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Befriending Kurtosis with R

bk
October 07, 2023

Befriending Kurtosis with R

bk

October 07, 2023
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  1. ʙ ՄࢹԽύοέʔδͰઑ౓ͱٔΕΔʙ
    ઑ౓ͱ஥ྑ͘ͳΓ͍ͨ

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  2. ໨࣍
    2
    ઑ౓ͱ͸


    ϕʔλ෼෍ͱ͸


    ઑ౓ΛՄࢹԽͯ͠ΈΔ


    ·ͱΊ


    ࢀߟจݙ ɾɾɾɾɾɾɾɾɾɾɾɾɾɾɾɾɾɾɾɾɾɾɾɾɾɾɾɾ
    p.3,4
    p.5-7
    p.8-16
    p.17,18
    ɾɾɾɾɾɾɾɾɾɾɾɾɾɾɾɾɾɾɾɾɾɾɾɾɾɾɾɾɾ
    ɾɾɾɾɾɾɾɾɾɾɾɾɾɾɾɾɾɾɾɾɾɾ
    ɾɾɾɾɾɾɾɾɾɾɾɾɾɾɾɾɾɾɾɾɾɾɾɾɾ
    ɾɾɾɾɾɾɾɾɾɾɾɾɾɾɾɾɾɾɾɾɾɾɾɾɾɾɾɾ
    p.19
    B

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  3. ઑ౓ͱ͸

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  4. ઑ౓ͱ͸
    4
    ֬཰෼෍ͷ, ઑΓͷఔ౓Λද͢ࢦඪ΋ఆٛͰ͖Δ. ͢ͳΘͪ, ࢛৐ͷظ଴஋


    ͸, த৺ͷपғͷ෦෼ͷઑΓ۩߹Λද͢.
    α4 =
    E(x − μ)4
    σ4
    ౦ژେֶڭཆֶ෦౷ܭֶڭࣨ. ʰ౷ܭֶೖ໳ʱ. ౦ژେֶग़൛ձ, 1991-07-10
    *ਖ਼ن෼෍ͷઑ౓Ͱ͋Δ3ΛҾ͍ͯɺ0Λج४ʹ͢Δ৔߹΋͋Δɻ


    ࠓճ͸3ΛҾ͔ͣɺ্هͷࢦඪΛͦͷ··࢖༻͢Δɻ

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  5. B
    ϕʔλ෼෍ͱ͸

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  6. ϕʔλ෼෍ͱ͸
    6
    ۩ମతͳઑ౓Λࢉग़͢ΔͨΊʹɺઑ౓ΛٻΊΔ෼෍Λஔ͘ɻ


    ࠓճ͸2ͭͷ฼਺Λ࣋ͪɺܗঢ়͕ॊೈͳϕʔλ෼෍Λѻ͏ɻ
    ͔ΒͬΆͷ͠ΐ͜. ʮʲRʳϕʔλ෼෍ͷ࡞ਤʯ. https://www.anarchive-beta.com/entry/2022/07/02/210203

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  7. ϕʔλ෼෍ͷύϥϝʔλมԽͱઑ౓
    7
    ฼਺alphaͱઑ౓ʢkurtosisʣͷؔ܎Λਤࣔɻ


    y࣠ʹுΓ෇͍ͨܗͷઑ౓͸େ͖͍͕ɺҰ౓Ұ༷෼෍ʹ͍ۙͮͯখ͘͞ͳΓɺ


    ͦͷޙਖ਼ن෼෍ʹ͖ۙͮͳ͕Β؇΍͔ʹେ͖͘ͳΔɻ

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  8. ઑ౓ΛՄࢹԽͯ͠ΈΔ

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  9. ઑ౓ͷࣜΛ෼ղ
    9
    ϕʔλ෼෍ͷઑ౓ΛՄࢹԽͰ͖ΔΑ͏ʹ෼ղ͢Δɻ


    ෼ࢠ͸ฏۉपΓͷ4࣍Ϟʔϝϯτɻੵ෼ͷܗʹ͢Δͱภࠩͷ4৐ͱ֬཰ີ౓ؔ਺ɻ


    ෼฼͸෼ࢄͷ2৐ɻࠓճ͸͋·Γ৮Εͳ͍ɻ
    E[(x − μ)4]
    σ4
    =
    ∫ (x − μ)4 f(x) dx
    σ4

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  10. alpha=6.1ͷ෼෍
    10
    alpha=6.1ɺbeta=2ͷϕʔλ෼෍Ͱઑ౓ΛՄࢹԽ͍ͯ͘͠ɻ

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  11. alpha=6.1ͷภࠩͷ4৐ͱ֬཰ີ౓ؔ਺
    11
    ઑ౓ͷ෼ࢠʹ͋Δภࠩͷ4৐ͱ֬཰ີ౓ؔ਺Λਤࣔɻ


    ෼ࢠ͸͜ΕΒͷֻ͚߹ΘͤʹͳΔɻ
    (x − μ)4
    f(x)
    ∫ (x − μ)4 f(x) dx
    σ4
    f(x)
    (x − μ)4

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  12. alpha=6.1ͷภࠩͷ4৐ͱ֬཰ີ౓ؔ਺
    12
    ෼ࢠͷܭࢉΛਐΊͯɺภࠩͷ4৐ͱ֬཰ີ౓ؔ਺Λֻ͚ͨؔ਺Λϓϩοτɻ


    ฏۉपΓ͸ภࠩͷ4৐͕0ʹۙͮͨ͘Ίɺ஋͕খ͘͞ͳΔɻ


    ฏۉ͔Β཭Εɺ֬཰ີ౓ؔ਺΋ߴΊͳ0.25ʙ0.5͋ͨΓͷ஋͕େ͖͘ͳΔɻ
    mean
    ∫ (x − μ)4 f(x) dx
    σ4
    (x − μ)4 f(x)
    (x − μ)4 f(x)

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  13. alpha=0.14ͷ෼෍
    13
    ࣍ʹalpha=0.14ɺbeta=2ͷϕʔλ෼෍Ͱઑ౓ΛՄࢹԽ͢Δɻ


    ෼ࢄ͸ઌ΄Ͳͷalpha=6.1ͷ෼෍ͱɺ0.02લޙͰ΄΅มΘΒͳ͍ɻ

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  14. alpha=0.14ͷภࠩͷ4৐ͱ֬཰ີ౓ؔ਺
    14
    alpha=6.1Ͱݟ͖ͯͨͷͱಉ༷ʹɺ֬཰ີ౓ؔ਺ͱภࠩͷ4৐ΛՄࢹԽɻ


    ภࠩͷ4৐ͷมԽ͕ݟ΍͍͢Α͏ʹɺॎ࣠ͷεέʔϧΛ0ʙ3ʹௐ੔͍ͯ͠Δɻ
    (x − μ)4
    f(x)
    ∫ (x − μ)4 f(x) dx
    σ4
    f(x)
    (x − μ)4

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  15. alpha=0.14ͷภࠩͷ4৐ͱ֬཰ີ౓ؔ਺
    15
    ภࠩͷ4৐ͱ֬཰ີ౓ؔ਺Λֻ͚ͨ΋ͷΛਤࣔɻ


    ฏۉ͸0͔Βগ͠཭ΕΔͨΊɺy࣠෇ۙͰ஋͕ٸʹ্͕Δɻ


    ·ͨɺฏۉ͔Β཭ΕͨП0.5ʙ1.0ͷؒͷ஋͕େ͖͍ɻ
    (x − μ)4 f(x)
    mean
    ∫ (x − μ)4 f(x) dx
    σ4
    (x − μ)4 f(x)

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  16. alpha=6.1ͱalpha=0.14ͷൺֱ
    16
    alpha=6.1ͱ0.14ͷภࠩͷ4৐ͱ֬཰ີ౓ؔ਺Λֻ͚ͨ΋ͷΛಉ࣌ʹՄࢹԽɻ


    alpha=0.14ͷ෼෍͸ฏۉ͔Β཭Εͨ0.75෇ۙͰ஋͕େ͖͍ɻ


    શମͰɺalpha=6.1ΑΓ΋alpha=0.14ͷํ͕ઑ౓͕େ͖͍ͱ͍͏݁Ռʹɻ
    ∫ (x − μ)4 f(x) dx
    σ4
    (x − μ)4 f(x)

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  17. ·ͱΊ

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  18. ·ͱΊ
    18
    ɾઑ౓͕େ͖͍ɺͱ͸ʁ


    ෼෍ͷฏۉपΓͷີ౓͕ബ͘ɺ


    ฏۉ͔Β཭Εͨ෦෼ͷີ౓͕ް͍͜ͱ


    ɾRݴޠͷՄࢹԽύοέʔδͰཧղΛਂΊΔ


    ɾggplot2


    ɾgganimate


    ɾgghighlight

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  19. ࢀߟจݙ
    19
    •౦ژେֶڭཆֶ෦౷ܭֶڭࣨ. ʰ౷ܭֶೖ໳ʱ. ౦ژେֶग़൛ձ, 1991-07-10


    • ͔ΒͬΆͷ͠ΐ͜, ʮʲRʳϕʔλ෼෍ͷ࡞ਤʯ, https://www.anarchive-beta.com/entry/2022/07/02/210203


    • ౷ܭֶʮઑ౓ʯ Kurtosis, https://www.youtube.com/watch?v=iEOE3OCuB8U


    • ֬཰࿦ ߨٛ #003 Ϟʔϝϯτ฼ؔ਺, https://www.youtube.com/watch?v=tZl8M96m46Y


    • ΞΠίϯૉࡐμ΢ϯϩʔυαΠτʮicooon-monoʯ, https://icooon-mono.com/

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  20. Eɹnɹjɹoɹyɹ

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