class: inverse, center, middle, title-slide # ヤバ<del>い</del>くない農薬の話 ### ヤバくないよ! --- class: center, middle ## 農薬の名前の話をします --- class: center, middle ## 農薬の名前、ご存知ですか？ --- class: center, middle ### 農薬には3つの名前があるとされています --- ## 例) ベネビアOD -- - **農薬の名称**...ベネビアOD - いわゆる「商品名」です。 -- - **種類名**...シアントラニリプロール水和剤 - 「成分名 + 剤型」です。 -- - **化学名(CAS名)**...3-ブロモ-1-(3-クロロ-2-ピリジニル)-N-[4-シアノ-2-メチル-6-[(メチルアミノ)カルボニル]フェニル]-1H-ピラゾール-5-カルボキサミド - 何か長ったらしいやつです。 -- .center[ #### ✨他に通称として「サイアジピル®」というのがあります✨ ] --- class: middle ## 今回注目するのはこちら ### **農薬の名称**は何文字なのか？ ### **種類名**は何文字なのか？ --- ## しつもんです ### みなさんの好きな確率分布はなんですか？ -- ### そうですね。**✨ポアソン分布✨**ですね。 --- ## Poisson distribution ### 確率質量関数 .large[$$P（X = k） = \frac{\lambda^k e^{-\lambda}}{k!}$$] ### 特徴 - パラメータがひとつしかないので簡単！ - 平均 = 分散 = `\(\lambda\)` - カウントデータに対する驚きの汎用性！ - 1時間あたりのアクセス数 - 1年間に発生する地震の回数 - キャベツ1株に産み付けられたモンシロチョウの卵の数 --- class:middle ## 仮説 ### 農薬名の文字数はポアソン分布しているのではないか？ --- ## 前処理しておいたデータを使います <div data-pagedtable="false"> <script data-pagedtable-source 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</script> </div> --- class:inverse, middle, center ## 1. 農薬の名称（商品名）について --- ## 全体の傾向を確認する <div data-pagedtable="false"> <script data-pagedtable-source type="application/json"> {"columns":[{"label":[""],"name":["_rn_"],"type":[""],"align":["left"]},{"label":["stat"],"name":[1],"type":["chr"],"align":["left"]},{"label":["formatted"],"name":[2],"type":["chr"],"align":["left"]}],"data":[{"1":"missing","2":"0","_rn_":"1"},{"1":"complete","2":"4251","_rn_":"2"},{"1":"n","2":"4251","_rn_":"3"},{"1":"mean","2":"10.24","_rn_":"4"},{"1":"sd","2":"3.32","_rn_":"5"},{"1":"p0","2":"3","_rn_":"6"},{"1":"p25","2":"8","_rn_":"7"},{"1":"p50","2":"10","_rn_":"8"},{"1":"p75","2":"12","_rn_":"9"},{"1":"p100","2":"35","_rn_":"10"},{"1":"hist","2":"▃▇▅▁▁▁▁▁","_rn_":"11"}],"options":{"columns":{"min":{},"max":[10]},"rows":{"min":[10],"max":[10]},"pages":{}}} </script> </div> - 平均が `\(10.24\)` 、分散が `\(3.32^2 = 11.02\)` なので、平均と分散が近いです!! - 期待が大きい --- ## 全体の傾向を確認する <!-- --> --- ### `\(\lambda = 10.24\)` のポアソン分布を重ねてみます <!-- --> ✨やりました✨ --- class:middle ## 結論 - 農薬の名称（商品名）は `\(\lambda = 10.24\)` のポアソン分布に従っている。 -- - （ポアソン分布は `\(\lambda = 10\)` あたりから正規分布と区別がつかなくなるので、正規分布で近似してもよいです。むしろその方がいろいろ楽…） --- class: inverse, middle, center ## 2. 農薬の種類名（成分名+剤型）について --- ### 農薬の種類名はポアソン分布しません 正規分布でもないです。というかナントカ分布では表現できなさげです。 <!-- --> --- ### なぜなのか 種類名は成分が混ざると長くなります。 - 例）ベニカXネクストスプレー - 種類名...**還元澱粉糖化物・クロチアニジン・ピリダリル・ペルメトリン・マンデストロビン水和剤** - 還元澱粉糖化物...エコピタ - クロチアニジン...ダントツ - ピリダリル...プレオ - ペルメトリン...アディオン - マンデストロビン...スクレア --- class: center, middle ### 混合数で場合分けすればよいのでは…？ --- ### 混合数で場合分け <!-- --> ✨やりました!!✨ --- class: center, middle ### 単一の成分名がポアソン分布に従っているのであれば、混合数別の種類名も**それぞれ**ポアソン分布に従っているはずです --- class: center, middle ## なぜなのか？ -- ### ポアソン分布は**再生性**を有します --- ## **再生性** is 何 > 同じ分布族に含まれる確率分布を持つ2つの独立な確率変数に対して、その和の確率分布もまた同じ族に含まれる性質のこと > --- Wikipedia -- ポアソン分布の和はポアソン分布に従う、ということです --- class: center, middle ### 確認してみましょう --- <!-- --> -- # 微妙…!! --- ### 平均と分散を確認してみます <div data-pagedtable="false"> <script data-pagedtable-source type="application/json"> {"columns":[{"label":["混合数"],"name":[1],"type":["int"],"align":["right"]},{"label":["平均"],"name":[2],"type":["dbl"],"align":["right"]},{"label":["分散"],"name":[3],"type":["dbl"],"align":["right"]}],"data":[{"1":"1","2":"9.3","3":"10.6"},{"1":"2","2":"17.6","3":"15.9"},{"1":"3","2":"26.2","3":"14.2"},{"1":"4","2":"35.5","3":"12.6"},{"1":"5","2":"38.7","3":"7.9"}],"options":{"columns":{"min":{},"max":[10]},"rows":{"min":[10],"max":[10]},"pages":{}}} </script> </div> 混合数3以上で明らかに過小分散（平均より分散が小さい）となっていることがわかります。 --- ### なぜなのか - 混合数3以上などという無茶をやる農薬はだいたい水稲剤です（偏見） --- ### 混合数1の農薬の適用作物名トップ5 <div data-pagedtable="false"> <script data-pagedtable-source type="application/json"> {"columns":[{"label":["作物名"],"name":[1],"type":["chr"],"align":["left"]},{"label":["n"],"name":[2],"type":["int"],"align":["right"]}],"data":[{"1":"キャベツ","2":"497"},{"1":"きゅうり","2":"480"},{"1":"トマト","2":"472"},{"1":"りんご","2":"470"},{"1":"ばれいしょ","2":"407"}],"options":{"columns":{"min":{},"max":[10]},"rows":{"min":[10],"max":[10]},"pages":{}}} </script> </div> --- ### 混合数2の農薬の適用作物名トップ5 <div data-pagedtable="false"> <script data-pagedtable-source type="application/json"> {"columns":[{"label":["作物名"],"name":[1],"type":["chr"],"align":["left"]},{"label":["n"],"name":[2],"type":["int"],"align":["right"]}],"data":[{"1":"移植水稲","2":"208"},{"1":"稲","2":"189"},{"1":"稲(箱育苗)","2":"146"},{"1":"きゅうり","2":"123"},{"1":"樹木等","2":"110"}],"options":{"columns":{"min":{},"max":[10]},"rows":{"min":[10],"max":[10]},"pages":{}}} </script> </div> （…おや？） --- ### 混合数3の農薬の適用作物名トップ5 <div data-pagedtable="false"> <script data-pagedtable-source type="application/json"> {"columns":[{"label":["作物名"],"name":[1],"type":["chr"],"align":["left"]},{"label":["n"],"name":[2],"type":["int"],"align":["right"]}],"data":[{"1":"移植水稲","2":"404"},{"1":"直播水稲","2":"168"},{"1":"稲","2":"98"},{"1":"稲(箱育苗)","2":"63"},{"1":"樹木等","2":"55"}],"options":{"columns":{"min":{},"max":[10]},"rows":{"min":[10],"max":[10]},"pages":{}}} </script> </div> （…水稲の比率が？） --- ### 混合数4の農薬の適用作物名トップ5 <div data-pagedtable="false"> <script data-pagedtable-source type="application/json"> {"columns":[{"label":["作物名"],"name":[1],"type":["chr"],"align":["left"]},{"label":["n"],"name":[2],"type":["int"],"align":["right"]}],"data":[{"1":"移植水稲","2":"161"},{"1":"直播水稲","2":"81"},{"1":"稲","2":"39"},{"1":"稲(箱育苗)","2":"19"},{"1":"果樹類","2":"2"}],"options":{"columns":{"min":{},"max":[10]},"rows":{"min":[10],"max":[10]},"pages":{}}} </script> </div> 混合数3以上などという無茶をやる農薬はだいたい水稲剤です（確信） --- ### 水稲剤の特殊な事情 .pull-left[ 水稲の農薬は多様な処理方法に対応するため、同じ成分で複数の剤型のものが同時に販売される傾向が強いです（たぶん）。 - 粒剤...ヨーグルトについてる砂糖みたいなやつ - 豆つぶ...豆つぶみたいなやつ - ジャンボ...でかいやつ ] .pull-right[] .footnote[（2018/11/7の登録情報です）] --- ### 混合数3以上でなぜ種類名が過小分散となるのか - そもそもそんなに複数混ぜられる農薬がない - 水稲剤が多い - 成分が同じで剤型だけ違う農薬が出がち（文字数はほぼ一緒） という理由から、農薬数に対して文字数のバリエーションが少なくなるため、分散が小さくなる（同じ値が出やすい）、と考えられます。 -- （<del>飽きてきたので</del>ここらでやめます） --- class:middle ### 結論 - 農薬の種類名（成分＋剤型）は、混合数3以上ではポアソン分布から外れる。 --- class: inverse, middle, center ## おわり #### 本スライドはRのxaringanパッケージを使用して作成しました