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B3_Seminar_05

kakubari
February 24, 2017

 B3_Seminar_05

ビックデータ解析入門3

kakubari

February 24, 2017
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  1. べき分布とモーメント ˔ϞʔϝϯτʹΑΔ෼෍ͷಛ௃͚ͮ —  ཧ࿦্औΓѻ͍΍͍͢ —  ࣮ࡍʹଟ͘ͷ౷ܭख๏ͰҊʹԾఆ͞Ε͍ͯΔ  ଟ͘ͷ৔߹ɺਖ਼ن෼෍΍ࢦ਺෼෍Ͱ͋Δɻ  

      Ὃ ݱ࣮Ͱ͸ɺҟͳΔ෼෍ʹै͏֬཰ม਺͕͋Δɻ  ͦͷΑ͏ͳ֬཰ม਺ʹै͍ͬͯΔσʔλͰ͸ɺ ؍ଌ͞Εͨ෼෍ʹରͯ͠౷ܭख๏͕ద੾Ͱ͋Δ͔஫ҙ ὎΂͖తͳ੄Λ࣋ͭ෼෍ 
  2. べき分布とモーメント  P(≥ x) = Ax−α Լهͷྦྷੵ෼෍ؔ਺ʹै͏෼෍Λ΂͖෼෍ͱ͍͏ɻ   

            "͸ن֨Խఆ਺  ὎΂͖෼෍͸͕ͦ͢ް͍͜ͱΛಛ௃ͱ͢Δ෼෍ ʢۃ୺ʹେ͖ͳ஋Λ࣋ͭݱ৅͕ਖ਼ن෼෍ΑΓى͜Γ΍͍͢ʣ   (x ≥ A 1 α ) (1)
  3. べき分布とモーメント ˔΂͖෼෍ͷੑ࣭   ଟ͘ͷখ͞ͳ஋ͱ਺গͳ͍ܻҧ͍ʹେ͖ͳ஋ΛͱΔ΋ ͷΛؚΉ   ਖ਼ن෼෍ΑΓߴ͍֬཰Ͱܻҧ͍ʹେ͖ͳ஋ΛͱΔ   ྦྷੵ෼෍ؔ਺Λ྆ର਺Ͱϓϩοτ͢Δͱ௚ઢʹͳΔɻ ௚ઢͷ܏͖͸΂͖ࢦ਺ЋͰ͋Δɻ

      Ћ㱡̎Ͱ͸෼ࢄɺЋ㱡̍Ͱ͸ฏۉ͕ଘࡏ͠ͳ͍ɻʢЋ࣍ Ҏ্ͷϞʔϝϯτ͕ଘࡏ͠ͳ͍ʣ   Ћ̍Ͱ͸ɺ࠷େ஋ͷγΣΞ͕αϯϓϧ਺/ˠ㱣Ͱ΋̌ ʹͳΒͳ͍ɻ  ɹ  S max = max(x 1 , x 2 ,!, x N ) x i k=1 N ∑
  4. 広い意味でのべき分布  ͕ࣜݫີʹ੒Γཱͭ͜ͱ͸ݱ࣮ʹ͸ͳ͍ɻ     Ὃ ஋ͷઈର஋͕େ͖͍ྖҬͰɺ ΂͖ؔ਺ͰۙࣅͰ͖ΔΑ͏ͳ෼෍

     ΂͖ͷ੄Λ࣋ͭ෼෍ͱ͍͍ɺ૯ͯ͡΂͖෼෍ͱݺͿɻ ྫʣɾٯΨϯϚ෼෍ ɹɹɾθʔλ෼෍ ɹɹଞʹ΋ଟ਺͋Δɻ