\u76ee\u6b21<\/p>
- 1<\/span> \u30ab\u30a42\u4e57\u5206\u5e03\u306e\u57fa\u672c\u60c5\u5831<\/a>
- 1.1<\/span> \u78ba\u7387\u5bc6\u5ea6\u95a2\u6570\u3068\u7d2f\u7a4d\u5206\u5e03\u95a2\u6570<\/a><\/li><\/ul><\/li>
- 2<\/span> \u30ab\u30a4\uff12\u4e57\u5206\u5e03\u306e\u518d\u751f\u6027<\/a><\/li>
- 3<\/span> \u30ab\u30a4\uff12\u4e57\u5206\u5e03\u3068\u30ac\u30f3\u30de\u5206\u5e03<\/a><\/li>
- 4<\/span> \u30ab\u30a4\uff12\u4e57\u5206\u5e03\u3068\\(t\\)\u5206\u5e03<\/a><\/li>
- 5<\/span> \u30ab\u30a4\uff12\u4e57\u5206\u5e03\u3068\\(F\\)\u5206\u5e03<\/a><\/li>
- 6<\/span> \u30b3\u30af\u30e9\u30f3\u306e\u5b9a\u7406\u3068\u30ab\u30a4\uff12\u4e57\u5206\u5e03<\/a><\/li>
- 7<\/span> \u30ab\u30a4\uff12\u4e57\u5206\u5e03\u3068\u95a2\u9023\u6df1\u3044\u78ba\u7387\u5206\u5e03<\/a><\/li><\/ul><\/div>\n
\u30ab\u30a42\u4e57\u5206\u5e03\u306e\u57fa\u672c\u60c5\u5831<\/span><\/h2>\n\n\n\n
\u203b\u3000\u8868\u306f\u6a2a\u306b\u30b9\u30af\u30ed\u30fc\u30eb\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n
\n\n\n
\n \u30d1\u30e9\u30e1\u30fc\u30bf<\/td>\n \\(n\\)
\u30ab\u30a42\u4e57\u5206\u5e03\u306e\u81ea\u7531\u5ea6\u3068\u3082\u8a00\u308f\u308c\u307e\u3059\u3002<\/td>\n<\/tr>\n\n \u78ba\u7387\u5909\u6570\u306e\u7bc4\u56f2<\/td>\n \\(0\\leq x \\)<\/td>\n<\/tr>\n \n \u78ba\u7387\u5bc6\u5ea6\u95a2\u6570<\/a><\/td>\n \\(\\displaystyle \\frac{ 1 }{ 2^{\\frac{1}{2}n}\\Gamma\\left( \\frac{n}{2} \\right) }e^{-\\frac{x}{2}}x^{\\frac{n}{2}-1} \\)<\/td>\n<\/tr>\n \n \u7d2f\u7a4d\u5206\u5e03\u95a2\u6570<\/a><\/td>\n \\(\\displaystyle \\frac{\\Gamma_{\\frac{x}{2}}\\left( \\frac{n}{2} \\right)}{\\Gamma\\left( \\frac{n}{2} \\right)}\\)
\u305f\u3060\u3057\u3001\\(\\Gamma_{x}\\left( n \\right)\\)\u306f\u4e0d\u5b8c\u5168\u30ac\u30f3\u30de\u95a2\u6570\u3067\u3042\u308a\u6b21\u5f0f\u3067\u5b9a\u7fa9\u3055\u308c\u307e\u3059\u3002
\\(\\displaystyle \\Gamma_{x}(n)=\\int_{0}^{x}e^{-t}t^{n-1}dt\\)<\/td>\n<\/tr>\n\n \u7a4d\u7387\u6bcd\u95a2\u6570<\/a><\/td>\n \\(\\displaystyle (1-2t)^{-\\frac{n}{2}},\\ \\ \\ t<\\frac{1}{2} \\)<\/td>\n<\/tr>\n \n \u7279\u6027\u95a2\u6570<\/a><\/td>\n \\(\\displaystyle (1-2it)^{-\\frac{n}{2}} \\)<\/td>\n<\/tr>\n \n \u30ad\u30e5\u30e0\u30e9\u30f3\u30c8\u6bcd\u95a2\u6570<\/a><\/td>\n \\(\\displaystyle \\frac{n}{2}\\log(1-2t)\\)<\/td>\n<\/tr>\n \n \\(r\\)\u6b21\u30ad\u30e5\u30e0\u30e9\u30f3\u30c8<\/a><\/td>\n \\(\\displaystyle 2^{r-1}n(r-1)!,\\ \\ \\ r\\geq 0\\)<\/td>\n<\/tr>\n \n \\(r\\)\u6b21\u30e2\u30fc\u30e1\u30f3\u30c8<\/a>
\uff08\u539f\u70b9\u307e\u308f\u308a\uff09<\/td>\n\\(\\displaystyle 2^{r}\\prod_{i=0}^{r-1}\\left( \\frac{n}{2}+i \\right) = \\frac{2^{r}\\Gamma\\left( \\frac{n}{2}+r \\right)}{\\Gamma\\left( \\frac{n}{2} \\right)}\\)<\/td>\n<\/tr>\n \n \u671f\u5f85\u5024<\/a><\/td>\n \\( \\displaystyle n \\)<\/td>\n<\/tr>\n \n \u5206\u6563<\/a><\/td>\n \\( \\displaystyle 2n \\)<\/td>\n<\/tr>\n \n \u4e2d\u4f4d\u6570<\/td>\n \n \\( \\displaystyle n-\\frac{2}{3} \\)\uff08\u5341\u5206\u306b\u5927\u304d\u306a\\(n\\)\u306b\u5bfe\u3057\u3066\u8fd1\u4f3c\u7684\u306b\u8868\u3057\u305f\u3082\u306e\u3067\u3059\uff09<\/p>\n<\/td>\n<\/tr>\n
\n \u30e2\u30fc\u30c9<\/a><\/td>\n \\( \\displaystyle n-2,\\ \\ \\ n\\geq 2 \\)<\/td>\n<\/tr>\n \n \u5e73\u5747\u504f\u5dee<\/a><\/td>\n \\( \\displaystyle \\frac{e^{-\\frac{n}{2}}n^{\\frac{n}{2}}}{2^{\\frac{n}{2}-1}\\Gamma\\left( \\frac{n}{2} \\right)} \\)<\/td>\n<\/tr>\n \n \u6b6a\u5ea6<\/a><\/td>\n \n \\(\\displaystyle \\sqrt{\\frac{8}{n}}\\)<\/p>\n<\/td>\n<\/tr>\n
\n \u5c16\u5ea6<\/a><\/td>\n \\( \\displaystyle 3+\\frac{12}{n}\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/figure>\n\n\n \u8a3c\u660e\u4e00\u89a7<\/h3>\n\n\n\n
\u3000<\/p>\n\n\n\n
\u78ba\u7387\u5bc6\u5ea6\u95a2\u6570\u3068\u7d2f\u7a4d\u5206\u5e03\u95a2\u6570<\/span><\/h3>\n\n\n\n
\u69d8\u3005\u306a\u81ea\u7531\u5ea6\u306b\u5bfe\u3059\u308b\u30ab\u30a4\uff12\u4e57\u5206\u5e03\u306e\u78ba\u7387\u5bc6\u5ea6\u95a2\u6570\u3068\u7d2f\u7a4d\u5206\u5e03\u95a2\u6570\u3067\u3059\u3002<\/p>\n\n\n\n
![\"\"](\"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-content\/uploads\/2020\/08\/\u30ab\u30a42\u4e57\u5206\u5e03\uff08\u78ba\u7387\u5bc6\u5ea6\u95a2\u6570\uff09.png\")
<\/figure>\n\n\n\n![\"\"](\"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-content\/uploads\/2020\/08\/\u7d2f\u7a4d\u5206\u5e03\u95a2\u6570\uff08\u30ab\u30a42\u4e57\u5206\u5e03\uff09.png\")
<\/figure>\n\n\n\n\u30ab\u30a4\uff12\u4e57\u5206\u5e03\u306e\u518d\u751f\u6027<\/span><\/h2>\n\n\n\n
\u3000\u30ab\u30a4\uff12\u4e57\u5206\u5e03\u306b\u5f93\u3046\u4e92\u3044\u306b\u72ec\u7acb\u306a\u78ba\u7387\u5909\u6570\\(X_{i}\\sim \\chi^{2}(n_{i})\\)\uff08\\(i=1,\\cdots,n\\)\uff09\u306b\u5bfe\u3057\u3066\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306a\u3053\u3068\u304c\u6210\u308a\u7acb\u3061\u307e\u3059\u3002
\\begin{align}
\\sum_{i=1}^{n}X_{i} \\sim \\chi^{2}\\left( \\sum_{i=1}^{n}n_{i}\\right)
\\end{align}<\/div>\u8a3c\u660e\u306f\u3068\u3066\u3082\u7c21\u5358\u3067\u3059\u3002\u78ba\u7387\u5909\u6570\\(X_{i}\\)\u306e\u7a4d\u7387\u6bcd\u95a2\u6570\u3092\\(M_{X_{i}}(t)\\)\u3068\u3059\u308b\u3068\u3001\\begin{align}
M_{\\sum_{i=1}^{n}X_{i}}(t) &= \\mathrm{E}[\\exp[t(X_{1}+\\cdots+X_{n})]] \\\\
&= \\prod_{i=1}^{n}\\mathrm{E}[\\exp[tX_{i}]] \\\\
&= \\prod_{i=1}^{n}M_{X_{i}}(t) \\\\
&= \\prod_{i=1}^{n}(1-2t)^{-\\frac{n_{i}}{2}} \\\\
&= (1-2t)^{-\\frac{\\sum_{i=1}^{n}n_{i}}{2}}
\\end{align}<\/div>\u304c\u6210\u308a\u7acb\u3064\u3053\u3068\u304b\u3089\u3001\uff1c\u7a4d\u7387\u6bcd\u95a2\u6570\u306e\u6027\u8cea\uff1e<\/a>\u3088\u308a\u3001\\(X_{1}+\\cdots+X_{n}\\)\u306f\u81ea\u7531\u5ea6\\(n_{1}+\\cdots+n_{n}\\)\u306e\u30ab\u30a4\uff12\u4e57\u5206\u5e03\u306b\u5f93\u3046\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059\u3002<\/p>\n\n\n\n\n - 2<\/span> \u30ab\u30a4\uff12\u4e57\u5206\u5e03\u306e\u518d\u751f\u6027<\/a><\/li>
- 1.1<\/span> \u78ba\u7387\u5bc6\u5ea6\u95a2\u6570\u3068\u7d2f\u7a4d\u5206\u5e03\u95a2\u6570<\/a><\/li><\/ul><\/li>
![\"\u7a4d\u7387\u6bcd\u95a2\u6570\u3068\u306f\u3010\u5b9a\u7fa9\u3068\u6027\u8cea\u3092\u89e3\u8aac\u3011\"](\"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-content\/uploads\/2020\/06\/9fc17caf-9cad-4670-b857-eb43ec911ab9-100x100.png\")
<\/div>\n ![\"\u30ac\u30f3\u30de\u5206\u5e03\"](\"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-content\/uploads\/2020\/07\/\u30ac\u30f3\u30de\u5206\u5e03\uff08\u78ba\u7387\u5bc6\u5ea6\u95a2\u6570\u03b14\uff09-100x100.png\")
<\/div>\n ![\"\"](\"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-content\/uploads\/2020\/07\/\u6b63\u898f\u5206\u5e03\u306e\u95a2\u9023\u5206\u5e03\uff08\u30de\u30c3\u30d7\uff09.png\")
<\/figure>\n","protected":false},"excerpt":{"rendered":"