{"id":386,"date":"2024-06-28T15:27:20","date_gmt":"2024-06-28T15:27:20","guid":{"rendered":"http:\/\/www.ohsumin.com\/?p=386"},"modified":"2025-06-11T01:23:00","modified_gmt":"2025-06-11T01:23:00","slug":"skew-t-distribution","status":"publish","type":"post","link":"http:\/\/www.inmining.co.kr\/?p=386","title":{"rendered":"Skew t-\ubd84\ud3ec"},"content":{"rendered":"\n<ol class=\"wp-block-list\">\n<li><a href=\"#t\">skew t-\ubd84\ud3ec\uc758 \uc815\uc758<\/a><\/li>\n\n\n\n<li><a href=\"#Python\">skew t-\ubd84\ud3ec in Python<\/a><\/li>\n\n\n\n<li><a href=\"#tr\">skew t-\ubd84\ud3ec in R<\/a><\/li>\n<\/ol>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<h3 class=\"wp-block-heading has-medium-font-size\"><span class=\"ez-toc-section\" id=\"Skew_t_%EB%B6%84%ED%8F%AC%EC%9D%98_%EC%A0%95%EC%9D%98%EC%99%80_%ED%8A%B9%EC%A7%95\"><\/span>Skew t \ubd84\ud3ec\uc758 \uc815\uc758\uc640 \ud2b9\uc9d5<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-8f761849 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:33.33%\">\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"924\" src=\"http:\/\/www.statdc.com\/sm24_wp\/wp-content\/uploads\/2024\/06\/20240719_194528-1024x924.png\" alt=\"\" class=\"wp-image-1294\" srcset=\"http:\/\/www.inmining.co.kr\/sm24_wp\/wp-content\/uploads\/2024\/06\/20240719_194528-1024x924.png 1024w, http:\/\/www.inmining.co.kr\/sm24_wp\/wp-content\/uploads\/2024\/06\/20240719_194528-300x271.png 300w, http:\/\/www.inmining.co.kr\/sm24_wp\/wp-content\/uploads\/2024\/06\/20240719_194528-768x693.png 768w, http:\/\/www.inmining.co.kr\/sm24_wp\/wp-content\/uploads\/2024\/06\/20240719_194528-920x830.png 920w, http:\/\/www.inmining.co.kr\/sm24_wp\/wp-content\/uploads\/2024\/06\/20240719_194528.png 1047w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:66.66%\">\n<p class=\"wp-block-paragraph\">Skew t-\ubd84\ud3ec(Skew t-distribution)\ub294 \uc2a4\ud29c\ub358\ud2b8 t \ubd84\ud3ec\uc758 \uc77c\ubc18\ud654\ub41c \ud615\ud0dc\ub85c, \ube44\ub300\uce6d\uc131\uc744 \ud3ec\ud568\ud558\uc5ec \ubd84\ud3ec\uc758 \ud615\ud0dc\ub97c \uc870\uc815\ud560 \uc218 \uc788\uc2b5\ub2c8\ub2e4. \uc774 \ubd84\ud3ec\ub294 \uc815\uaddc \ubd84\ud3ec\uac00 \ube44\ub300\uce6d \ub370\uc774\ud130\ub97c \uc798 \uc124\uba85\ud558\uc9c0 \ubabb\ud558\ub294 \uacbd\uc6b0\uc5d0 \uc720\uc6a9\ud569\ub2c8\ub2e4. Skew t \ubd84\ud3ec\ub294 \uc704\uce58, \ucc99\ub3c4, \uc790\uc720\ub3c4, \ube44\ub300\uce6d\uc131(\uc2a4\ud050\ub2c8\uc2a4) \ub4f1\uc758 \ub9e4\uac1c\ubcc0\uc218\ub97c \uac00\uc9c0\uace0 \uc788\uc73c\uba70, \uc774 \ub9e4\uac1c\ubcc0\uc218\ub97c \ud1b5\ud574 \ub2e4\uc591\ud55c \ub370\uc774\ud130\uc758 \ud2b9\uc131\uc744 \uc798 \uc124\uba85\ud560 \uc218 \uc788\uc2b5\ub2c8\ub2e4.<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>\uc704\uce58(Parameter <strong>\\(\\xi\\)<\/strong>)<\/strong>: \ubd84\ud3ec\uc758 \uc911\uc2ec \uc704\uce58\ub97c \ub098\ud0c0\ub0c5\ub2c8\ub2e4.<\/li>\n\n\n\n<li><strong>\ucc99\ub3c4(Parameter \\(\\omega\\))<\/strong>: \ubd84\ud3ec\uc758 \ud655\uc0b0 \uc815\ub3c4\ub97c \ub098\ud0c0\ub0c5\ub2c8\ub2e4.<\/li>\n\n\n\n<li><strong>\uc790\uc720\ub3c4(Parameter \\(\\nu\\))<\/strong>: \ubd84\ud3ec\uc758 \uaf2c\ub9ac \ubd80\ubd84\uc758 \ub450\uaed8\ub97c \uacb0\uc815\ud569\ub2c8\ub2e4. \uc790\uc720\ub3c4\uac00 \ub192\uc744\uc218\ub85d \uc815\uaddc \ubd84\ud3ec\uc5d0 \uac00\uae4c\uc6cc\uc9d1\ub2c8\ub2e4.<\/li>\n\n\n\n<li><strong>\ube44\ub300\uce6d\uc131(Parameter \\(\\alpha\\))<\/strong>: \ubd84\ud3ec\uc758 \ube44\ub300\uce6d \uc815\ub3c4\ub97c \uc870\uc815\ud569\ub2c8\ub2e4.  ( <strong>\\(\\alpha\\)<\/strong> &gt; 0)\uc774\uba74 \uc624\ub978\ucabd\uc73c\ub85c \uce58\uc6b0\uce58\uace0, ( <strong>\\(\\alpha\\)<\/strong> &lt; 0)\uc774\uba74 \uc67c\ucabd\uc73c\ub85c \uce58\uc6b0\uce69\ub2c8\ub2e4.<\/li>\n<\/ol>\n<\/div>\n<\/div>\n\n\n\n<p class=\"wp-block-paragraph\">\\(\\)<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Skew_t_%EB%B6%84%ED%8F%AC%EC%9D%98_%ED%99%95%EB%A5%A0_%EB%B0%80%EB%8F%84_%ED%95%A8%EC%88%98pdf\"><\/span>Skew t \ubd84\ud3ec\uc758 \ud655\ub960 \ubc00\ub3c4 \ud568\uc218(pdf)<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Skew t \ubd84\ud3ec\uc758 \ud655\ub960 \ubc00\ub3c4 \ud568\uc218\ub294 \ubcf5\uc7a1\ud55c \ud615\ud0dc\ub97c \uac00\uc9c0\ubbc0\ub85c \uc218\uc2dd\uc73c\ub85c \uc815\ud655\ud558\uac8c \ud45c\ud604\ud558\uae30 \uc5b4\ub835\uc9c0\ub9cc, \uc77c\ubc18\uc801\uc73c\ub85c \ube44\ub300\uce6d t \ubd84\ud3ec\uc758 3\ucc28 \uc911\uc2ec\uc801\ub960(third central moment)\uc744 \ud65c\uc6a9\ud558\uc5ec \ube44\ub300\uce6d\ub3c4\ub97c \uce21\uc815\ud560 \uc218 \uc73c\uba70, 3\ucc28 \uc911\uc2ec\uc801\ub960\uc740 \ube44\ub300\uce6d\ub3c4\uc758 \ucc99\ub3c4\uc778 \uc65c\ub3c4(skewness)\ub97c \uacc4\uc0b0\ud558\ub294 \ub370 \uc0ac\uc6a9\ub429\ub2c8\ub2e4.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\ube44\ub300\uce6d t \ubd84\ud3ec\uc758 \ud655\ub960 \ubc00\ub3c4 \ud568\uc218\ub294 \ub2e4\uc74c\uacfc \uac19\uc774 \uc815\uc758\ub420 \uc218 \uc788\uc2b5\ub2c8\ub2e4:<br>\\[ f(x|\\nu, \\lambda) = 2 t_\\nu(x) T_\\nu(\\lambda x \\sqrt{\\frac{\\nu+1}{\\nu+x^2}}) \\]<br>\uc5ec\uae30\uc11c \\( t_\\nu(x) \\)\ub294 \uc790\uc720\ub3c4 \\(\\nu\\)\ub97c \uac00\uc9c4 \ud45c\uc900 t \ubd84\ud3ec\uc758 \ubc00\ub3c4 \ud568\uc218\uc774\uace0, \\( T_\\nu \\)\ub294 \uc790\uc720\ub3c4 \\(\\nu\\)\ub97c \uac00\uc9c4 \ud45c\uc900 t \ubd84\ud3ec\uc758 \ub204\uc801 \ubd84\ud3ec \ud568\uc218\uc785\ub2c8\ub2e4. \\(\\lambda\\)\ub294 \ube44\ub300\uce6d\uc131\uc744 \uc81c\uc5b4\ud558\ub294 \ub9e4\uac1c\ubcc0\uc218\uc785\ub2c8\ub2e4.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">3\ucc28 \uc911\uc2ec\uc801\ub960\uc744 \uacc4\uc0b0\ud558\ub824\uba74, \ube44\ub300\uce6d t \ubd84\ud3ec\uc758 \ud655\ub960 \ubc00\ub3c4 \ud568\uc218\ub97c \uc774\uc6a9\ud558\uc5ec \ub2e4\uc74c\uacfc \uac19\uc740 \uc801\ubd84\uc744 \uacc4\uc0b0\ud569\ub2c8\ub2e4:<br>\\[ \\mu_3 = E[(X &#8211; \\mu)^3] = \\int_{-\\infty}^{\\infty} (x &#8211; \\mu)^3 f(x|\\nu, \\lambda) dx \\]<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\uc774 \uc801\ubd84\uc758 \uad6c\uccb4\uc801\uc778 \ud574\uc11d\uc801\uc778 \uacc4\uc0b0\uc740 \ub9e4\uc6b0 \ubcf5\uc7a1\ud560 \uc218 \uc788\uc73c\uba70, \uc77c\ubc18\uc801\uc73c\ub85c \uc218\uce58\uc801 \ubc29\ubc95\uc744 \uc0ac\uc6a9\ud558\uc5ec \uacc4\uc0b0\ud569\ub2c8\ub2e4. \uadf8\ub7ec\ub098 \uc65c\ub3c4\ub97c \uc815\uc758\ud558\ub294 3\ucc28 \uc911\uc2ec\uc801\ub960\uc744 \ud1b5\ud574 \ube44\ub300\uce6d t \ubd84\ud3ec\uc758 \uc65c\ub3c4\ub97c \uad6c\ud560 \uc218 \uc788\uc2b5\ub2c8\ub2e4.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\uc65c\ub3c4\ub294 \ub2e4\uc74c\uacfc \uac19\uc774 \uc815\uc758\ub429\ub2c8\ub2e4:<br>\\[ \\text{\uc65c\ub3c4} = \\frac{\\mu_3}{\\sigma^3} \\]<br>\uc5ec\uae30\uc11c \\(\\mu_3\\)\ub294 3\ucc28 \uc911\uc2ec\uc801\ub960, \\(\\sigma\\)\ub294 \ud45c\uc900\ud3b8\ucc28\uc785\ub2c8\ub2e4.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\ube44\ub300\uce6d t \ubd84\ud3ec\uc758 \uacbd\uc6b0, \uc65c\ub3c4\ub294 \ube44\ub300\uce6d\uc131 \ub9e4\uac1c\ubcc0\uc218 \\(\\lambda\\)\uc5d0 \uc758\uc874\ud558\uba70, \uc774\ub294 \ube44\ub300\uce6d\uc131\uc744 \uc124\uba85\ud558\ub294 \ub370 \uc911\uc694\ud55c \uc5ed\ud560\uc744 \ud569\ub2c8\ub2e4.<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\"> \\[ f(x; \\xi, \\omega, \\nu, \\alpha) = 2 \\cdot t\\left(\\frac{x &#8211; \\xi}{\\omega}; \\nu\\right) \\cdot T\\left(\\alpha \\cdot \\left(\\frac{x &#8211; \\xi}{\\omega}\\right) \\cdot \\sqrt{\\frac{\\nu + 1}{\\nu + (x &#8211; \\xi)^2 \/ \\omega^2}}; \\nu + 1\\right) \\]<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\uc5ec\uae30\uc11c ( t\ub294 \uc790\uc720\ub3c4\uac00 \\(\\nu\\)\uc778 \ud45c\uc900 t \ubd84\ud3ec\uc758 \ud655\ub960 \ubc00\ub3c4 \ud568\uc218\uc774\uace0, ( T )\ub294 \uc790\uc720\ub3c4\uac00 (\\(\\nu\\))\uc778 \ud45c\uc900 t \ubd84\ud3ec\uc758 \ub204\uc801 \ubd84\ud3ec \ud568\uc218\uc785\ub2c8\ub2e4.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Skew_t_%EB%B6%84%ED%8F%AC%EC%9D%98_%ED%99%9C%EC%9A%A9\"><\/span>Skew t \ubd84\ud3ec\uc758 \ud65c\uc6a9<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Skew t \ubd84\ud3ec\ub294 \uae08\uc735 \ub370\uc774\ud130 \ubd84\uc11d, \uc0dd\uba85\uacfc\ud559, \uacf5\ud559 \ub4f1 \ub2e4\uc591\ud55c \ubd84\uc57c\uc5d0\uc11c \ube44\ub300\uce6d\uc131\uc744 \uace0\ub824\ud55c \ub370\uc774\ud130 \ubd84\uc11d\uc5d0 \uc0ac\uc6a9\ub429\ub2c8\ub2e4. \ud2b9\ud788, \uadf9\ub2e8\uac12\uc774\ub098 \ube44\ub300\uce6d\uc801\uc778 \ub370\uc774\ud130\ub97c \ubaa8\ub378\ub9c1\ud560 \ub54c \uc720\uc6a9\ud569\ub2c8\ub2e4.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<h3 class=\"wp-block-heading has-medium-font-size\" id=\"Python\"><span class=\"ez-toc-section\" id=\"%E2%96%A0_Python%EC%9D%84_%EC%9D%B4%EC%9A%A9%ED%95%9C_%EC%8A%A4%ED%81%90_t_%EB%B6%84%ED%8F%AC_%EC%8B%9C%EB%AE%AC%EB%A0%88%EC%9D%B4%EC%85%98\"><\/span><strong>\u25a0 <\/strong>Python\uc744 \uc774\uc6a9\ud55c \uc2a4\ud050 t \ubd84\ud3ec \uc2dc\ubbac\ub808\uc774\uc158<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">matplotlib \uc124\uce58<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">pip install matplotlib<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\uc6b0\uc120 \uc2e4\ud589\ud574<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"863\" height=\"426\" src=\"http:\/\/www.statdc.com\/sm24_wp\/wp-content\/uploads\/2024\/06\/image.png\" alt=\"\" class=\"wp-image-1297\" srcset=\"http:\/\/www.inmining.co.kr\/sm24_wp\/wp-content\/uploads\/2024\/06\/image.png 863w, http:\/\/www.inmining.co.kr\/sm24_wp\/wp-content\/uploads\/2024\/06\/image-300x148.png 300w, http:\/\/www.inmining.co.kr\/sm24_wp\/wp-content\/uploads\/2024\/06\/image-768x379.png 768w\" sizes=\"auto, (max-width: 863px) 100vw, 863px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\uc815\uc0c1 \uc124\uce58 \uc644\ub8cc \uc2dc <\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"589\" src=\"http:\/\/www.statdc.com\/sm24_wp\/wp-content\/uploads\/2024\/06\/20240719_195331-1024x589.png\" alt=\"\" class=\"wp-image-1300\" srcset=\"http:\/\/www.inmining.co.kr\/sm24_wp\/wp-content\/uploads\/2024\/06\/20240719_195331-1024x589.png 1024w, http:\/\/www.inmining.co.kr\/sm24_wp\/wp-content\/uploads\/2024\/06\/20240719_195331-300x173.png 300w, http:\/\/www.inmining.co.kr\/sm24_wp\/wp-content\/uploads\/2024\/06\/20240719_195331-768x442.png 768w, http:\/\/www.inmining.co.kr\/sm24_wp\/wp-content\/uploads\/2024\/06\/20240719_195331-920x529.png 920w, http:\/\/www.inmining.co.kr\/sm24_wp\/wp-content\/uploads\/2024\/06\/20240719_195331.png 1081w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Python\uc5d0\uc11c\ub294 &#8220;scipy&#8221;\ub77c\uc774\ube0c\ub7ec\ub9ac\uc640 &#8220;statsmodels&#8221; \ub77c\uc774\ube0c\ub7ec\ub9ac\ub97c \uc0ac\uc6a9\ud558\uc5ec \uc2a4\ud050 t \ubd84\ud3ec\ub97c \uc2dc\ubbac\ub808\uc774\uc158\ud560 \uc218 \uc788\uc2b5\ub2c8\ub2e4.<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>import numpy as np\nimport matplotlib.pyplot as plt\nfrom scipy.stats import skewnorm, t\n\n# \ub9e4\uac1c\ubcc0\uc218 \uc124\uc815\nalpha = 5   # \ube44\ub300\uce6d\uc131\ndf = 10     # \uc790\uc720\ub3c4\nloc = 0     # \uc704\uce58\nscale = 1   # \ucc99\ub3c4\n\n# \uc2a4\ud050 t \ubd84\ud3ec \ub370\uc774\ud130 \uc0dd\uc131\ndata = t(df, loc=loc, scale=scale).rvs(1000) + skewnorm(alpha, loc=loc, scale=scale).rvs(1000)\n\n# \ud788\uc2a4\ud1a0\uadf8\ub7a8 \uadf8\ub9ac\uae30\nplt.hist(data, bins=30, density=True, edgecolor='black', alpha=0.7)\nplt.title('Histogram of Skew t Distribution')\nplt.xlabel('Value')\nplt.ylabel('Density')\nplt.show()<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">\uc704 \ucf54\ub4dc\ub294 \uc2a4\ud050 t \ubd84\ud3ec\ub97c \uc2dc\ubbac\ub808\uc774\uc158\ud558\uc5ec \ud788\uc2a4\ud1a0\uadf8\ub7a8\uc73c\ub85c \uc2dc\uac01\ud654\ud55c \uac83\uc785\ub2c8\ub2e4. &#8220;scipy.stats&#8221;\ubaa8\ub4c8\uc758 &#8221; skewnorm&#8221;\ud568\uc218\uc640 t \ud568\uc218\ub97c \uc0ac\uc6a9\ud558\uc5ec \ube44\ub300\uce6d\uc131\uacfc \uc790\uc720\ub3c4\ub97c \uc870\uc808\ud55c \ub370\uc774\ud130\ub97c \uc0dd\uc131\ud569\ub2c8\ub2e4.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"603\" height=\"237\" src=\"http:\/\/www.statdc.com\/sm24_wp\/wp-content\/uploads\/2024\/06\/image-2.png\" alt=\"\" class=\"wp-image-1302\" srcset=\"http:\/\/www.inmining.co.kr\/sm24_wp\/wp-content\/uploads\/2024\/06\/image-2.png 603w, http:\/\/www.inmining.co.kr\/sm24_wp\/wp-content\/uploads\/2024\/06\/image-2-300x118.png 300w\" sizes=\"auto, (max-width: 603px) 100vw, 603px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"574\" height=\"462\" src=\"http:\/\/www.statdc.com\/sm24_wp\/wp-content\/uploads\/2024\/06\/image-3.png\" alt=\"\" class=\"wp-image-1303\" srcset=\"http:\/\/www.inmining.co.kr\/sm24_wp\/wp-content\/uploads\/2024\/06\/image-3.png 574w, http:\/\/www.inmining.co.kr\/sm24_wp\/wp-content\/uploads\/2024\/06\/image-3-300x241.png 300w\" sizes=\"auto, (max-width: 574px) 100vw, 574px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\uc2a4\ud050 t \ubd84\ud3ec\ub294 \ub370\uc774\ud130\uc758 \ube44\ub300\uce6d\uc131\uc744 \ud3ec\ud568\ud558\uc5ec \ub2e4\uc591\ud55c \ubd84\ud3ec \ud615\ud0dc\ub97c \uc124\uba85\ud560 \uc218 \uc788\ub294 \uc720\uc6a9\ud55c \ub3c4\uad6c\ub85c, \uc774\ub97c \ud1b5\ud574 \ubcf5\uc7a1\ud55c \ub370\uc774\ud130\ub97c \ubcf4\ub2e4 \uc815\ud655\ud558\uac8c \ubaa8\ub378\ub9c1\ud560 \uc218 \uc788\uc2b5\ub2c8\ub2e4.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<h3 class=\"wp-block-heading has-medium-font-size\" id=\"tr\"><span class=\"ez-toc-section\" id=\"%E2%96%A0_Skew_t-distribution_in_R\"><\/span><strong>\u25a0 Skew t-distribution in R<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">R \ud504\ub85c\uadf8\ub798\ubc0d\uc5d0\uc11c\ub294 &#8220;skew-t&#8221;\ubd84\ud3ec\ub97c \uc2dc\ubbac\ub808\uc774\uc158\ud558\uace0 \ubd84\uc11d\ud558\uae30 \uc704\ud574 \ub2e4\uc591\ud55c \ud328\ud0a4\uc9c0\ub97c \uc0ac\uc6a9\ud560 \uc218 \uc788\uc2b5\ub2c8\ub2e4. \ub300\ud45c\uc801\uc73c\ub85c &#8220;sn&#8221;  \ud328\ud0a4\uc9c0\uac00 \uc788\uc73c\uba70, \uc774 \ud328\ud0a4\uc9c0\ub294 \uc2a4\ud050 t \ubd84\ud3ec\ub97c \ud3ec\ud568\ud55c \uc5ec\ub7ec \uc2a4\ud050 \ubd84\ud3ec\ub97c \ub2e4\ub8f0 \uc218 \uc788\ub294 \uae30\ub2a5\uc744 \uc81c\uacf5\ud569\ub2c8\ub2e4.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\ub2e4\uc74c\uc740 &#8220;sn&#8221;   \ud328\ud0a4\uc9c0\ub97c \uc0ac\uc6a9\ud558\uc5ec \uc2a4\ud050 t \ubd84\ud3ec\ub97c \uc2dc\ubbac\ub808\uc774\uc158\ud558\uace0, \uc774\ub97c \uc2dc\uac01\ud654\ud558\ub294 \uc608\uc81c \ucf54\ub4dc\uc785\ub2c8\ub2e4.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"1_SN_%ED%8C%A8%ED%82%A4%EC%A7%80_%EC%84%A4%EC%B9%98_%EB%B0%8F_%EB%A1%9C%EB%93%9C\"><\/span>1.  SN \ud328\ud0a4\uc9c0 \uc124\uce58 \ubc0f \ub85c\ub4dc<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<pre class=\"wp-block-code\"><code># \ud328\ud0a4\uc9c0 \uc124\uce58\ninstall.packages(\"sn\")\n\n# \ud328\ud0a4\uc9c0 \ub85c\ub4dc\nlibrary(sn)<\/code><\/pre>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"667\" height=\"377\" src=\"http:\/\/www.statdc.com\/sm24_wp\/wp-content\/uploads\/2024\/06\/image-4.png\" alt=\"\" class=\"wp-image-1306\" srcset=\"http:\/\/www.inmining.co.kr\/sm24_wp\/wp-content\/uploads\/2024\/06\/image-4.png 667w, http:\/\/www.inmining.co.kr\/sm24_wp\/wp-content\/uploads\/2024\/06\/image-4-300x170.png 300w\" sizes=\"auto, (max-width: 667px) 100vw, 667px\" \/><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"2_Skew_t_%EB%B6%84%ED%8F%AC_%EB%8D%B0%EC%9D%B4%ED%84%B0_%EC%83%9D%EC%84%B1\"><\/span>2. Skew t \ubd84\ud3ec \ub370\uc774\ud130 \uc0dd\uc131<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">R \uc5d0\uc11c &#8216;rst&#8217;\ud568\uc218 \ud65c\uc131\ud654 \ud558\uae30 \uc704\ud558\uc5ec<br>\uc6b0\uc120 <br>library(sn) <br>\uc2e4\ud589<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"581\" height=\"230\" src=\"http:\/\/www.statdc.com\/sm24_wp\/wp-content\/uploads\/2024\/06\/image-5.png\" alt=\"\" class=\"wp-image-1308\" srcset=\"http:\/\/www.inmining.co.kr\/sm24_wp\/wp-content\/uploads\/2024\/06\/image-5.png 581w, http:\/\/www.inmining.co.kr\/sm24_wp\/wp-content\/uploads\/2024\/06\/image-5-300x119.png 300w\" sizes=\"auto, (max-width: 581px) 100vw, 581px\" \/><\/figure>\n\n\n\n<pre class=\"wp-block-code\"><code># \ub9e4\uac1c\ubcc0\uc218 \uc124\uc815\nxi &lt;- 0       # \uc704\uce58 (location)\nomega &lt;- 1    # \ucc99\ub3c4 (scale)\nalpha &lt;- 5    # \ube44\ub300\uce6d\uc131 (skewness)\nnu &lt;- 10      # \uc790\uc720\ub3c4 (degrees of freedom)\n\n# \uc2a4\ud050 t \ubd84\ud3ec \ub370\uc774\ud130 \uc0dd\uc131\nset.seed(123)  # \uc7ac\ud604\uc131\uc744 \uc704\ud574 \uc2dc\ub4dc \uc124\uc815\ndata &lt;- rst(n=1000, xi=xi, omega=omega, alpha=alpha, nu=nu)<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"3_%ED%9E%88%EC%8A%A4%ED%86%A0%EA%B7%B8%EB%9E%A8_%EB%B0%8F_%EB%B0%80%EB%8F%84_%ED%95%A8%EC%88%98_%EC%8B%9C%EA%B0%81%ED%99%94\"><\/span>3. \ud788\uc2a4\ud1a0\uadf8\ub7a8 \ubc0f \ubc00\ub3c4 \ud568\uc218 \uc2dc\uac01\ud654<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<pre class=\"wp-block-code\"><code># \ud788\uc2a4\ud1a0\uadf8\ub7a8 \uadf8\ub9ac\uae30\nhist(data, breaks=30, probability=TRUE, main=\"Histogram of Skew t Distribution\", xlab=\"Value\", col=\"lightblue\", border=\"black\")\n\n# \ubc00\ub3c4 \ud568\uc218 \ucd94\uac00\nlines(density(data), col=\"red\", lwd=2)<\/code><\/pre>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-8f761849 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"505\" height=\"449\" src=\"http:\/\/www.statdc.com\/sm24_wp\/wp-content\/uploads\/2024\/06\/image-6.png\" alt=\"\" class=\"wp-image-1309\" srcset=\"http:\/\/www.inmining.co.kr\/sm24_wp\/wp-content\/uploads\/2024\/06\/image-6.png 505w, http:\/\/www.inmining.co.kr\/sm24_wp\/wp-content\/uploads\/2024\/06\/image-6-300x267.png 300w\" sizes=\"auto, (max-width: 505px) 100vw, 505px\" \/><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"467\" height=\"444\" src=\"http:\/\/www.statdc.com\/sm24_wp\/wp-content\/uploads\/2024\/06\/image-8.png\" alt=\"\" class=\"wp-image-1311\" srcset=\"http:\/\/www.inmining.co.kr\/sm24_wp\/wp-content\/uploads\/2024\/06\/image-8.png 467w, http:\/\/www.inmining.co.kr\/sm24_wp\/wp-content\/uploads\/2024\/06\/image-8-300x285.png 300w\" sizes=\"auto, (max-width: 467px) 100vw, 467px\" \/><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"491\" height=\"453\" src=\"http:\/\/www.statdc.com\/sm24_wp\/wp-content\/uploads\/2024\/06\/image-7.png\" alt=\"\" class=\"wp-image-1310\" srcset=\"http:\/\/www.inmining.co.kr\/sm24_wp\/wp-content\/uploads\/2024\/06\/image-7.png 491w, http:\/\/www.inmining.co.kr\/sm24_wp\/wp-content\/uploads\/2024\/06\/image-7-300x277.png 300w\" sizes=\"auto, (max-width: 491px) 100vw, 491px\" \/><\/figure>\n<\/div>\n<\/div>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"4_Skew_t_%EB%B6%84%ED%8F%AC%EC%9D%98_%EB%B0%80%EB%8F%84_%ED%95%A8%EC%88%98%EC%99%80_%EB%88%84%EC%A0%81_%EB%B6%84%ED%8F%AC_%ED%95%A8%EC%88%98_%EA%B7%B8%EB%A6%AC%EA%B8%B0\"><\/span>4. Skew t \ubd84\ud3ec\uc758 \ubc00\ub3c4 \ud568\uc218\uc640 \ub204\uc801 \ubd84\ud3ec \ud568\uc218 \uadf8\ub9ac\uae30<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<pre class=\"wp-block-code\"><code># \ubc00\ub3c4 \ud568\uc218\nx &lt;- seq(-5, 5, length=100)\ny_density &lt;- dst(x, xi=xi, omega=omega, alpha=alpha, nu=nu)\n\n# \ubc00\ub3c4 \ud568\uc218 \uc2dc\uac01\ud654\nplot(x, y_density, type=\"l\", col=\"blue\", lwd=2, main=\"Density Function of Skew t Distribution\", xlab=\"Value\", ylab=\"Density\")\n\n# \ub204\uc801 \ubd84\ud3ec \ud568\uc218\ny_cdf &lt;- pst(x, xi=xi, omega=omega, alpha=alpha, nu=nu)\n\n# \ub204\uc801 \ubd84\ud3ec \ud568\uc218 \uc2dc\uac01\ud654\nplot(x, y_cdf, type=\"l\", col=\"green\", lwd=2, main=\"CDF of Skew t Distribution\", xlab=\"Value\", ylab=\"Probability\")<\/code><\/pre>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-8f761849 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"498\" height=\"459\" src=\"http:\/\/www.statdc.com\/sm24_wp\/wp-content\/uploads\/2024\/06\/image-9.png\" alt=\"\" class=\"wp-image-1312\" srcset=\"http:\/\/www.inmining.co.kr\/sm24_wp\/wp-content\/uploads\/2024\/06\/image-9.png 498w, http:\/\/www.inmining.co.kr\/sm24_wp\/wp-content\/uploads\/2024\/06\/image-9-300x277.png 300w\" sizes=\"auto, (max-width: 498px) 100vw, 498px\" \/><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"502\" height=\"450\" src=\"http:\/\/www.statdc.com\/sm24_wp\/wp-content\/uploads\/2024\/06\/image-10.png\" alt=\"\" class=\"wp-image-1313\" srcset=\"http:\/\/www.inmining.co.kr\/sm24_wp\/wp-content\/uploads\/2024\/06\/image-10.png 502w, http:\/\/www.inmining.co.kr\/sm24_wp\/wp-content\/uploads\/2024\/06\/image-10-300x269.png 300w\" sizes=\"auto, (max-width: 502px) 100vw, 502px\" \/><\/figure>\n<\/div>\n<\/div>\n\n\n\n<p class=\"wp-block-paragraph\">\uc704\uc758 \ucf54\ub4dc\ub294 &#8220;sn&#8221; \ud328\ud0a4\uc9c0\ub97c \uc0ac\uc6a9\ud558\uc5ec \uc2a4\ud050 t \ubd84\ud3ec \ub370\uc774\ud130\ub97c \uc0dd\uc131\ud558\uace0, \uadf8 \ud788\uc2a4\ud1a0\uadf8\ub7a8\uacfc \ubc00\ub3c4 \ud568\uc218\ub97c \uc2dc\uac01\ud654\ud558\ub294 \uc608\uc81c\uc785\ub2c8\ub2e4. \ub610\ud55c, \ubc00\ub3c4 \ud568\uc218\uc640 \ub204\uc801 \ubd84\ud3ec \ud568\uc218\ub3c4 \uac01\uac01\uc758 \uadf8\ub798\ud504\ub85c \uc2dc\uac01\ud654\ud569\ub2c8\ub2e4.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"5_R_%EC%BD%94%EB%93%9C%EB%A5%BC_%ED%86%B5%ED%95%B4_%EC%9D%B4%ED%95%B4%ED%95%9C_%EB%82%B4%EC%9A%A9_%EC%9A%94%EC%95%BD\"><\/span>5. R \ucf54\ub4dc\ub97c \ud1b5\ud574 \uc774\ud574\ud55c \ub0b4\uc6a9 \uc694\uc57d<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\ud328\ud0a4\uc9c0 \uc124\uce58 \ubc0f \ub85c\ub4dc<\/strong>: &#8220;sn&#8221;\ud328\ud0a4\uc9c0\ub97c \uc124\uce58\ud558\uace0 \ub85c\ub4dc<\/li>\n\n\n\n<li><strong>\ub370\uc774\ud130 \uc0dd\uc131<\/strong>: &#8220;rst&#8221;\ud568\uc218\ub97c \uc0ac\uc6a9\ud558\uc5ec \uc2a4\ud050 t \ubd84\ud3ec \ub370\uc774\ud130\ub97c \uc0dd\uc131<\/li>\n\n\n\n<li><strong>\ud788\uc2a4\ud1a0\uadf8\ub7a8 \uc2dc\uac01\ud654<\/strong>: \ud788\uc2a4\ud1a0\uadf8\ub7a8\uc744 \uadf8\ub824 \ub370\uc774\ud130 \ubd84\ud3ec\ub97c \uc2dc\uac01\uc801 \ud655\uc778<\/li>\n\n\n\n<li><strong>\ubc00\ub3c4 \ud568\uc218\uc640 \ub204\uc801 \ubd84\ud3ec \ud568\uc218 \uc2dc\uac01\ud654<\/strong>: &#8220;dst&#8221;\uc640 &#8220;pst&#8221; \ud568\uc218\ub97c \uc0ac\uc6a9\ud558\uc5ec \uac01\uac01 \ubc00\ub3c4 \ud568\uc218\uc640 \ub204\uc801 \ubd84\ud3ec \ud568\uc218\ub97c \uacc4\uc0b0 \ubc0f \uc2dc\uac01\ud654<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Skew t \ubd84\ud3ec\uc758 \uc815\uc758\uc640 \ud2b9\uc9d5 Skew t-\ubd84\ud3ec(Skew t-distribution)\ub294 \uc2a4\ud29c\ub358\ud2b8 t \ubd84\ud3ec\uc758 \uc77c\ubc18\ud654\ub41c \ud615\ud0dc\ub85c, \ube44\ub300\uce6d\uc131\uc744 \ud3ec\ud568\ud558\uc5ec \ubd84\ud3ec\uc758 \ud615\ud0dc\ub97c \uc870\uc815\ud560&#8230;<\/p>\n","protected":false},"author":1,"featured_media":388,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[6],"tags":[],"class_list":["post-386","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-stat","wpcat-6-id"],"_links":{"self":[{"href":"http:\/\/www.inmining.co.kr\/index.php?rest_route=\/wp\/v2\/posts\/386","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/www.inmining.co.kr\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/www.inmining.co.kr\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/www.inmining.co.kr\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/www.inmining.co.kr\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=386"}],"version-history":[{"count":75,"href":"http:\/\/www.inmining.co.kr\/index.php?rest_route=\/wp\/v2\/posts\/386\/revisions"}],"predecessor-version":[{"id":1379,"href":"http:\/\/www.inmining.co.kr\/index.php?rest_route=\/wp\/v2\/posts\/386\/revisions\/1379"}],"wp:featuredmedia":[{"embeddable":true,"href":"http:\/\/www.inmining.co.kr\/index.php?rest_route=\/wp\/v2\/media\/388"}],"wp:attachment":[{"href":"http:\/\/www.inmining.co.kr\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=386"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/www.inmining.co.kr\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=386"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/www.inmining.co.kr\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=386"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}