November 2020
Intermediate to advanced
396 pages
8h 34m
Japanese
book
データサイエンスのための統計学入門 第2版 ―予測、分類、統計モデリング、統計的機械学習とR/Pythonプログラミング
by Peter Bruce, Andrew Bruce, Peter Gedeck, 黒川 利明, 大橋 真也
Content preview from データサイエンスのための統計学入門 第2版 ―予測、分類、統計モデリング、統計的機械学習とR/Pythonプログラミング
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2.12
ポアソン分布と関連する分布
■
87
2.12.1
ポアソン分布
過去の集約データ（例：年間のインフルエンザ感染者数）からは時間や空間単位で事
象の平均回数（例：
1
日当たりまたは人口単位当たりの感染者数）を推定できるが、
1
つ
の時間
/
空間単位で次との差がどうなるかも知りたいと思うものだ。ポアソン分布は、
そういう単位標本が多数あるときに、時間や空間単位ごとの事象分布を示す。待ち行
列に関して、「サーバに到達したインターネットトラフィックを
5
秒以内に完全に処理す
るのを
95 %
確実にするには、どの程度のキャパシティが必要か」などという問いに答え
るのに役立つ。
ポアソン分布の重要なパラメータは
λ
（ラムダ）で、特定の時間や空間で生じる事象
数の平均だ。ポアソン分布の分散も
λ
だ。
待ち行列シミュレーションの一部では、ポアソン分布で乱数発生させる技法がよく使
われる。
R
の
rpois
関数で、乱数の個数とラムダを引数に指定すると計算できる。
（
R
）
rpois(100, lambda=2)
対応する
SciPy
関数は
stats.poisson.rvs
だ。
（
Python
）
stats.poisson.rvs(2, size=100)
このコードは
λ
＝
2
のポアソン分布で
100
個の乱数を生成する。例えば、
1
分当たり
平均して平均
2
回のカスタマーサービスの呼び出しがあるなら、このコードは
100
分間
のシミュレーションの呼び出し回数を返す。
2.12.2
指数分布
ポアソン分布のものと同じパラメータ
λ
を使って、指数分布では、
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I'm always learning. So when I got on to O'Reilly, I was like a kid in a candy store. There are playlists. There are answers. There's on-demand training. It's worth its weight in gold, in terms of what it allows me to do.