{"id":18140,"date":"2024-02-22T17:40:47","date_gmt":"2024-02-22T17:40:47","guid":{"rendered":"https:\/\/science-hub.click\/%E5%AF%BE%E6%95%B0%E3%83%AD%E3%82%B8%E3%82%B9%E3%83%86%E3%82%A3%E3%83%83%E3%82%AF%E6%B3%95%E5%89%87-%E5%AE%9A%E7%BE%A9\/"},"modified":"2024-02-22T17:40:47","modified_gmt":"2024-02-22T17:40:47","slug":"%E5%AF%BE%E6%95%B0%E3%83%AD%E3%82%B8%E3%82%B9%E3%83%86%E3%82%A3%E3%83%83%E3%82%AF%E6%B3%95%E5%89%87-%E5%AE%9A%E7%BE%A9","status":"publish","type":"post","link":"https:\/\/science-hub.click\/?p=18140","title":{"rendered":"\u5bfe\u6570\u30ed\u30b8\u30b9\u30c6\u30a3\u30c3\u30af\u6cd5\u5247 – \u5b9a\u7fa9"},"content":{"rendered":"

\u5c0e\u5165<\/h2>
\u4e38\u592a\u7269\u6d41<\/th><\/tr>
\n\"\"<\/figure>
\u51e1\u4f8b\u306e\u03b1 = 1<\/span>\u304a\u3088\u3073\u03b2<\/span>\u306e\u5834\u5408<\/div><\/div><\/div><\/td><\/tr>
\n\"\"<\/figure>
\u51e1\u4f8b\u3067\u306f\u03b1 = 1<\/span>\u304a\u3088\u3073\u03b2<\/span> <\/div><\/div><\/div><\/td><\/tr>
<\/td><\/tr>
\u8a2d\u5b9a<\/th>\u03b1 > 0<\/span>\u30b9\u30b1\u30fc\u30eb\u03b2 > 0 \u306e<\/span>\u5f62\u5f0f<\/td><\/tr>
\u30b5\u30dd\u30fc\u30c8<\/th>
$$ {x\\in[0,\\infty)} $$<\/div><\/td><\/tr>
\u78ba\u7387\u5bc6\u5ea6<\/a><\/span>(\u8cea\u91cf\u95a2\u6570) <\/th>
$$ { \\frac{ (\\beta\/\\alpha)(x\/\\alpha)^{\\beta-1} } { \\left[ 1+(x\/\\alpha)^{\\beta} \\right]^2 }} $$<\/div><\/td><\/tr>
\u5206\u5e03\u95a2\u6570<\/a><\/span><\/th>
$$ {{ 1 \\over 1+(x\/\\alpha)^{-\\beta} }} $$<\/div><\/td><\/tr>
\u5e0c\u671b<\/th>
$$ {{\\alpha\\,\\pi\/\\beta \\over \\sin(\\pi\/\\beta)}} $$<\/div> \u03b2 > 1<\/span>\u306e\u5834\u5408\u3001\u305d\u308c\u4ee5\u5916\u306e\u5834\u5408\u306f\u5b9a\u7fa9\u3055\u308c\u306a\u3044<\/td><\/tr>
\u4e2d\u592e\u5024<\/a><\/span>\uff08\u4e2d\u592e\uff09 <\/th>
$$ {\\alpha\\,} $$<\/div><\/td><\/tr>
\u30d5\u30a1\u30c3\u30b7\u30e7\u30f3<\/th>
$$ {\\alpha\\left(\\frac{\\beta-1}{\\beta+1}\\right)^{1\/\\beta}} $$<\/div> \u03b2 > 1<\/span>\u306e\u5834\u5408\u3001\u305d\u308c\u4ee5\u5916\u306e\u5834\u5408\u306f 0<\/td><\/tr>
\u5206\u6563<\/a><\/span><\/th><\/tr><\/table>

\u78ba\u7387\u7406\u8ad6<\/a><\/span>\u3068\u7d71\u8a08\u5b66<\/a><\/span>\u3067\u306f\u3001\u5bfe\u6570\u30ed\u30b8\u30b9\u30c6\u30a3\u30c3\u30af\u6cd5\u5247<\/b>(\u7d4c\u6e08\u5b66\u3067\u306f\u30d5\u30a3\u30b9\u30af\u5206\u5e03<\/b>\u3068\u3057\u3066\u3082\u77e5\u3089\u308c\u3066\u3044\u307e\u3059) \u306f\u3001\u975e\u8ca0\u306e\u78ba\u7387\u5909\u6570<\/a><\/span>\u306e\u9023\u7d9a\u78ba\u7387\u6cd5\u5247<\/a><\/span>\u3067\u3059\u3002\u3053\u308c\u306f\u3001\u8a3a\u65ad<\/a><\/span>\u307e\u305f\u306f\u6cbb\u7642\u5f8c\u306e\u304c\u3093<\/a><\/span>\u306b\u3088\u308b\u6b7b\u4ea1\u7387\u306a\u3069\u3001\u5f37\u5ea6\u304c\u6700\u521d\u306b\u5897\u52a0\u3057\u3001\u305d\u306e\u5f8c\u6e1b\u5c11\u3059\u308b\u30a4\u30d9\u30f3\u30c8\u306e\u5bff\u547d<\/a><\/span>\u3092\u7814\u7a76\u3059\u308b\u969b\u306b\u4f7f\u7528\u3055\u308c\u307e\u3059\u3002\u307e\u305f\u3001\u6c34\u6587\u5b66\u3067\u306f\u5ddd<\/a><\/span>\u306e\u6d41\u308c<\/a><\/span>\u3084\u964d\u6c34\u91cf\u306e\u30ec\u30d9\u30eb\u3092\u30e2\u30c7\u30eb\u5316\u3059\u308b\u305f\u3081\u306b\u4f7f\u7528\u3055\u308c\u3001\u7d4c\u6e08\u5b66\u3067\u306f\u6240\u5f97\u683c\u5dee\u3092\u30e2\u30c7\u30eb\u5316\u3059\u308b\u305f\u3081\u306b\u4f7f\u7528\u3055\u308c\u307e\u3059\u3002<\/p>

\u5bfe\u6570\u30ed\u30b8\u30b9\u30c6\u30a3\u30c3\u30af\u6cd5\u5247\u306f\u3001\u305d\u306e\u5bfe\u6570<\/span>\u304c\u30ed\u30b8\u30b9\u30c6\u30a3\u30c3\u30af<\/a><\/span>\u6cd5\u5247\u306b\u5f93\u3063\u3066\u5206\u5e03\u3059\u308b\u78ba\u7387\u5909\u6570<\/a><\/span>\u306e\u6cd5\u5247\u3067\u3059\u3002\u3053\u308c\u306f\u5bfe\u6570\u6b63\u898f\u5206\u5e03\u306b\u3088\u304f\u4f3c\u3066\u3044\u307e\u3059\u304c\u3001\u88fe\u304c\u592a\u3044\u3053\u3068\u3067\u533a\u5225\u3055\u308c\u307e\u3059\u3002\u3055\u3089\u306b\u3001\u305d\u306e\u5206\u5e03\u95a2\u6570\u306f\u5bfe\u6570\u6b63\u898f\u3068\u306f\u7570\u306a\u308a\u3001\u660e\u793a\u7684\u306a\u8868\u73fe\u304c\u53ef\u80fd\u3067\u3059\u3002<\/p>

\u7279\u5fb4<\/h2>

\u5206\u5e03\u306b\u306f\u3055\u307e\u3056\u307e\u306a\u30d1\u30e9\u30e1\u30fc\u30bf\u5316\u304c\u3042\u308a\u307e\u3059\u3002\u3053\u3053\u3067\u9078\u629e\u3057\u305f\u3082\u306e\u306b\u3088\u308a\u3001\u30d1\u30e9\u30e1\u30fc\u30bf\u30fc\u306e\u5408\u7406\u7684\u306a\u89e3\u91c8\u304c\u53ef\u80fd\u306b\u306a\u308a\u3001\u5206\u5e03\u95a2\u6570\u306e\u5f0f\u304c\u7c21\u7565\u5316\u3055\u308c\u307e\u3059\u3002\u30d1\u30e9\u30e1\u30fc\u30bf<\/a><\/span>\u03b1>0 \u306f\u30b9\u30b1\u30fc\u30eb \u30d1\u30e9\u30e1\u30fc\u30bf\u3067\u3042\u308a\u3001\u5206\u5e03\u306e\u4e2d\u592e\u5024\u306e\u5f79\u5272\u3082\u679c\u305f\u3057\u307e\u3059<\/a><\/span>\u3002\u30d1\u30e9\u30e1\u30fc\u30bf\u03b2\uff1e\uff10\u306f\u5f62\u72b6\u30d1\u30e9\u30e1\u30fc\u30bf\u3067\u3042\u308b\u3002 \u03b2 > 1<\/span>\u306e\u5834\u5408\u3001\u5206\u5e03\u306f\u5358\u5cf0\u6027\u3068\u306a\u308a\u3001 \u03b2 \u304c<\/span>\u5897\u52a0\u3059\u308b\u3068\u5206\u6563\u306f<\/a><\/span>\u6e1b\u5c11\u3057\u307e\u3059\u3002<\/p>

\u5206\u5e03\u95a2\u6570\u306f<\/p>

$$ {\\begin{align} F(x; \\alpha, \\beta) & = { 1 \\over 1+(x\/\\alpha)^{-\\beta} } \\\\ & = {(x\/\\alpha)^\\beta \\over 1+(x\/\\alpha)^ \\beta } \\\\ & = {x^\\beta \\over \\alpha^\\beta+x^\\beta} \\end{align}} $$<\/div><\/dd><\/dl>

\u3053\u3053\u3067\u3001 x<\/i> > 0<\/span> \u3001 \u03b1 > 0<\/span> \u3001 \u03b2 > 0 \u3067\u3059\u3002<\/span><\/p>

\u78ba\u7387<\/a><\/span>\u5bc6\u5ea6<\/a><\/span>\u306f<\/p>

$$ {f(x; \\alpha, \\beta) = \\frac{ (\\beta\/\\alpha)(x\/\\alpha)^{-\\beta-1} } { \\left[ 1+(x\/\\alpha)^{-\\beta} \\right]^2 }.} $$<\/div><\/dd><\/dl>

\u30a2\u30d7\u30ea\u30b1\u30fc\u30b7\u30e7\u30f3<\/h2>
\n\"\"<\/figure>
\u30cf\u30b6\u30fc\u30c9\u6a5f\u80fd<\/span>\u3002 \u03b1 = 1\u3001<\/span>\u51e1\u4f8b\u306b\u793a\u3059\u03b2<\/span>\u306e\u5024<\/div><\/div><\/div>

\u751f\u5b58\u5206\u6790<\/span><\/h3>

\u5bfe\u6570\u30ed\u30b8\u30b9\u30c6\u30a3\u30c3\u30af\u5206\u5e03\u306f\u3001\u751f\u5b58 (\u5bff\u547d) \u5206\u6790\u306e\u305f\u3081\u306e\u30d1\u30e9\u30e1\u30c8\u30ea\u30c3\u30af \u30e2\u30c7\u30eb\u3092\u63d0\u4f9b\u3057\u307e\u3059\u3002\u901a\u5e38\u306e\u30ef\u30a4\u30d6\u30eb\u5206\u5e03<\/span>\u3068\u306f\u7570\u306a\u308a\u3001\u3053\u306e\u5bc6\u5ea6\u3067\u306f\u975e\u5358\u8abf\u306a\u30ea\u30b9\u30af (\u5931\u6557) \u95a2\u6570\u304c\u53ef\u80fd\u306b\u306a\u308a\u307e\u3059\u3002\u3064\u307e\u308a\u3001 \u03b2 > 1 \u306e\u5834\u5408\u3001<\/span>\u30ea\u30b9\u30af\u95a2\u6570\u306f\u5358\u5cf0\u6027\u306b\u306a\u308a\u307e\u3059 ( \u03b2<\/span> \u2264 1 \u306e\u5834\u5408\u3001\u30ea\u30b9\u30af\u306f\u5358\u8abf\u306b\u6e1b\u5c11\u3057\u307e\u3059)\u3002\u5206\u5e03\u95a2\u6570\u306e\u660e\u793a\u7684\u306a\u5f0f\u304c\u3042\u308b\u3053\u3068\u306f\u3001\u5207\u308a\u6368\u3066\u3089\u308c\u305f<\/i>(\u307e\u305f\u306f\u6253\u3061\u5207\u3089\u308c\u305f<\/i>) \u30c7\u30fc\u30bf\u3092\u4f7f\u7528\u3057\u305f\u751f\u5b58\u5206\u6790\u306b\u3068\u3063\u3066\u5229\u70b9\u3067\u3059\u3002<\/p>

\u751f\u5b58\u6a5f\u80fd\u3068\u3044\u3046\u306e\u306f\u3001 <\/p>

$$ {S(t) = 1 – F(t) = [1+(t\/\\alpha)^{\\beta}]^{-1},\\, } $$<\/div><\/dd><\/dl>

\u305d\u3057\u3066\u30ea\u30b9\u30af\u95a2\u6570\u306f<\/p>

$$ { h(t) = \\frac{f(t)}{S(t)} = \\frac{(\\beta\/\\alpha)(x\/\\alpha)^{\\beta-1}} {[1+(x\/\\alpha)^{\\beta}]}.} $$<\/div><\/dd><\/dl>

\u6c34\u6587\u5b66<\/span><\/h3>

\u5bfe\u6570\u30ed\u30b8\u30b9\u30c6\u30a3\u30c3\u30af\u5206\u5e03\u306b\u3088\u308a\u3001\u5ddd\u306e\u6d41\u308c\u3084\u964d\u6c34\u91cf\u3055\u3048\u3082\u30e2\u30c7\u30eb\u5316\u3059\u308b\u3053\u3068\u304c\u53ef\u80fd\u306b\u306a\u308a\u307e\u3057\u305f\u3002<\/p>

\u7d4c\u6e08<\/span><\/h3>

\u5bfe\u6570\u30ed\u30b8\u30b9\u30c6\u30a3\u30c3\u30af\u5206\u5e03\u3092\u4f7f\u7528\u3059\u308b\u3068\u3001\u7d4c\u6e08\u5b66\u3067\u306f\u3001\u591a\u304f\u306e\u5834\u5408\u3001\u30d5\u30a3\u30b9\u30af\u5206\u5e03<\/b>\u3068\u3044\u3046\u540d\u524d\u3067\u3001\u6240\u5f97\u306e\u4e0d\u5e73\u7b49\u3092\u7c21\u5358\u306b\u30e2\u30c7\u30eb\u5316\u3067\u304d\u307e\u3059\u3002\u305d\u306e\u30b8\u30cb\u4fc2\u6570<\/a><\/span>\u306f1\/\u03b2<\/span>\u3067\u3059\u3002<\/p>

\u30d7\u30ed\u30d1\u30c6\u30a3<\/h2>

\u77ac\u9593<\/span><\/h3>

k<\/i><\/span>\u756a\u76ee\u306e\u30e2\u30fc\u30e1\u30f3\u30c8\u306fk<\/i> < \u03b2 \u306e<\/span>\u5834\u5408\u306b\u306e\u307f\u5b58\u5728\u3057\u3001\u6b21\u306e\u5f0f\u3067\u4e0e\u3048\u3089\u308c\u307e\u3059\u3002 <\/p>

$$ {\\begin{align} \\operatorname{E}(X^k) & = \\alpha^k\\,\\operatorname{B}(1-k\/\\beta,\\, 1+k\/\\beta) \\\\ & = \\alpha^k\\, {k\\,\\pi\/\\beta \\over \\sin(k\\,\\pi\/\\beta)} \\end{align}} $$<\/div><\/dd><\/dl>

\u3053\u3053\u3067\u3001B() \u306f\u30d9\u30fc\u30bf\u95a2\u6570\u3067\u3059\u3002\u6570\u5b66\u7684\u671f\u5f85\u5024<\/a><\/span>\u3001\u5206\u6563\u3001\u6b6a\u5ea6<\/a><\/span>\u4fc2\u6570\u3001\u304a\u3088\u3073\u5c16\u5ea6\u4fc2\u6570\u306e\u5f0f\u306f\u3001\u524d\u306e\u5f0f\u304b\u3089\u53d6\u5f97\u3055\u308c\u307e\u3059\u3002 b<\/i> = \u03c0 \/ \u03b2<\/span>\u3068\u8a2d\u5b9a\u3059\u308b\u3068\u3001\u5e73\u5747\u306f<\/a><\/span>\u6b21\u306e\u5f62\u5f0f\u306b\u306a\u308a\u307e\u3059\u3002 <\/p>

$$ { \\operatorname{E}(X) = \\alpha b \/ \\sin b , \\quad \\beta>1,} $$<\/div><\/dl>

\u305d\u3057\u3066\u5206\u6563\u306f\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059<\/p>

$$ { \\operatorname{Var}(X) = \\alpha^2 \\left( 2b \/ \\sin 2b -b^2 \/ \\sin^2 b \\right), \\quad \\beta>2.} $$<\/div><\/dl>

\u5c16\u5ea6\u3068\u6b6a\u5ea6<\/i>\u3092\u660e\u793a\u7684\u306b\u8868\u73fe\u3059\u308b\u3068\u3001\u518d\u73fe\u306b\u6642\u9593\u304c\u304b\u304b\u308a\u307e\u3059\u3002 \u03b2 \u304c<\/span>\u7121\u9650\u5927<\/a><\/span>\u306b\u306a\u308b\u50be\u5411\u304c\u3042\u308b\u305f\u3081\u3001\u5e73\u5747 (\u671f\u5f85\u5024) \u306f\u03b1<\/span>\u306b\u306a\u308b\u50be\u5411\u304c\u3042\u308a\u3001\u5206\u6563\u3068\u6b6a\u5ea6\u306f<\/i>\u4e21\u65b9\u3068\u3082 0 \u306b\u306a\u308b\u50be\u5411\u304c\u3042\u308a\u3001\u5c16\u5ea6\u306f 6\/5 \u306b\u306a\u308b\u50be\u5411\u304c\u3042\u308a\u307e\u3059 (\u4ee5\u4e0b\u3082\u53c2\u7167)\u3002<\/p>

\u5206\u4f4d\u6570<\/span><\/h3>

\u5206\u5e03\u95a2\u6570\u306e\u9006\u95a2\u6570<\/a><\/span>\u306f\u6b21\u306e\u3088\u3046\u306b\u6c42\u3081\u3089\u308c\u307e\u3059<\/a><\/span>\u3002 <\/p>

$$ {F^{-1}(p;\\alpha, \\beta) = \\alpha\\left( \\frac{p}{1-p} \\right)^{1\/\\beta}.} $$<\/div><\/dd><\/dl>

\u3057\u305f\u304c\u3063\u3066\u3001\u4e2d\u592e\u5024\u306f\u03b1<\/span> \u3001\u6700\u521d\u306e\u56db\u5206\u4f4d<\/a><\/span>\u306f3 1 \/ \u03b2<\/sup> \u03b1<\/span> \u3001\u6700\u5f8c\u306e\u56db\u5206\u4f4d\u306f3 \u2212 1 \/ \u03b2<\/sup> \u03b1<\/span>\u3068\u306a\u308a\u307e\u3059\u3002<\/p><\/div>

\u53c2\u8003\u8cc7\u6599<\/h2>
  1. Lei \u2013 aragonais<\/a><\/li>
  2. \u0646\u0638\u0627\u0645 \u0623\u0633\u0627\u0633\u064a \u2013 arabe<\/a><\/li>
  3. \u0646\u0638\u0627\u0645 \u0627\u0633\u0627\u0633\u0649 \u2013 arabe \u00e9gyptien<\/a><\/li>
  4. Llei \u2013 asturien<\/a><\/li>
  5. Kamachi \u2013 aymara<\/a><\/li>
  6. Qanun \u2013 azerba\u00efdjanais<\/a><\/li><\/ol><\/div>\n
    \n

    \n \u5bfe\u6570\u30ed\u30b8\u30b9\u30c6\u30a3\u30c3\u30af\u6cd5\u5247 – \u5b9a\u7fa9\u30fb\u95a2\u9023\u52d5\u753b\n <\/h2>\n
    \n \n
    \n
    \n