{"version":"1.0","url":"https://weeeeddie.hatenablog.com/entry/2024/10/12/181443","html":"<iframe src=\"https://hatenablog-parts.com/embed?url=https%3A%2F%2Fweeeeddie.hatenablog.com%2Fentry%2F2024%2F10%2F12%2F181443\" title=\"Zipf\u306e\u6cd5\u5247\u3063\u3066\u7d50\u5c40\u3069\u3046\u3044\u3046\u6271\u3044\u306a\u3093\u3060\u3063\u3051\uff1f\u4eca\u66f4\u4ed6\u4eba\u306b\u805e\u3051\u306a\u3044\u306e\u3067Piantadosi (2014)\u3092\u8aad\u3093\u3067\u3053\u3063\u305d\u308a\u52c9\u5f37 - \u8349\u832b\u832b\" class=\"embed-card embed-blogcard\" scrolling=\"no\" frameborder=\"0\" style=\"display: block; width: 100%; height: 190px; max-width: 500px; margin: 10px 0px;\"></iframe>","categories":[],"author_name":"ryoryo-ueda","title":"Zipf\u306e\u6cd5\u5247\u3063\u3066\u7d50\u5c40\u3069\u3046\u3044\u3046\u6271\u3044\u306a\u3093\u3060\u3063\u3051\uff1f\u4eca\u66f4\u4ed6\u4eba\u306b\u805e\u3051\u306a\u3044\u306e\u3067Piantadosi (2014)\u3092\u8aad\u3093\u3067\u3053\u3063\u305d\u308a\u52c9\u5f37","blog_url":"https://weeeeddie.hatenablog.com/","provider_url":"https://hatena.blog","author_url":"https://blog.hatena.ne.jp/ryoryo-ueda/","blog_title":"\u8349\u832b\u832b","published":"2024-10-12 18:14:43","description":"\u80cc\u666f \u8a00\u8a9e\u5b66\u5206\u91ce\u3067\u306f\u3001Zipf\u306e\u6cd5\u5247\uff08Zipf's law\uff09\u3068\u547c\u3070\u308c\u308b\u7d71\u8a08\u7684\u666e\u904d\u6027\u8cea\u304c\u77e5\u3089\u308c\u3066\u3044\u307e\u3059\u3002 Zipf\u306e\u6cd5\u5247\u3068\u306f\u3001\u51fa\u73fe\u983b\u5ea6\u304c $r$ \u756a\u76ee\u306b\u591a\u3044\u5358\u8a9e\u306b\u3064\u3044\u3066\u3001\u305d\u306e\u51fa\u73fe\u983b\u5ea6\u304c\u304a\u304a\u3088\u305d $\\dfrac{1}{r}$ \u306b\u6bd4\u4f8b\u3059\u308b\u3068\u3044\u3046\u7d4c\u9a13\u5247\u3067\u3059\u3002 \u3059\u306a\u308f\u3061 $r$ \u756a\u76ee\u306e\u5358\u8a9e\u306e\u51fa\u73fe\u983b\u5ea6\u3092 $f(r)$ \u3068\u3057\u305f\u3068\u304d\u3001 $$ f(r) \\propto r^{-\\alpha} $$ \u304c\u6210\u308a\u7acb\u3064\u3068\u3044\u3046\u7d4c\u9a13\u5247\u3067\u3059\uff08\u3053\u3053\u3067 $\\alpha \\approx 1$ \u3067\u3059\u304c\u3001\u53b3\u5bc6\u306b\u306f $\\sum_{r=1}^{\\infty} f(r) < \\infty$ \u3068\u306a\u308b\u305f\u3081\u306b $\\alpha>1$ \u3067\u3042\u308b\u5fc5\u8981\u304c\u3042\u308a\u2026","provider_name":"Hatena Blog","width":"100%","type":"rich","height":"190","image_url":null}