{"id":885,"date":"2019-02-02T06:23:56","date_gmt":"2019-02-01T21:23:56","guid":{"rendered":"http:\/\/141.164.34.82\/?p=885"},"modified":"2022-02-03T17:28:21","modified_gmt":"2022-02-03T08:28:21","slug":"skewness-and-kurtosis","status":"publish","type":"post","link":"http:\/\/ds.sumeun.org\/?p=885","title":{"rendered":"\uc65c\ub3c4\uc640 \ucca8\ub3c4"},"content":{"rendered":"<h1>\uc65c\ub3c4\uc640 \ucca8\ub3c4(Skewness and Kurtosis)<\/h1>\n<ul>\n<li>\uc5ec\uae30\uc11c\ub294 \ud45c\ubcf8 \uc65c\ub3c4\uc640 \ud45c\ubcf8 \ucca8\ub3c4\ub97c \uad6c\ud558\ub294 <code>package:e1071<\/code>\uc758 <code>skewness<\/code> \ud568\uc218\uc640 <code>kurtosis<\/code> \ud568\uc218\ub97c \uc0b4\ud3b4\ubcf8\ub2e4.<\/li>\n<li>\ucc28\ub840\n<ul>\n<li>\ud45c\ubcf8 \ubd84\uc0b0<\/li>\n<li>\ud45c\ubcf8 \uc65c\ub3c4<\/li>\n<li>\ud45c\ubcf8 \ucca8\ub3c4<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<h2>\ud45c\ubcf8 \ubd84\uc0b0<\/h2>\n<ul>\n<li>\uba3c\uc800 \uc5b4\ub5a4 \ud655\ub960 \ubcc0\uc218 \\(X\\) \uc758 \ubd84\uc0b0\uc740 \ub2e4\uc74c\uacfc \uac19\uc774 \uad6c\ud55c\ub2e4. \uc774\ub294 \ubaa8\uc9d1\ub2e8\uc758 \ubd84\uc0b0\uc774\ub2e4.\n<ul>\n<li>\uc774\uc0b0\ud615\uc778 \uacbd\uc6b0 : \\(\\mathbb{V}\\text{ar}(X) = \\sum{\\mathbb{P}(X=x_i)\\cdot x_i}\\)<\/li>\n<li>\uc5f0\uc18d\ud615\uc778 \uacbd\uc6b0 : \\(\\int f(X=x) x dx\\)<\/li>\n<\/ul>\n<\/li>\n<li>\uc6b0\ub9ac\uac00 \ubaa8\uc9d1\ub2e8\uc744 \ubaa8\ub450 \uc54c \uc218 \uc5c6\uc744 \ub54c, \ud45c\ubcf8\uc744 \ud1b5\ud574 \ubaa8\uc9d1\ub2e8\uc758 \ubd84\uc0b0\uc744 \ucd94\uc815\ud560 \uc218 \uc788\ub2e4. \ub9cc\uc57d \ud45c\ubcf8\uc5d0 \ub300\ud574 \ubaa8\uc9d1\ub2e8 \ud45c\ubcf8\uc744 \uad6c\ud560 \ub54c\uc640 \ub3d9\uc77c\ud55c \ubc29\uc2dd\uc744 \uc4f4\ub2e4\uba74, \ud45c\ubcf8\uc758 \ud06c\uae30\uac00 \ucee4\uc9d0\uc5d0 \ub530\ub77c \ub9e4\uc6b0 \uc815\ud655\ud55c \uac12\uc744 \uad6c\ud560 \uc218 \uc788\uc744 \uac83\uc774\ub2e4. \ud558\uc9c0\ub9cc \ubd84\uc0b0\uc744 \uad6c\ud560 \ub54c \uc0ac\uc6a9\ud558\ub294 \ud3c9\uade0\uc774 \ubaa8\ud3c9\uade0\uacfc \uc815\ud655\ud558\uac8c \uc77c\uce58\ud558\uc9c0 \uc54a\uae30 \ub54c\ubb38\uc5d0 \ud45c\ubcf8 \ubd84\uc0b0\uc740 \ubaa8\ubd84\uc0b0\uc744 \uacfc\uc18c\ucd94\uc815\ud558\ub294 \uacbd\ud5a5\uc774 \uc788\ub2e4. \uc774\ub97c \ubcf4\uc815\ud558\uae30 \uc704\ud574 \ud45c\ubcf8 \ubd84\uc0b0\uc744 \uad6c\ud560 \ub54c\uc5d0\ub294 \ud45c\ubcf8\uc758 \ud06c\uae30 \\(n\\) \uc774 \uc544\ub2c8\ub77c \\(n-1\\) \ub85c \ub098\ub220\uc900\ub2e4.\n<ul>\n<li>\ud45c\ubcf8 \ubd84\uc0b0 : \\(\\sum \\frac{(x_i &#8211; \\bar{x})^2}{n-1}\\)<\/li>\n<\/ul>\n<\/li>\n<li>R\uc758 <code>var()<\/code> \ud568\uc218\ub294 \ud45c\ubcf8 \ubd84\uc0b0\uc744 \uad6c\ud574\uc900\ub2e4.<\/li>\n<\/ul>\n<h2>\ud45c\ubcf8 \uc65c\ub3c4<\/h2>\n<ul>\n<li><strong>\ubaa8<\/strong>\uc9d1\ub2e8\uc758 \uc65c\ub3c4\ub294 \ub2e4\uc74c\uacfc \uac19\uc774 \uad6c\ud55c\ub2e4.\n<ul>\n<li>\\(\\mathbb{E}[\\left(\\frac{X-\\mu}{\\sigma}\\right)^3]\\)<\/li>\n<li>\uac04\ub2e8\ud558\uac8c \uc124\uba85\ud558\uba74 \ud655\ub960\ubcc0\uc218 \\(X\\) \ub97c \ud45c\uc900\ud654\uc2dc\ud0a8 \\(\\frac{X-\\mu}{\\sigma}\\) \uc758 \uc138\uc81c\uacf1\uc758 \ud3c9\uade0\uc774\ub2e4.<\/li>\n<\/ul>\n<\/li>\n<li><strong>\ubaa8<\/strong>\uc9d1\ub2e8\uc758 \uc65c\ub3c4\ub97c \ud45c\ubcf8\uc744 \ud1b5\ud574 \ucd94\uc815\ud558\uace0\uc790 \ud55c\ub2e4\uace0 \ud574\ubcf4\uc790. \uc6b0\ub9ac\ub294 \ub300\ubd80\ubd84\uc758 \uacbd\uc6b0 \ubaa8\ud3c9\uade0 \\(\\mu\\) \uc640 \ubaa8\ud45c\uc900\ud3b8\ucc28 \\(\\sigma\\) \ub97c \ubaa8\ub450 \ubaa8\ub974\uae30 \ub54c\ubb38\uc5d0 \ud45c\ubcf8 \ud3c9\uade0\uacfc \ud45c\ubcf8 \ud45c\uc900\ud3b8\ucc28\ub97c \uc801\uc808\ud788 \uc0ac\uc6a9\ud558\uace0, \uacfc\uc18c \ucd94\uc815 \ub610\ub294 \uacfc\ub300 \ucd94\uc815\uc758 \ubb38\uc81c\ub97c \ud574\uacb0\ud574\uc57c \ud560 \uac83\uc774\ub2e4. \uc774\uc5d0 \ub300\ud574\uc11c\ub294 \uc138 \uac00\uc9c0 \ubc29\ubc95\uc774 \uc81c\uc548\ub418\uc5c8\ub2e4. \uc5ec\uae30\uc11c \\(s\\) \ub294 \ud45c\ubcf8\ud45c\uc900\ud3b8\ucc28\uc774\uace0, \\(m_2 = \\sum_i (x_i-\\mu)^2\/n\\) \uacfc \\(m_3 = \\sum_i (x_i-\\mu)^2\/n\\) \ub294 \ud45c\ubcf8 2\ucc28 \uc911\uc2ec\uc801\ub960(central moment), \ud45c\ubcf8 3\ucc28 \uc911\uc2ec\uc801\ub960(central moment)\uc774\ub2e4.\n<ul>\n<li>Type 1: \\(g_1 = m_3\/m_2^{3\/2}\\) . \uc8fc\ub85c \uc608\uc804 \uad50\uacfc\uc11c\uc5d0\uc11c \uc4f0\uc600\ub2e4.<\/li>\n<li>Type 2: \\(G_1 = g_1 * \\sqrt{n(n-1)}\/(n-2)\\) . SAS\uc640 SPSS\uc5d0\uc11c \uc4f0\uc778\ub2e4.<\/li>\n<li>Type 3: \\(b_1 = m_3\/s^3=g_1\\left(\\frac{n-1}{n}\\right)^{3\/2}\\)<\/li>\n<\/ul>\n<\/li>\n<li>R\uc758 \ud568\uc218 <code>e1071::skewness(x= , type= )<\/code>\uc5d0\uc11c <code>type<\/code>\uc744 \uc124\uc815\ud574\uc904 \uc218 \uc788\ub2e4. \uae30\ubcf8\uac12\uc740 <code>3<\/code>\uc774\uace0, \ubaa8\ub4e0 Type\uc774 \uc815\uaddc\ubd84\ud3ec\uc5d0\uc11c \ube44\ud3b8\ud5a5 \ucd94\uc815\ub7c9\uc774\ub77c\uace0 \ud55c\ub2e4.[<sup>1]<\/sup><\/li>\n<\/ul>\n<h2>\ud45c\ubcf8 \ucca8\ub3c4<\/h2>\n<ul>\n<li>\ubaa8\uc9d1\ub2e8\uc758 \ucca8\ub3c4\ub294 \ub2e4\uc74c\uacfc \uac19\uc774 \uad6c\ud55c\ub2e4.\n<ul>\n<li>\\(\\frac{\\mathbb{E}[(X-\\mu)^4]}{(\\mathbb{V}ar[X])^2}\\)<\/li>\n<\/ul>\n<\/li>\n<li>\ud45c\ubcf8 \ucca8\ub3c4\uc5d0\ub3c4 3\uac00\uc9c0 Type\uc774 \uc788\ub2e4.\n<ul>\n<li>Type 1: \\(g_2 = m_4 \/ m_2 ^2 &#8211; 3\\) . \uc608\uc804 \uad50\uacfc\uc11c\uc5d0\uc11c \ub9ce\uc774 \uc4f0\uc600\ub2e4.<\/li>\n<li>Type 2: \\(G_2 = ((n+1)g_2 + 6) * (n-1) \/ ((n-2)(n-3))\\) . SAS\uc640 SPSS\uc5d0\uc11c \uc4f0\uc778\ub2e4.<\/li>\n<li>Type 3: \\(b_2 = m_4 \/s^4 &#8211; 3 = (g_2+3)(1-1\/n)^2-3\\) . MINITAB\uacfc BMDP\uc5d0\uc11c \uc4f0\uc778\ub2e4.<\/li>\n<li>Type 2\ub9cc \uc815\uaddc\ubd84\ud3ec\uc5d0\uc11c \ube44\ud3b8\ud5a5\uc801\uc774\ub2e4.<\/li>\n<li>R\uc5d0\uc11c\ub294 <code>e1071::kurtosis(x=, type= )<\/code>\uc5d0\uc11c type\uc744 \uc124\uc815\ud560 \uc218 \uc788\ub2e4.<\/li>\n<\/ul>\n<\/li>\n<li>\ubaa8\ucca8\ub3c4\uc640 \ud45c\ubcf8 \ucca8\ub3c4\uc758 \ube44\uad50\n<ul>\n<li>\ubaa8\ucca8\ub3c4\uc758 \uacbd\uc6b0 \ud56d\uc0c1 1\ubcf4\ub2e4 \ud06c\ub2e4. \uc815\uaddc\ubd84\ud3ec\uc758 \uacbd\uc6b0 \ubaa8\ucca8\ub3c4\uac00 3\uc774\ubbc0\ub85c \uc815\uaddc\ubd84\ud3ec\uc640\uc758 \ube44\uad50\ub97c \uc704\ud574 3\uc744 \ube7c\ub294 \uacbd\uc6b0\ub3c4 \uc788\ub2e4. \uc774\ub807\uac8c \ucca8\ub3c4\uc5d0 3\uc744 \ube80 \uac12\uc744 excess kurtosis\ub77c\uace0 \ud55c\ub2e4.<\/li>\n<li>\uc704\uc5d0\uc11c \uc18c\uac1c\ud55c \ud45c\ubcf8 \ucca8\ub3c4\ub294 \ubaa8\ucca8\ub3c4\uc5d0 3\uc744 \ube80 excess kurtosis\ub97c \ucd94\uc815\ud558\ub294 \uac12\uc774\ub77c\uace0 \ud560 \uc218 \uc788\ub2e4. \ub530\ub77c\uc11c \ubaa8\uc9d1\ub2e8\uc774 \uc815\uaddc\ubd84\ud3ec\ub97c \ub530\ub978\ub2e4\uba74 \ud45c\ubcf8 \ucca8\ub3c4\ub294 0\uacfc \uac00\uae4c\uc774 \ubd84\ud3ec\ud560 \uac83\uc774\ub2e4.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>[<sup>1]:<\/sup> <code>package:e1071<\/code> \ubb38\uc11c, Joanes and Gill(1998)<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\uc65c\ub3c4\uc640 \ucca8\ub3c4(Skewness and Kurtosis) \uc5ec\uae30\uc11c\ub294 \ud45c\ubcf8 \uc65c\ub3c4\uc640 \ud45c\ubcf8 \ucca8\ub3c4\ub97c \uad6c\ud558\ub294 package:e1071\uc758 skewness \ud568\uc218\uc640 kurtosis \ud568\uc218\ub97c \uc0b4\ud3b4\ubcf8\ub2e4. \ucc28\ub840 \ud45c\ubcf8 \ubd84\uc0b0 \ud45c\ubcf8 \uc65c\ub3c4 \ud45c\ubcf8 \ucca8\ub3c4 \ud45c\ubcf8 \ubd84\uc0b0 \uba3c\uc800 \uc5b4\ub5a4 \ud655\ub960 \ubcc0\uc218 \\(X\\) \uc758 \ubd84\uc0b0\uc740 \ub2e4\uc74c\uacfc \uac19\uc774 \uad6c\ud55c\ub2e4. \uc774\ub294 \ubaa8\uc9d1\ub2e8\uc758 \ubd84\uc0b0\uc774\ub2e4. \uc774\uc0b0\ud615\uc778 \uacbd\uc6b0 : \\(\\mathbb{V}\\text{ar}(X) = \\sum{\\mathbb{P}(X=x_i)\\cdot x_i}\\) \uc5f0\uc18d\ud615\uc778 \uacbd\uc6b0 : \\(\\int f(X=x) x dx\\) \uc6b0\ub9ac\uac00 \ubaa8\uc9d1\ub2e8\uc744 \ubaa8\ub450 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":2468,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[32,29],"tags":[38,37,35,36,33,34],"jetpack_featured_media_url":"http:\/\/ds.sumeun.org\/wp-content\/uploads\/2019\/02\/tree-g416bf20a5_640.jpg","_links":{"self":[{"href":"http:\/\/ds.sumeun.org\/index.php?rest_route=\/wp\/v2\/posts\/885"}],"collection":[{"href":"http:\/\/ds.sumeun.org\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/ds.sumeun.org\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/ds.sumeun.org\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/ds.sumeun.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=885"}],"version-history":[{"count":4,"href":"http:\/\/ds.sumeun.org\/index.php?rest_route=\/wp\/v2\/posts\/885\/revisions"}],"predecessor-version":[{"id":2469,"href":"http:\/\/ds.sumeun.org\/index.php?rest_route=\/wp\/v2\/posts\/885\/revisions\/2469"}],"wp:featuredmedia":[{"embeddable":true,"href":"http:\/\/ds.sumeun.org\/index.php?rest_route=\/wp\/v2\/media\/2468"}],"wp:attachment":[{"href":"http:\/\/ds.sumeun.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=885"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/ds.sumeun.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=885"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/ds.sumeun.org\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=885"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}