071\u30d1\u30c3\u30b1\u30fc\u30b8\u306e\u30a4\u30f3\u30b9\u30c8\u30fc\u30eb\u304c\u5fc5\u8981\u3060\u3002<\/p>\n\n\n\n
install.packages<\/span>(<\/span>\"e1071\"<\/span>)<\/span>\n<\/code><\/pre>\n\n\n\n
\u4e00\u56de\u306e\u30bb\u30c3\u30b7\u30e7\u30f3\u3067\u4f7f\u3044\u59cb\u3081\u306e\u6642\u306b\u4e00\u56de\u3060\u3051library()\u3067\u547c\u3073\u51fa\u3059\u3002<\/p>\n\n\n\n
library<\/span>(<\/span>e1071)<\/span>\n<\/code><\/pre>\n\n\n\n
\u6b6a\u5ea6\u3092\u8a08\u7b97\u3059\u308b\u95a2\u6570\u306fskewness()<\/p>\n\n\n\n
\u4f8b\u3068\u3057\u3066x1\u3068\u3044\u3046\u30c7\u30fc\u30bf\u304c\u3042\u308b\u3068\u3059\u308b\u3002<\/p>\n\n\n\n
x1 <-<\/span> c<\/span>(<\/span>6.0<\/span>,<\/span>10.0<\/span>,<\/span>7.6<\/span>,<\/span>3.5<\/span>,<\/span>1.4<\/span>,<\/span>2.5<\/span>,<\/span>5.6<\/span>,<\/span>3.0<\/span>,<\/span>2.2<\/span>,<\/span>5.0<\/span>,<\/span> 3.3<\/span>,<\/span>7.6<\/span>,<\/span>5.8<\/span>,<\/span>6.7<\/span>,<\/span>2.8<\/span>,<\/span>4.8<\/span>,<\/span>6.3<\/span>,<\/span>5.3<\/span>,<\/span>5.4<\/span>,<\/span>3.3<\/span>,<\/span> 3.4<\/span>,<\/span>3.8<\/span>,<\/span>3.3<\/span>,<\/span>5.7<\/span>,<\/span>6.3<\/span>,<\/span>8.4<\/span>,<\/span>4.6<\/span>,<\/span>2.8<\/span>,<\/span>7.9<\/span>,<\/span>8.9<\/span>)<\/span>\n<\/code><\/pre>\n\n\n\n
\u30d2\u30b9\u30c8\u30b0\u30e9\u30e0\u3092\u898b\u3066\u307f\u308b\u3068\u3001\u5de6\u53f3\u5bfe\u79f0\u3067\u306f\u306a\u304f\u3086\u304c\u3093\u3067\u3044\u308b\u3002<\/p>\n\n\n\n
hist<\/span>(<\/span>x1)<\/span>\n<\/code><\/pre>\n\n\n\n
\"\"<\/figure>\n\n\n\n
<\/span><\/p>\n\n\n\n
\u3053\u306e\u3068\u304d\u6b6a\u5ea6\u3092\u8a08\u7b97\u3059\u308b\u3068\u30010.361<\/p>\n\n\n\n
><\/span> skewness<\/span>(<\/span>x1)<\/span>\n[<\/span>1<\/span>]<\/span> 0.3614441<\/span>\n<\/code><\/pre>\n\n\n\n
\u3061\u306a\u307f\u306b\u3001\u5148\u307b\u3069\u898b\u305f\u307b\u307c\u6b63\u898f\u5206\u5e03\u3057\u3066\u3044\u308b chickwts$weight\u306eskewness\u3082\u8a08\u7b97\u3057\u3066\u307f\u308b\u3068\u3001\u307b\u307c\u30bc\u30ed\u3002<\/p>\n\n\n\n
\u5206\u5e03\u304c\u3086\u304c\u3093\u3067\u3044\u308b\u3068\u6570\u5024\u306e\u7d76\u5bfe\u5024\u304c\u5927\u304d\u304f\u306a\u308b\u3002<\/p>\n\n\n\n
><\/span> skewness<\/span>(<\/span>chickwts$<\/span>weight)<\/span>\n[<\/span>1<\/span>]<\/span> -<\/span>0.01136593<\/span>\n<\/code><\/pre>\n\n\n\n
skewness\u306f3\u7a2e\u985e\u3042\u308b\u3002<\/p>\n\n\n\n
SAS\u3084SPSS\u3067\u306fType=2\u3060\u3002<\/p>\n\n\n\n
Type=2\u3092\u4f7f\u3046\u306e\u304c\u7121\u96e3\u3060\u308d\u3046\u3002<\/p>\n\n\n\n
><\/span> skewness<\/span>(<\/span>x1,<\/span> type=<\/span>2<\/span>)<\/span>\n[<\/span>1<\/span>]<\/span> 0.4006154<\/span>\n<\/code><\/pre>\n\n\n\n
\"\"<\/figure>\n\n\n\n\n\n\n\n
\u5c16\u5ea6\uff08\u305b\u3093\u3069\uff09Kurtosis<\/h2>\n\n\n\n
\u5c16\u5ea6\u306f\u6b63\u898f\u5206\u5e03\u3068\u6bd4\u3079\u3066\u3001\u92ed\u3044\u30d4\u30fc\u30af\u304b\u920d\u3044\u30d4\u30fc\u30af\u304b\u3092\u8868\u3059\u3002<\/p>\n\n\n\n
><\/span> kurtosis<\/span>(<\/span>x1)<\/span>\n[<\/span>1<\/span>]<\/span> -<\/span>0.8275311<\/span>\n><\/span> kurtosis<\/span>(<\/span>chickwts$<\/span>weight)<\/span>\n[<\/span>1<\/span>]<\/span> -<\/span>0.9651994<\/span>\n<\/code><\/pre>\n\n\n\n
\u5c16\u5ea6\u306fx1\u3068chickwts$weight\u3067\u306f\u3001\u305d\u308c\u307b\u3069\u7570\u306a\u3089\u306a\u3044\u3002<\/p>\n\n\n\n
\u5c16\u5ea6\u30823\u7a2e\u985e\u3042\u308a\u3053\u308c\u3082Type=2\u304c\u7121\u96e3\u3060\u3002<\/p>\n\n\n\n
\u6b63\u898f\u5206\u5e03\u3067\u3042\u3063\u305f\u5834\u5408\u3001\u504f\u3089\u306a\u3044\u306e\u304cType=2\u3060\u3051\u3060\u3002<\/p>\n\n\n\n
\"\"<\/figure>\n\n\n\n\n\n\n\n
><\/span> kurtosis<\/span>(<\/span>x1,<\/span> type=<\/span>2<\/span>)<\/span>\n[<\/span>1<\/span>]<\/span> -<\/span>0.5726655<\/span>\n><\/span> kurtosis<\/span>(<\/span>chickwts$<\/span>weight,<\/span> type=<\/span>2<\/span>)<\/span>\n[<\/span>1<\/span>]<\/span> -<\/span>0.8843778<\/span>\n<\/code><\/pre>\n\n\n\n
\u30e9\u30f3\u30c0\u30e0\u5909\u6570\u3067\u8a66\u3057\u3066\u307f\u308b<\/h3>\n\n\n\n
\u3053\u3053\u3067\u3001\u6b63\u898f\u5206\u5e03\u3057\u3066\u3044\u308b\u30e9\u30f3\u30c0\u30e0\u5909\u6570\u3092\u4f5c\u3063\u3066\u3001\u8a66\u3057\u3066\u307f\u3088\u3046\u3002<\/p>\n\n\n\n
100\u500b\u30681000\u500b\u3067\u6bd4\u3079\u3066\u307f\u308b\u3002<\/p>\n\n\n\n
x100\u306f100\u500b\u306e\u30e9\u30f3\u30c0\u30e0\u5909\u6570\u3002<\/p>\n\n\n\n
x1000\u306f1000\u500b\u306e\u30e9\u30f3\u30c0\u30e0\u5909\u6570\u3002<\/p>\n\n\n\n
set.seed<\/span>(<\/span>20180504<\/span>)<\/span>\nx100 <-<\/span> rnorm<\/span>(<\/span>100<\/span>)<\/span>\nhist<\/span>(<\/span>x100)<\/span>\n<\/code><\/pre>\n\n\n\n
\"\"<\/figure>\n\n\n\n
<\/span><\/p>\n\n\n\n
x1000 <-<\/span> rnorm<\/span>(<\/span>1000<\/span>)<\/span>\nhist<\/span>(<\/span>x1000)<\/span>\n<\/code><\/pre>\n\n\n\n
\"\"<\/figure>\n\n\n\n
<\/span><\/p>\n\n\n\n
><\/span> kurtosis<\/span>(<\/span>x100,<\/span> type=<\/span>2<\/span>)<\/span>\n[<\/span>1<\/span>]<\/span> -<\/span>0.2333893<\/span>\n><\/span> kurtosis<\/span>(<\/span>x1000,<\/span> type=<\/span>2<\/span>)<\/span>\n[<\/span>1<\/span>]<\/span> -<\/span>0.002990156<\/span>\n<\/code><\/pre>\n\n\n\n
\u30d2\u30b9\u30c8\u30b0\u30e9\u30e0\u3092\u898b\u308b\u3068\u3001100\u500b\u3088\u308a1000\u500b\u306e\u307b\u3046\u304c\u3088\u308a\u6b63\u898f\u5206\u5e03\u3089\u3057\u3044\u3002<\/p>\n\n\n\n
\u5c16\u5ea6\u306f100\u3088\u308a\u30821000\u306e\u307b\u3046\u304c\u30bc\u30ed\u306b\u8fd1\u3044\u3002<\/p>\n\n\n\n
\u5c16\u5ea6\u306f\u3068\u304c\u308a\u65b9\u304c\u3088\u308a\u6b63\u898f\u5206\u5e03\u306b\u8fd1\u3044\u304b\u3069\u3046\u304b\u3092\u8868\u3059\u6307\u6a19\u3060\u3002<\/p>\n\n\n\n
\u307e\u3068\u3081<\/h2>\n\n\n\n
\u901a\u5e38\u306f\u30c7\u30fc\u30bf\u3092\u773a\u3081\u3066\u307f\u308b\u3068\u304d\u306f\u3001\u5e73\u5747\u5024\u3068\u6a19\u6e96\u504f\u5dee\u3067\u3088\u3044\u3002<\/p>\n\n\n\n
\u30b0\u30e9\u30d5\u3082\u5927\u4e8b\u3067\u3001\u30d2\u30b9\u30c8\u30b0\u30e9\u30e0\u3067\u5206\u5e03\u3082\u898b\u305f\u307b\u3046\u304c\u826f\u3044\u3002<\/p>\n\n\n\n
\u30d2\u30b9\u30c8\u30b0\u30e9\u30e0\u304c\u5de6\u53f3\u5bfe\u79f0\u306e\u91e3\u308a\u9418\u578b\u306e\u5206\u5e03\u3067\u306f\u306a\u3055\u305d\u3046\u306a\u3089\u3001\u4e2d\u592e\u5024\u3082\u78ba\u8a8d\u3059\u308b\u3068\u3088\u3044\u3002<\/p>\n\n\n\n
\u6b6a\u5ea6\u3084\u5c16\u5ea6\u306f\u5fc5\u8981\u306b\u5fdc\u3058\u3066\u7b97\u51fa\u3059\u308b\u3002<\/p>\n\n\n\n
\u53c2\u8003\u6587\u732e<\/h2>\n\n\n\n
Package \u2018e1071\u2019<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"
R \u3067 skewness \u3084 kurtosis \u3092\u8a08\u7b97\u3059\u308b\u65b9\u6cd5\u3002<\/p>\n","protected":false},"author":2,"featured_media":2894,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"swell_btn_cv_data":"","_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":false,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2}},"categories":[5,25],"tags":[],"class_list":["post-494","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-r","category-25"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"https:\/\/best-biostatistics.com\/toukei-er\/wp-content\/uploads\/2018\/08\/20180828215311.png","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/posts\/494","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/comments?post=494"}],"version-history":[{"count":2,"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/posts\/494\/revisions"}],"predecessor-version":[{"id":2895,"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/posts\/494\/revisions\/2895"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/media\/2894"}],"wp:attachment":[{"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/media?parent=494"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/categories?post=494"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/tags?post=494"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}