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bivariate_normal_distribution_simulation's Introduction

2変量正規分布のアニメーション

2変量正規分布の同時確率密度関数の、条件付き分布の期待値が母回帰直線を表すイメージがあまりつかなかったため、 3Dアニメーションにしてみました。 1本目はx,yともに標準正規分布の同時確率密度関数のプロットで、こちらの相関係数を変化させた時の分布を表しています。 2本目は1本目と同様の現象を真上から観察し、加えて各xでのyの期待値をプロットし、これが回帰直線の傾きと一致することを確かめました。

ラベルが一部潰れているのはご容赦を🙇

デモ動画

1. 相関係数の変化に伴う 2 変量正規分布の 3D プロット

correlation_animation.mp4

2. 条件付き期待値のプロットを含むアニメーション

correlation_animation_with_conditional_means.mp4

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