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Befriending Kurtosis with R
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bk
October 07, 2023
Programming
1
960
Befriending Kurtosis with R
bk
October 07, 2023
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Transcript
ʙ ՄࢹԽύοέʔδͰઑͱٔΕΔʙ ઑͱྑ͘ͳΓ͍ͨ
࣍ 2 ઑͱ ϕʔλͱ ઑΛՄࢹԽͯ͠ΈΔ ·ͱΊ ࢀߟจݙ ɾɾɾɾɾɾɾɾɾɾɾɾɾɾɾɾɾɾɾɾɾɾɾɾɾɾɾɾ p.3,4 p.5-7
p.8-16 p.17,18 ɾɾɾɾɾɾɾɾɾɾɾɾɾɾɾɾɾɾɾɾɾɾɾɾɾɾɾɾɾ ɾɾɾɾɾɾɾɾɾɾɾɾɾɾɾɾɾɾɾɾɾɾ ɾɾɾɾɾɾɾɾɾɾɾɾɾɾɾɾɾɾɾɾɾɾɾɾɾ ɾɾɾɾɾɾɾɾɾɾɾɾɾɾɾɾɾɾɾɾɾɾɾɾɾɾɾɾ p.19 B
ઑͱ
ઑͱ 4 ֬ͷ, ઑΓͷఔΛද͢ࢦඪఆٛͰ͖Δ. ͢ͳΘͪ, ࢛ͷظ , த৺ͷपғͷ෦ͷઑΓ۩߹Λද͢. α4 =
E(x − μ)4 σ4 ౦ژେֶڭཆֶ෦౷ܭֶڭࣨ. ʰ౷ܭֶೖʱ. ౦ژେֶग़൛ձ, 1991-07-10 *ਖ਼نͷઑͰ͋Δ3ΛҾ͍ͯɺ0Λج४ʹ͢Δ߹͋Δɻ ࠓճ3ΛҾ͔ͣɺ্هͷࢦඪΛͦͷ··༻͢Δɻ
B ϕʔλͱ
ϕʔλͱ 6 ۩ମతͳઑΛࢉग़͢ΔͨΊʹɺઑΛٻΊΔΛஔ͘ɻ ࠓճ2ͭͷΛ࣋ͪɺܗঢ়͕ॊೈͳϕʔλΛѻ͏ɻ ͔ΒͬΆͷ͠ΐ͜. ʮʲRʳϕʔλͷ࡞ਤʯ. https://www.anarchive-beta.com/entry/2022/07/02/210203
ϕʔλͷύϥϝʔλมԽͱઑ 7 alphaͱઑʢkurtosisʣͷؔΛਤࣔɻ y࣠ʹுΓ͍ͨܗͷઑେ͖͍͕ɺҰҰ༷ʹ͍ۙͮͯখ͘͞ͳΓɺ ͦͷޙਖ਼نʹ͖ۙͮͳ͕Β؇͔ʹେ͖͘ͳΔɻ
ઑΛՄࢹԽͯ͠ΈΔ
ઑͷࣜΛղ 9 ϕʔλͷઑΛՄࢹԽͰ͖ΔΑ͏ʹղ͢Δɻ ࢠฏۉपΓͷ4࣍Ϟʔϝϯτɻੵͷܗʹ͢Δͱภࠩͷ4ͱ֬ີؔɻ ࢄͷ2ɻࠓճ͋·Γ৮Εͳ͍ɻ E[(x − μ)4] σ4 =
∫ (x − μ)4 f(x) dx σ4
alpha=6.1ͷ 10 alpha=6.1ɺbeta=2ͷϕʔλͰઑΛՄࢹԽ͍ͯ͘͠ɻ
alpha=6.1ͷภࠩͷ4ͱ֬ີؔ 11 ઑͷࢠʹ͋Δภࠩͷ4ͱ֬ີؔΛਤࣔɻ ࢠ͜ΕΒͷֻ͚߹ΘͤʹͳΔɻ (x − μ)4 f(x) ∫ (x
− μ)4 f(x) dx σ4 f(x) (x − μ)4
alpha=6.1ͷภࠩͷ4ͱ֬ີؔ 12 ࢠͷܭࢉΛਐΊͯɺภࠩͷ4ͱ֬ີؔΛֻ͚ͨؔΛϓϩοτɻ ฏۉपΓภࠩͷ4͕0ʹۙͮͨ͘Ίɺ͕খ͘͞ͳΔɻ ฏۉ͔ΒΕɺ֬ີؔߴΊͳ0.25ʙ0.5͋ͨΓͷ͕େ͖͘ͳΔɻ mean ∫ (x − μ)4
f(x) dx σ4 (x − μ)4 f(x) (x − μ)4 f(x)
alpha=0.14ͷ 13 ࣍ʹalpha=0.14ɺbeta=2ͷϕʔλͰઑΛՄࢹԽ͢Δɻ ࢄઌ΄Ͳͷalpha=6.1ͷͱɺ0.02લޙͰ΄΅มΘΒͳ͍ɻ
alpha=0.14ͷภࠩͷ4ͱ֬ີؔ 14 alpha=6.1Ͱݟ͖ͯͨͷͱಉ༷ʹɺ֬ີؔͱภࠩͷ4ΛՄࢹԽɻ ภࠩͷ4ͷมԽ͕ݟ͍͢Α͏ʹɺॎ࣠ͷεέʔϧΛ0ʙ3ʹௐ͍ͯ͠Δɻ (x − μ)4 f(x) ∫ (x
− μ)4 f(x) dx σ4 f(x) (x − μ)4
alpha=0.14ͷภࠩͷ4ͱ֬ີؔ 15 ภࠩͷ4ͱ֬ີؔΛֻ͚ͨͷΛਤࣔɻ ฏۉ0͔Βগ͠ΕΔͨΊɺy࣠ۙͰ͕ٸʹ্͕Δɻ ·ͨɺฏۉ͔ΒΕͨП0.5ʙ1.0ͷؒͷ͕େ͖͍ɻ (x − μ)4 f(x) mean
∫ (x − μ)4 f(x) dx σ4 (x − μ)4 f(x)
alpha=6.1ͱalpha=0.14ͷൺֱ 16 alpha=6.1ͱ0.14ͷภࠩͷ4ͱ֬ີؔΛֻ͚ͨͷΛಉ࣌ʹՄࢹԽɻ alpha=0.14ͷฏۉ͔ΒΕͨ0.75ۙͰ͕େ͖͍ɻ શମͰɺalpha=6.1ΑΓalpha=0.14ͷํ͕ઑ͕େ͖͍ͱ͍͏݁Ռʹɻ ∫ (x − μ)4 f(x)
dx σ4 (x − μ)4 f(x)
·ͱΊ
·ͱΊ 18 ɾઑ͕େ͖͍ɺͱʁ ͷฏۉपΓͷີ͕ബ͘ɺ ฏۉ͔ΒΕͨ෦ͷີ͕ް͍͜ͱ ɾRݴޠͷՄࢹԽύοέʔδͰཧղΛਂΊΔ ɾggplot2 ɾgganimate ɾgghighlight
ࢀߟจݙ 19 •౦ژେֶڭཆֶ෦౷ܭֶڭࣨ. ʰ౷ܭֶೖʱ. ౦ژେֶग़൛ձ, 1991-07-10 • ͔ΒͬΆͷ͠ΐ͜, ʮʲRʳϕʔλͷ࡞ਤʯ, https://www.anarchive-beta.com/entry/2022/07/02/210203
• ౷ܭֶʮઑʯ Kurtosis, https://www.youtube.com/watch?v=iEOE3OCuB8U • ֬ ߨٛ #003 Ϟʔϝϯτؔ, https://www.youtube.com/watch?v=tZl8M96m46Y • ΞΠίϯૉࡐμϯϩʔυαΠτʮicooon-monoʯ, https://icooon-mono.com/
Eɹnɹjɹoɹyɹ