整合性の評価と補正
著者 野田 容助
権利 Copyrights 日本貿易振興機構（ジェトロ）アジア
経済研究所 / Institute of Developing
Economies, Japan External Trade Organization (IDE‑JETRO) http://www.ide.go.jp
シリーズタイトル アジア経済研究所統計資料シリーズ
シリーズ番号 93
雑誌名 貿易指数と貿易構造の変化
ページ 19‑44
発行年 2009
出版者 日本貿易振興機構アジア経済研究所/Institute of Developing Economies (IDE‑JETRO)
URL http://doi.org/10.20561/00044766
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╙䋱ㇱ㩷 Part 1
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╙ 1 ┨
UN Comtrade ⾏ᤃ࠺࠲ߦ߅ߌࠆᢛวᕈߩ⹏ଔߣᱜ
㊁↰ኈഥ
ߪߓߦ
UN⛔⸘ዪ㧔International Trade Statistics Section, UN Statistics Division㧕✬㓸ߦࠃࠆUN Comtrade ⾏ ᤃ࠺࠲ߪຠಽ㘃ߦߟߡ㓏ጀ⊛ߦ᭴ᚑߐࠇࠆ ߔߴߡߩᩴࡌ࡞ಽ㘃ࠦ࠼ࠍࠎߢࠆ߇ޔਅ
ᩴࡌ࡞ಽ㘃ࠦ࠼ߩขᒁ㗵ࠍว⸘ߒߡ߽ᔅߕ ߒ߽ኻᔕߔࠆᩴࡌ࡞ಽ㘃ࠦ࠼ߩขᒁ㗵ߦ
৻⥌ߔࠆߣߪ㒢ࠄߥߚޔ⾏ᤃ࠺࠲ߩᢛวᕈ ࠍᬌ⸛ߔࠆ߇ࠆߎߣ߇⍮ࠄࠇߡࠆޕ㊁
↰ᷓየ㧔2005㧕ߪUN Comtrade ⾏ᤃ࠺࠲ߦ߅ ߌࠆᢛวᕈߩ⹏ଔ߅ࠃ߮ᱜߦߟߡߩၮᧄ⊛ߥ
⠨߃ߣߒߡޔຠ✚㗵ߣ⋧ᚻ࿖⇇ࠍၮḰߣߒߡ 㓏ጀ⊛ߦ᭴ᚑߐࠇߡࠆ⾏ᤃ࠺࠲ߩຠಽ㘃ߩ
․ᓽࠍᩴࡌ࡞ಽ㘃ࠦ࠼ߦၮߠߊขᒁ㗵ߣ߁
┙႐߆ࠄᢛวᕈߩ⹏ଔߩߺߥࠄߕߘߩᢛวᕈߩᰳ
ᅤߒߡࠆ⾏ᤃ࠺࠲ߩᱜᣇᴺߦߟߡ⚫ߒ ߡࠆޕ
ᧄ┨ߪ㊁↰ᷓየ㧔2005㧕ߩᡷ⸓ ߢࠅޔ⾏
ᤃ࠺࠲ߩຠಽ㘃ߦ߅ߌࠆᩴࡌ࡞ಽ㘃ࠦ࠼
ߩขᒁ㗵ߩᢛวᕈࠍ␜⊛ߦ␜ߔߣߣ߽ߦޔSITC ߩၮᧄ㗄⋡ޔขᒁ㗵ࠍ⠨ᘦߒߚ⚦ಽ㘃ߢࠆ mdccಽ㘃㧔the most detailed classification code: mdcc㧕ޔ
ᱜߐࠇߚmdccಽ㘃ߢ✬㓸ߐࠇߚ⾏ᤃ࠺࠲ߩߘ ࠇߘࠇᚑߔࠆᣇᴺࠍ␜ߒߡࠆޕ⋧ᚻ࿖ߣຠ
ಽ㘃ߩᢛวᕈ߇⸽ߐࠇߡࠆ⾏ᤃ࠺࠲ߦߟ
ߡߪmdccಽ㘃ࠦ࠼ߩขᒁ㗵ߩว⸘ߪຠ✚㗵ߦ
৻⥌ߔࠆ߇ޔᔅߕߒ߽㓏ጀ⊛ߥ᭴ㅧߦߪߥߞߡ
ߥߣ߁ᕈ⾰ࠍᜬߞߡࠆޕUN Comtrade⾏ᤃ࠺
࠲ߩᩴࡌ࡞ಽ㘃ࠦ࠼߅ࠃ߮mdccಽ㘃ࠦ࠼
ߦ߽ߣߠߊขᒁ㗵ߩ⹏ଔߦߟߡߪޔ㊁↰ᷓ
የ㧔2005㧕ࠍޔ㊁↰㧔2001㧕ޔ㊁↰㧔2003ߦ ࠃࠅߎࠇ߹ߢߚ߮ߚ߮ᬌ⸛ߒߡ߈ߡࠆޕߒ߆ߒޔ ߘߎߢߪߘࠇߙࠇߩຠಽ㘃ࠦ࠼ߦߟߡߩ
♽ࠍᔨ⊛ߦ⺑ߒߡߪࠆ߇ᱜ⏕ߦቯᑼൻߒߡ ߪߥޕᧄ┨ߢߪᩴࡌ࡞ಽ㘃ࠦ࠼ޔmdccಽ 㘃ࠦ࠼╬ߦߟߡߩಽ㘃ࠦ࠼♽ࠍቯᑼൻߒ ߡౕࠍߍߡ␜ߒߡࠆޕຠಽ㘃ߦ㑐ߒߡ ߪᢛวᕈ߇⸽ߐࠇߡߥ⾏ᤃ࠺࠲ߩᱜߦ ߟߡޔ㊁↰ᷓየ㧔2005㧕ߪߩᩴࡌ࡞ಽ 㘃ࠦ࠼ࠍ↪ߒߡᢛวᕈࠍ㜞ࠆߎߣࠍឭ᩺ߒ ߡࠆߩߦኻߒߡޔᧄ┨ߢߪหߓᩴࡌ࡞ಽ㘃ࠦ
࠼ߦᱜ㗄⋡ࠍㅊടߒߡᢛวᕈࠍ⸽ߔࠆᣇᴺ ࠍណ↪ߒߡࠆޕ
ᧄ┨ߪUN Comtrade⾏ᤃ࠺࠲ߦ߅ߌࠆຠಽ
㘃ߩ․ᓽޔ⚦ಽ㘃ߣߒߡߩmdcc ಽ㘃ޔ⋧ᚻ࿖
߇ᱜߐࠇߡࠆ⾏ᤃ࠺࠲ߦኻߔࠆຠಽ㘃ߦ ߅ߌࠆᢛวᕈߩ⹏ଔޔຠಽ㘃ߩਇᢛวߦ߅ߌࠆ
ᱜޔ߆ࠄ᭴ᚑߐࠇߡࠆޕ
1 㧚⾏ᤃ࠺࠲ߩຠಽ㘃ࠦ࠼
ᧄ┨ߢኻ⽎ߣߔࠆ⾏ᤃ࠺࠲ߪUNߩᚑߦࠃ
ࠆon-lineᬌ⚝ߦࠃࠅᓧࠄࠇࠆUN Comtrade⾏ᤃ࠺
࠲ߢࠆޕߎߩ⾏ᤃ࠺࠲ߪ7ߟߩಽ㘃ࠞ࠹ࠧ
ߣ3ߟߩ⛔⸘୯߇ሽߔࠆޕߔߥࠊߜޔಽ㘃
ࠞ࠹ࠧߪႎ๔࿖㧔reporter code: rc㧕ޔᐕ㧔y㧕ޔ ャಽ㧔trade flow code ߹ߚߪ direction of
trade: d㧕ޔຠಽ㘃♽㧔classification ߹ߚߪsystem of commodity classification: sc㧕ޔຠಽ㘃ࠦ࠼
㧔commodity code: c㧕ޔ⋧ᚻ࿖㧔partner code: pc㧕ޔ ᢙ㊂න㧔quantity unit: qu㧕߇ࠅޔߘߩಽ㘃ࠞ࠹
ࠧߏߣߦ⛔⸘୯ߢࠆขᒁ㗵㧔value: v㧕ޔkg ࠍනߣߔࠆ㊀㊂␜ߩᢙ㊂㧔netweight quantity based on kg: qw㧕ޔᢙ㊂㧔supplenmentary quantity: q㧕 ߢࠆޕ
UN Comtrade⾏ᤃ࠺࠲ߢ↪ߐࠇࠆ⾏ᤃຠ
ಽ㘃♽ߪၮᧄ⊛ߦ2⒳㘃ሽߒޔUNᚑߩᮡ
Ḱ࿖㓙ຠ⾏ᤃಽ㘃㧔Standard International Trade Classification: SITC㧕ߣ㑐⒢දജℂળ㧔Customs
Co-operation Council㧕߇ᚑߔࠆ࿖㓙⛔৻ຠಽ
㘃ࠆߪ⛔৻ࠪࠬ࠹ࡓ㧔Harmonized Commodity Description and Cording System: HS㧕ߢࠆޕSITC ߩຠಽ㘃♽ߪSITC-Original㧔SITC-O㧕ࠍೋ
ߣߒߡޔSITCᡷ⸓ 㧔SITC-Revision㧕ࠆߪᡷ
⸓╙1 㧔SITC-R1㧕ޔSITCᡷ⸓╙2 㧔SITC-R2㧕ޔ
SITCᡷ⸓╙3 㧔SITC-R3㧕ߣᦨᣂ ߩSITCᡷ
⸓╙4 㧔SITC-R4㧕߇ߘࠇߙࠇᡷ⸓ ߣߒߡሽ
ߒޔຠ✚㗵ߩ߽ߣߦ1ᩴࡌ࡞ಽ㘃ࠦ࠼߆ ࠄ5ᩴࡌ࡞ಽ㘃ࠦ࠼߹ߢߩ㓏ጀ⊛ߦ᭴ᚑߐࠇ ࠆຠಽ㘃ࠦ࠼ࠍࠎߢࠆޕSITC♽ߩຠ
ಽ㘃ࠦ࠼ߪߔߴߡߩຠࠍࠊߔTOTALޔ1ᩴ
ࡌ࡞ಽ㘃ࠦ࠼ߢࠆᄢಽ㘃㧔Section㧕ޔ2ᩴ
ࡌ࡞ಽ㘃ࠦ࠼ߩਛಽ㘃㧔Division㧕ޔ3 ᩴࡌ࡞
ಽ㘃ࠦ࠼ߩዊಽ㘃㧔Group㧕ޔ4 ᩴࡌ࡞ಽ㘃ࠦ
࠼ߩ⚦ಽ㘃㧔Sub-group㧕߇ࠅޔߐࠄߦ⚦ಽ 㘃ࠦ࠼ߣߒߡߩ4ᩴࡌ࡞ಽ㘃ࠦ࠼ߣ5ᩴ
ࡌ࡞ಽ㘃ࠦ࠼ࠍၮᧄ㗄⋡㧔ࠕࠗ࠹ࡓ㧦Itemޔ
߹ߚߪBasic Heading㧕߆ࠄ᭴ᚑߐࠇߡࠆޕ
4 ᩴࡌ࡞ಽ㘃ࠦ࠼ߩਛߢߐࠄߦ⚦ߥౝ⸶
߇น⢻ߥ߽ߩߦߟߡߩߺ5ᩴࡌ࡞ಽ㘃ࠦ࠼
߇ሽߔࠆޕߒߚ߇ߞߡޔ5 ᩴࡌ࡞ಽ㘃ࠦ࠼
ߪઁߩಽ㘃ࠦ࠼ߣߪ᭴ᚑ߇⇣ߥߞߡ߅ࠅޔ㓏ጀ
᭴ㅧߦߥߞߡߥߎߣߦᵈᗧߔࠆᔅⷐ߇ࠆޕ ၮᧄ㗄⋡ߦ߅ߡ4ᩴࡌ࡞ಽ㘃ࠦ࠼ߪਅ
ࡌ࡞ߩ5ᩴࡌ࡞ಽ㘃ࠦ࠼߇ሽߒߥ߽ߩ߇
ኻ⽎ߦߥߞߡࠆޕߘࠇߙࠇߩᡷ⸓ ߦࠃࠅห৻
ಽ㘃ࠦ࠼ߢߞߡ߽ౝኈ߇⇣ߥࠆ߽ߩ߇ሽߒ ߡࠆ߇ޔಽ㘃♽ޔ㓏ጀ߅ࠃ߮ᩴࡌ࡞ߩ᭴ᚑ ߪห৻ᒻᑼߢࠆޕ
HS ߦ߅ߌࠆຠಽ㘃♽ߪ HS1988 ᐕᐲ ߩ
Original㧔HS-O㧕ࠍೋߣߒߡޔHS1996ᐕᐲ
ࠆߪᡷ⸓╙1 㧔HS-R1㧕ޔHS2002ᐕᐲ ࠆ
ߪᡷ⸓╙2 㧔HS-R2㧕ߣᦨᣂ ߩHS2007ᐕ ᐲ ࠆߪᡷ⸓╙3 㧔HS-R3㧕ߣߥࠆฦᡷ⸓
߇ሽߔࠆޕHS ♽ߩຠಽ㘃ࠦ࠼ߪ2ᩴ
ࡌ࡞ಽ㘃ࠦ࠼ߢࠆ㘃㧔Chapter㧕ޔ4ᩴࡌ࡞
ಽ㘃ࠦ࠼ߩ㗄㧔Heading㧕ޔ6 ᩴࡌ࡞ಽ㘃ࠦ
࠼ߩภ㧔Sub-heading㧕ߩઁޔChapterࠍಽഀߒߡᓧ
ࠄࠇࠆᦨࡌ࡞ߩㇱ㧔Section㧕߇ሽߔࠆޕ
1.1 UN Comtrade⾏ᤃ࠺࠲ߩขᒁ㗵
UN Comtrade⾏ᤃ࠺࠲ߦߪຠಽ㘃ߦ㑐ߒߡ
㓏ጀ᭴ㅧࠍ᭴ᚑߔࠆߘࠇߙࠇߩᩴࡌ࡞ಽ㘃ࠦ
࠼ߩขᒁ㗵ߩ࠺࠲߇ሽߔࠆޕk ᩴࡌ࡞ಽ㘃
ࠦ࠼߆ࠄ᭴ᚑߐࠇࠆຠಽ㘃ߩ㓸߹ࠅࠍޔ )}
( , ), ( { )
(k c1 k c ( ) k
C mk ߢࠊߒޔ⋧ᚻ࿖ࠍ }
, , ,
{World p1 pn
P ߣߔࠆޕߎߎߢޔ⋧ᚻ࿖
⇇ࠍWorldߢࠊߒޔ⋧ᚻ࿖ߩᢙࠍnޔkᩴࡌ
࡞ಽ㘃ಽ㘃ࠦ࠼ߩᢙࠍm(k)ߣߒߡࠆޕ߹ߚޔ 0
) 0 (
m ߣߔࠆޕຠಽ㘃߇ SITC ߩߣ߈ߪޔ 5
, ,
1
k ߢࠅޔHS ߩߣ߈ߪk 2,4,6ߢࠆޕ
⾏ᤃ࠺࠲ߣߒߡᓧࠄࠇࠆขᒁ㗵ߪႎ๔࿖ޔᐕޔ ャಽߏߣߦޔk ᩴࡌ࡞ಽ㘃ࠦ࠼ߢߐ ࠇߚຠಽ㘃ࠦ࠼ci(k) ߣ⋧ᚻ࿖ pj ࠍޔ
) ( ) (k C k
ci ߣpjPߦኻߒߡޔ (1-1) vrc,d,y(ci(k),pj)
ߣࠊߔߎߣ߇ߢ߈ࠆޕႎ๔࿖ޔᐕޔャಽޔ k ᩴࡌ࡞ಽ㘃ࠦ࠼ࠍ࿕ቯߒߡᷙੂ߇ήߣ߈ ߦߪ◲නߦޔv(ci(k),j)ࠆߪv(c,j)ߣߔߎ ߣߦߔࠆޕຠಽ㘃ߦߟߡຠ✚㗵ߩTotalࠍT ߢࠊߒޔ⋧ᚻ࿖ߩ⇇ࠍWorldࠍWߢࠊߔߎ ߣߦߔࠇ߫ޔv(T,W)ߪຠ✚㗵ߢࠅหᤨߦ⋧
ᚻ࿖⇇ߩขᒁ㗵ߢࠆޕ
UN Comtrade⾏ᤃ࠺࠲ߦ߅ߡຠಽ㘃ߪ
ຠ✚㗵ߣߔߴߡߩᩴࡌ࡞ಽ㘃ࠦ࠼ࠍࠎߢ
ߡ㓏ጀ᭴ㅧࠍᒻᚑߒߡࠆߩߦኻߒߡޔ⋧ᚻ࿖ߦ ߟߡߪ⇇ว⸘ߣ⋧ᚻ࿖ߩߺ߆ࠄ᭴ᚑߐࠇޔ
ၞว⸘߿⚻ᷣࡉࡠ࠶ࠢ⸘ߩࠃ߁ߥࡌ࡞ߩ ಽ㘃ߪሽߖߕ㓏ጀ᭴ㅧߪ߹ࠇߡߥߎߣߦ ᵈᗧߔࠆᔅⷐ߇ࠆޕ
UN Comtrade⾏ᤃ࠺࠲ࠍᗐቯߒߚߔߴߡߩᩴ
ࡌ࡞ಽ㘃ࠦ࠼ߣ3ࠞ࿖ࠍ⋧ᚻ࿖ߣߔࠆขᒁ㗵
߇ 1 ߦ␜ߐࠇߡࠆޕߎߩߪຠಽ㘃ߩ
SITC-R1ࠍ◲⚛ൻߒߡ0߆ࠄ0240߹ߢߒ߆ሽߒ
ߥߣቯߒޔ৻ㇱࠍୃᱜߒߡᚑߐࠇߚขᒁ㗵
ߢࠆޕߘߩߚޔಽ㘃ࠦ࠼ߪᔅߕߒ߽
SITC-R1ߣߪ৻⥌ߒߡߥޕຠಽ㘃ߪᢛวᕈ
߇⸽ߐࠇߡߥ⁁ᘒࠍቯߒߡ߅ࠅޔਅ
ࡌ࡞ಽ㘃ࠦ࠼ߩขᒁ㗵ࠍว⸘ߒߡ߽ࡌ࡞
ಽ㘃ࠦ࠼ߦ৻⥌ߒߡߥ߽ߩ߇ሽߔࠆߎߣ ߦ߽ᵈᗧߔࠆߎߣޕߎߩߢߪ․ߦ4ᩴࡌ࡞ಽ 㘃ࠦ࠼ߩ0121ߣ0129ߦߪขᒁ㗵߇ሽߖߕߦޔ 3ᩴࡌ࡞ಽ㘃ࠦ࠼ߩ012ߦߩߺขᒁ㗵߇ሽ
ߔࠆߣቯߐࠇߡࠆޕ1ߦ߅ߡಽ㘃ࠦ࠼
ߦᓇࠍઃߌߡ␜ߐࠇߡࠆ m ߇ઃߡಽ㘃ࠦ
࠼ߪ╙4▵ߢ⺑ߔࠆࠃ߁ߦޔຠಽ㘃ߩᢛวᕈ ࠍ⸽ߔࠆߚߩᱜ㗄⋡ߢࠆޕ◲නൻߔࠆߚ
ߦ⋧ᚻ࿖ߦߟߡߪ3ࠞ࿖ߣߒߡขᒁ㗵ߪߔߴ ߡห৻ߣߒߡޔߒ߆߽⋧ᚻ࿖ߦߪ⺋Ꮕߪሽߒߥ
ߣቯߒߡࠆޕหߦ߅ߌࠆError of Pߪ╙3
▵ߦߡ⺑ߔࠆޕ
ታ㓙ߦᓧࠄࠇࠆ⾏ᤃ࠺࠲ߪᓇߩㇱಽࠍขࠅ㒰
ߚᢛวᕈߩᰳᅤߒߚ⾏ᤃ࠺࠲ߢࠆޕขᒁ㗵 ߩනࠍ US$ߣߔࠇ߫ޔຠ✚㗵v(T,W) ߪ
48US$ߢࠆޕ৻⥸⊛ߦߪᩴࡌ࡞ಽ㘃ࠦ࠼ߦ
߅ߌࠆขᒁ㗵ߩว⸘ߪຠ✚㗵ߦߪᔅߕߒ߽৻⥌
ߔࠆߣߪ㒢ࠄߥޕ1ߦ߅ߡታ㓙ߦᓧࠄࠇߚ ߎߣࠍᗐቯߒߚ⾏ᤃ࠺࠲ߩkᩴࡌ࡞ಽ㘃ࠦ
࠼ߩขᒁ㗵ว⸘ࠍ Total㧔k,N㧕ߢࠊߒߡࠆޕ
ᱜߐࠇߡߥ⾏ᤃ࠺࠲ߪNߢޔmdccಽ㘃
ࠦ࠼ߪmdccߣࠊߐࠇࠆޕหߢߪ2ᩴࡌ
࡞ಽ㘃ࠦ࠼એߢߪ৻⥌ߒߡߥߎߣࠍ␜ߒ ߡࠆޕᱜߐࠇߚ⾏ᤃ࠺࠲ࠍCߢࠊߒޔߘ ߩ k ᩴࡌ࡞ಽ㘃ࠦ࠼ߩขᒁ㗵ว⸘ߪ Total 㧔k,C㧕ߢࠊߐࠇߡࠆ
1.2 㓏ጀ⊛ߥᩴࡌ࡞ಽ㘃ࠦ࠼
UN Comtrade⾏ᤃ࠺࠲߽ߚ৻⥸⊛ߥ⾏ᤃ
࠺࠲ߦߪຠಽ㘃ߦ㑐ߒߡ㓏ጀ᭴ㅧࠍ᭴ᚑߔࠆ ߘࠇߙࠇߩᩴࡌ࡞ಽ㘃ࠦ࠼߇ሽߔࠆޕຠ
ಽ㘃ࠦ࠼ߩߔߴߡߩ㓸߹ࠅࠍ:ߢߔߎߣߦ ߔࠆޕຠಽ㘃߇SITCߩฦᡷ⸓ ߩߣ߈ߪޔ:ߩ ⷐ⚛ߪߔߴߡߩຠࠍߔ TOTAL ߣ㓏ጀ᭴ㅧࠍ ᜬߟ1ᩴࡌ࡞ಽ㘃ࠦ࠼߆ࠄ5ᩴࡌ࡞ಽ㘃ࠦ
࠼߹ߢߩᩴࡌ࡞ಽ㘃ࠦ࠼ߩ㓸߹ࠅ߆ࠄ᭴ᚑ ߐࠇޔ: {Total,C(k)k 15}ߣߥࠆޕTotalߪޔ
4
1
k ߦኻߒߡޔTotal c1(k)cm(k)(k) ߢࠆޕߥ߅ޔ5 ᩴࡌ࡞ಽ㘃ࠦ࠼ߪઁߩಽ㘃
ࠦ࠼ߣߪ᭴ᚑ߇⇣ߥߞߡ߅ࠅ㓏ጀ᭴ㅧߦߥߞߡ
ߥޕຠಽ㘃ࠦ࠼c߇:ߩⷐ⚛ߢࠆߎߣ ࠍ␜ߔ⼂㑐ᢙࠍ[ߣߒߡޔc:ߦኻߒߡߪ
1 ) (c
[ ޔc:ߦኻߒߡߪ[(c) 0ߣߔࠆޕߐࠄ ߦޔ0 ߆ࠄ 9 ߹ߢߩ 1 ᩴߩᢙሼߩ㓸߹ࠅࠍޔ
} 9 , ,1 , 0
{
AS ߣߔࠆޕSITCฦᡷ⸓ ߩkᩴࡌ
࡞ಽ㘃ࠦ࠼ߩ㓸߹ࠅߪޔk 1,,5ߦኻߒߡޔ (1-2)
} 1 ) (
), ) 1 ( (
| { )
( u
Z [
Z
Z C k AS k
C
ߣߔߎߣ߇ߢ߈ࠆޕߎߎߢޔC(0) Iߣߒߡ߅ ࠅޔ⸥ภߩC(k1)uASߪC(k1)ߣASߩ⋥Ⓧ㓸 วࠍࠊߒߡࠆޕC(k1)ߦኻߔࠆਅࡌ࡞
ಽ㘃ࠦ࠼ߩߣߒߡߩC(k1)uASߩⷐ⚛ߪ ᔅߕߒ߽ߔߴߡ߇:ߩዻߒߡࠆߣߪ㒢ࠄߥޕ ߘߩߚޔ㧔1-2㧕ᑼߢߪ[ࠍ↪ߒߡ:ߦዻߔࠆ
߽ߩߛߌࠍ㒢ቯߒߡࠆޕ
ຠಽ㘃߇HSߩOriginal߅ࠃ߮ฦᡷ⸓ ߩߣ ߈ߪkᩴࡌ࡞ಽ㘃ࠦ࠼ߩC(k)ࠍޔk 2,4,6ߣ ᄌᦝߔࠆߎߣߢSITCฦᡷ⸓ ߣหߓࠃ߁ߦ⸥
1 ຠಽ㘃SITC♽ߦ߅ߌࠆᩴࡌ࡞ಽ㘃ࠦ࠼ߣ⋧ᚻ࿖ߩ⾏ᤃࡑ࠻ࠢࠬߩขᒁ㗵ߩ
ᩴ P 1 2 3 4 5
p1 p2 p3 Error of P World ၮᧄ㗄⋡
N
mdccಽ㘃 N C 6QVCN
٤ ٤ ٤
٤٤ ٤٤ ٤٤ O ٨
٤ ٤ ٤ ٤ ٤ ٤
٤٤ ٤٤ ٤٤ ٤٤ ٤٤ ٤٤ O ٨
٤ ٤
٤
O O
٨
٨
٤ ٤ ٤
٤٤
٤٤ O ٨ Total㧔1,N㧕
Total㧔2,N㧕 Total㧔3,N㧕 Total㧔4,N㧕 Total㧔mdcc,N㧕 Total㧔1,C㧕 Total㧔2,C㧕 Total㧔3,C㧕 Total㧔4,C㧕 Total㧔mdcc,C㧕
㧔ᚲ㧕⪺⠪ᚑޕ
㧔ᵈ㧕ᧄߢߪຠಽ㘃ߩSITC-R1ࠍၮ␆ߣߒߡಽ㘃ࠦ࠼ߪTOTALࠍޔ0߆ࠄ0240߹ߢߒ߆ሽߒߥߣቯ ߒߡᚑߐࠇߡࠆޕᓇߩㇱಽߪᱜ㗄⋡ߢࠆޕ⋧ᚻ࿖ߦߟߡߪp1߆ࠄp3ߩ3ࠞ࿖ߢߘࠇࠄߩขᒁ㗵ߪߔߴߡ ห৻ߣߒߡޔߒ߆߽⋧ᚻ࿖ߦࠃࠆ⺋ᏅߪሽߒߥߣቯߒߡࠆޕTotal㧔k,N㧕ߪᱜߐࠇߡߥ⾏ᤃ࠺࠲ߦኻ ߔࠆkᩴࡌ࡞ಽ㘃ࠦ࠼ߩขᒁ㗵ߩ✚㗵ޔTotal㧔k,C㧕ߪᱜᷣߺ⾏ᤃ࠺࠲ߩߘࠇࠍࠊߔޕmdccಽ㘃ߩNߣC ߪᱜߥߒ߅ࠃ߮ᱜᷣߺߩ⾏ᤃ࠺࠲ࠍᵃߒߡࠆޕၮᧄ㗄⋡ߣmdccಽ㘃ߩ٤ߪኻ⽎ߣߥࠆߎߣࠍᗧߔࠆޕ
ߢ߈ࠆޕߒߚ߇ߞߡޔຠಽ㘃ࠦ࠼ߩߔߴߡߩ 㓸߹ࠅߪޔ: {Total,C(k) k 2,4,6}ߢࠆޕߐ ࠄߦޔ00 ߆ࠄ 99 ߹ߢߩ 2 ᩴߩᢙሼߩ㓸߹ࠅࠍ
} 99 , 98 , , 02 , 01 , 00
{ "
AH ߣ߅ߌ߫ޔHSߩkᩴ
ࡌ࡞ಽ㘃ࠦ࠼ߩ㓸߹ࠅߪޔk 2,4,6ߦኻߒߡޔ (1-3)
} 1 ) (
), ) 2 ( (
| { )
( u
Z [
Z
Z C k AH
k C
ߣߥࠆޕ
ౕߣߒߡޔ1ߩຠಽ㘃ߪSITCߦḰ
ߒߡࠆߩߢ㧔1-2㧕ᑼࠍㆡ↪ߒߡᩴࡌಽ㘃ࠦ
࠼ߩᚑࠍ⹜ߺࠆޕห߆ࠄຠಽ㘃ߪᱜ㗄⋡
એᄖࠍขࠅߒߡ Total ߽ߚߔߴߡߩຠಽ 㘃ࠦ࠼ࠍ߆ࠄ㗅⇟ߦ⸥ߔࠇ߫ޔ
} 0240 , , 0011 , 001 , 00 , 0 ,
{Total "
:
ߣߥࠆޕ1ᩴࡌ࡞ಽ㘃ࠦ࠼ߩ㓸߹ࠅߪ㧔1-2㧕 ᑼߦ߅ߡޔk 1ޔߣ߅ߡᓧࠄࠇࠆޕC(0) I ߥߩߢޔC(1)ߪ㨧0 ̖ 9㨩ߩⷐ⚛ߩਛ߆ࠄᓧࠄࠇ ࠆ:ߦዻߔࠆ߽ߩ㓸߹ࠅߢࠅޔ
} 0 { } 1 ) ( ,
| {
} 1 ) ( ), ) 0 ( (
| { ) 1 (
u
Z [ Z Z
Z [ Z
Z
S
S
A
A C C
ߣߥࠆޕC(1)ߪ1ߩⷐ⚛߆ࠄ᭴ᚑߐࠇࠆޕ㨧0㨩 એᄖߩⷐ⚛ߪޔZ{1"9}ߢࠅޔZ:ߥߩߢ
0 ) (Z
[ ߣߥࠅޔZC(1)ߣߥࠆ߆ࠄߢࠆޕᰴ
ߦޔ2ᩴࡌ࡞ಽ㘃ࠦ࠼ߩ㓸߹ࠅߪk 2ߣ߅ߌ
߫ޔ
u ) ) 1 (
(C AS (0uAS) {00,01,02,",09}
ߥߩߢC(2)ߪޔ } 02 , 01 , 00 {
} 1 ) ( ), 0 (
| { ) 2
( Z Z uAS [ Z
C
ߣߥࠆޕC(2)ߪ3ߩⷐ⚛ࠍࠎߢࠆߎߣ߇ࠊ ߆ࠆޕ3ᩴࡌ࡞ಽ㘃ࠦ࠼ߪޔ
u ) ) 2 (
(C AS {(00uAS)(01uAS) (02uAS)}
ߢࠅޔߎߩਛߩⷐ⚛ߦ߅ߡ:ߦዻߔࠆ߽ߩ㓸
߹ࠅߥߩߢޔ ) 3 (
C {001,011,012,022,023,024} ߣߥࠅޔ6 ߩⷐ⚛ࠍࠎߢࠆޕหߓࠃ߁ߦߒ ߡޔ4 ᩴࡌ࡞ಽ㘃ࠦ࠼ߩ㓸߹ࠅࠍ᳞ࠆߎߣ
߇ ߢ ߈ ޔ C(4) {0011,",0116,0118,0121, }
0240
", ߣߥࠆޕ5 ᩴࡌ࡞ಽ㘃ࠦ࠼ߪ
} 01189 , 01181 { ) 5 (
C ߣߥࠆޕ೨⠪ߪ13ޔᓟ⠪
ߪ2ߩⷐ⚛ࠍߘࠇߙࠇࠎߢࠆޕ
1.3 SITCߩၮᧄ㗄⋡
SITCߦ߅ߡ⚦ಽ㘃ߪၮᧄ㗄⋡ߢࠅޔၮᧄ 㗄⋡ߪ5ᩴࡌ࡞ಽ㘃ࠦ࠼߇ሽߒߥ4ᩴ
ࡌ࡞ಽ㘃ࠦ࠼ߣ5ᩴࡌ࡞ಽ㘃ࠦ࠼ߩ㓸߹ࠅ ߆ࠄ᭴ᚑߐࠇߡࠆޕၮᧄಽ㘃ߪSITCߩಽ㘃
♽ߩᔨߢࠅޔಽ㘃ࠦ࠼ߦኻᔕߔࠆขᒁ㗵 ࠍ⠨ᘦߒߡߥߎߣޔ߹ߚޔᩴࡌ࡞ಽ㘃ࠦ
࠼ߦኻߔࠆ㓏ጀ⊛ߥ᭴ㅧߢߪߥߎߣߦᵈᗧߔࠆ ᔅⷐ߇ࠆޕ
k ᩴࡌ࡞ಽ㘃ࠦ࠼ߩZC(k)ߦ߅ߡޔ k
m ߣߥࠆ⥄ὼᢙߩmߦኻߒߡޔZߩmᩴࡌ
࡞ ಽ 㘃 ࠦ ࠼ ࠍ ข ࠅ ߔ ߚ ߩ 㑐 ᢙ ࠍ )
( )
( C m
m Z
K ߣߔࠆޕ߃߫ޔ3ᩴࡌ࡞ಽ㘃ࠦ
࠼ߩ㨧001㨩ߦኻߒߡߪޔK2(001) {00}ߣߥࠆޕ
߹ߚޔKm(I) Iߢࠆޕ
5ᩴࡌ࡞ಽ㘃ࠦ࠼߇ሽߒߥ4ᩴࡌ࡞
ಽ㘃ࠦ࠼ߪC(4)\K4(C(5))ߣߒߡᓧࠄࠇޔ5 ᩴ
ࡌ࡞ಽ㘃ࠦ࠼ߪC(5)ߥߩߢޔਔ⠪ߩ㓸วߢ
ߐࠇࠆၮᧄ㗄⋡ߪޔ
(1-4) {C(4)\K4(C(5))}C(5)
ߣߥࠆޕߎߎߢޔ⸥ภߩC(4)\CߪC(4)߆ࠄCࠍ ขࠅ㒰ߊߎߣࠍᗧߒߡࠆޕ
1ߩຠಽ㘃ߪSITC-R1ߦḰߒߡࠆߩߢ ၮᧄ㗄⋡߇ሽߔࠆߚޔ㧔1-4㧕ᑼࠍㆡ↪ߒߡၮ ᧄ㗄⋡ߩᚑࠍ⹜ߺࠆޕຠಽ㘃ߪᱜ㗄⋡એᄖ ࠍኻ⽎ߣߔࠆޕK4(C(5)) {0118}ߥߩߢޔၮᧄ㗄
⋡ߩC(4)\K4(C(5))ߪC(4)ߩਛ߆ࠄ㨧0118㨩ߩⷐ
⚛ࠍขࠅ㒰ߚ߽ߩߦߥࠆޕߒߚ߇ߞߡޔၮᧄ㗄
⋡ߪC(4)ߦ߅ߌࠆⷐ⚛ߩ㨧0118㨩ࠍC(5)ߩⷐ⚛
ߩ㨧01181,01189㨩ߢ⟎߈឵߃ߚ߽ߩߢࠆޕၮᧄ
㗄⋡ߩߔߴߡߩ↪⚕ߪ1ߦ߅ߌࠆၮᧄ㗄⋡ߩᰣ ߦ٤ߢ␜ߐࠇޔ12ߩ4ᩴࡌ࡞ಽ㘃ࠦ࠼ߣ2
ߩ5ᩴࡌ࡞ಽ㘃ࠦ࠼ߩว⸘14ߩⷐ⚛߆ࠄ
᭴ᚑߐࠇߡࠆޕ
2 㧚⚦ಽ㘃ߣߒߡߩ mdcc ಽ㘃ࠦ࠼
㓏ጀ⊛ߦ᭴ᚑߐࠇߚຠಽ㘃ߩᩴࡌ࡞ಽ㘃ࠦ
࠼ߣߪߦޔႎ๔࿖ޔャಽޔᐕᲤߩ⾏ᤃ
࠺࠲ߦ߅ߡขᒁ㗵߇0ߢߥߊޔߒ߆߽ਅᩴ
ࡌ࡞ߩ㓏ጀߦዻߒߡࠆಽ㘃ࠦ࠼ࠍᜬߚߥ
ޟ⚦ಽ㘃ޠࠦ࠼ࠍࠕࠫࠕ⚻ᷣ⎇ⓥᚲߢߪmdcc ಽ㘃ࠦ࠼ߣࠎߢࠆޕຠಽ㘃ߩ⚦ಽ㘃ߣ ߥࠆSITC ฦᡷ⸓ ߩၮᧄ㗄⋡߇ขᒁ㗵ࠍ⠨ᘦߒ ߡߥߩߦኻߒߡޔmdccಽ㘃ࠦ࠼ߩ․ᓽߪ
⚦ಽ㘃ࠦ࠼ࠍㆬᛯߔࠆߣ߈ߦขᒁ㗵ࠍ⠨ᘦߒߡ
ࠆߎߣߢࠆޕߒ߆߽ޔᓟㅀߔࠆࠃ߁ߦ⇇ว
⸘ࠍ⋧ᚻ࿖ࠍ࿕ቯߔࠇ߫ᢛวᕈ߇⸽ߐ ࠇߡࠆߣ߈ޔmdccಽ㘃ࠦ࠼ߦኻᔕߔࠆขᒁ㗵 ࠍว⸘ߔࠆߣຠ✚㗵ߦ৻⥌ߔࠆߎߣߢࠆޕၮ ᧄ㗄⋡ߢߪᔅߕߒߡߘߩਔ⠪߇৻⥌ߔࠆߣߪ㒢ࠄ ߥޕ
UN Comtrade⾏ᤃ࠺࠲ߦ߅ߡSITC-R3ߢߪ
3ᩴࡌ࡞ಽ㘃ࠦ࠼ߩ334,673,676ߪਅᩴࡌ
࡞ಽ㘃ࠦ࠼ߥߒߦޔࠆߪਅᩴࡌ࡞ಽ㘃
ࠦ࠼ߣሽߒߡ↪ߐࠇߡࠆߎߣ߇ࠆޕၮ ᧄ㗄⋡ࠍኻ⽎ߣߒߡࠆߣߎࠇࠄߩ3ᩴࡌ࡞ಽ 㘃ࠦ࠼ߩෳᾖߪਇน⢻ߢࠆޕ߹ߚޔ㊁↰㧔2002㧕 ߦ߅ߡޔหߓ⚦ಽ㘃ࠦ࠼ߣߪ⸒ߞߡ߽ຠ
ಽ㘃߇♽⊛ߦቯ⟵ߐࠇߡࠆၮᧄ㗄⋡ߣታ㓙
ߩಽ㘃ߢࠆmdcc ಽ㘃ࠦ࠼ߪᔅߕߒ߽ห৻ߢ
ࠆߣߪ㒢ࠄߥߩߢ⾏ᤃ࠺࠲ࠍ↪ߩ㓙ߦߪ ߘߩਔ⠪ࠍᷙหߒߥࠃ߁ߦߣߩᵈᗧ߇ㅀߴࠄࠇ ߡࠆޕ
2.1 mdccಽ㘃ࠦ࠼
ຠಽ㘃ࠍSITCฦᡷ⸓ ߣߒߚߣ߈ޔkᩴࡌ
࡞߇cߢࠆk1ᩴࡌ࡞ಽ㘃ࠦ࠼ߩ㓸߹ࠅࠍޔ 5
, , 1"
k ߦኻߒߡޔ
(2-1)
} ) (
), 1 ( ), (
| { ) (
c
k C k C c c
D
k
S
Z K
Z Z
ߣߔࠆޕߎߎߢޔDS(c)C(k1)ߢࠅޔᒰὼ ߩߎߣߢࠆ߇ޔcC(k)ߦኻߒߡKk(DS(c)) c ߢࠆޕ߹ߚޔ㧔2-1㧕ᑼࠍ↪ߔࠇ߫ߔߴߡߩk1
ᩴࡌ࡞ಽ㘃ࠦ࠼ߩ㓸߹ࠅࠍࠊߔߎߣ߇ߢ߈ޔ 4
, , 0 "
k ߦኻߒߡޔ
(2-2) C(k1) {Z|cC(k),ZDS(c)}
ߣߥࠆ 1 ޕߎߎߢޔcC(k)ߣࠊߐࠇߡࠆ cߪC(k)ߦ߹ࠇߡࠆߔߴߡߩⷐ⚛ߢࠆߎߣ ࠍᗧߒߡࠆޕߔߴߡߩcC(k) ߦኻߔࠆ
) (c
DS ߩ㓸߹ࠅ߇ߔߴߡߩຠಽ㘃ࠦ࠼ߩ㓸
߹ࠅߩ:ߥߩߢޔ
(2-3)
} 4 0
), ( ), (
| {
) 5 ( )
1 ( } {
\
"
"
:
k
k C c c D
C C
Total Z S
Z
ߣߥࠆޕ
k ᩴࡌ࡞ಽ㘃ࠦ࠼ߢߐࠇߚຠಽ㘃ࠦ
࠼ߩcC(k)ߣ⋧ᚻ࿖ߩpjPߦኻߔࠆขᒁ㗵 ߪ㧔1-1㧕ᑼࠃࠅ◲නߦv(c,j)ߣࠊߔߎߣ߇ߢ߈ ࠆޕ⋧ᚻ࿖ߦߟߡߪޔjP\{World}ߦኻߒߡޔ
) , ( ) ,
(cW vc j
v t ߥߩߢޔขᒁ㗵ࠍ⋧ᚻ࿖⇇ߩ )
, (cW
v ߣߒߡ߽৻⥸ᕈࠍᄬࠊߥޕmdcc ಽ㘃ࠦ
࠼ߪขᒁ㗵ࠍ⠨ᘦߒߚߣ߈ߩ⚦ಽ㘃ࠦ࠼ߩ 㓸߹ࠅߥߩߢޔ
(2-4)
} 0 ) , ( ), (
, 0 ) , (
, 5 1 ), (
| {
z
W v c D W c v
k k C c c M
S S
Z Z
"
ߣߥࠆޕ߽ߜࠈࠎޔv(I,W) 0ߣߒߡࠆޕߎߎ ߢ㊀ⷐߥߎߣߪ㧔2-4㧕ᑼ߆ࠄࠊ߆ࠆࠃ߁ߦ mdcc ಽ㘃ࠦ࠼ߪᩴࡌ࡞ಽ㘃ࠦ࠼ߩkߣߪή㑐ଥ ߦᚑߐࠇߡࠆߎߣߢࠆޕߘߩߚޔmdcc ಽ㘃ࠦ࠼ߪᔅߕߒ߽ቢోߥᒻߢߩ㓏ጀ᭴ㅧ߆ࠄ
᭴ᚑߐࠇࠆᩴࡌ࡞ߩಽ㘃ࠦ࠼ߢߪߥߎߣߦ ᵈᗧߔࠆᔅⷐ߇ࠆޕ
ຠಽ㘃ࠍHSߩOriginal߅ࠃ߮ฦᡷ⸓ ߣߒ ߚߣ߈ޔ㧔2-1㧕ᑼߦኻᔕߐߖߡޔk ᩴࡌ࡞߇ c ߢࠆk2ᩴࡌ࡞ಽ㘃ࠦ࠼ߩ㓸߹ࠅࠍޔ
6 , 4 , 2
k ߦኻߒߡޔ (2-5)
} ) (
), 2 ( ), (
| { ) (
c
k C k C c c
D
k
H
Z K
Z Z
ߣߔࠆޕmdccಽ㘃ࠦ࠼ߪขᒁ㗵ࠍ⠨ᘦߒߚߣ߈ ߩ⚦ಽ㘃ࠦ࠼ߩ㓸߹ࠅߥߩߢޔ
(2-6)
} 0 ) , ( ), (
, 0 ) , (
, 6 , 4 , 2 ), (
| {
z
W v c D W c v
k k C c c M
H H
Z Z
ߣߥࠆޕຠಽ㘃߇SITCࠆߪHSߩߤߜࠄ߆ ߦߎߛࠊࠄߥߣ߈ߪmdcc ಽ㘃ࠦ࠼ߩ㓸߹ࠅ ࠍ◲නߦMߢߔߎߣߦߔࠆޕ
1ߩຠಽ㘃ߪSITC-R1ࠍၮ␆ߣߒߡᚑߐ ࠇߡࠆߩߢޔ㧔2-4㧕ᑼࠍㆡ↪ߒߡmdccಽ㘃ࠦ
࠼ߩᚑࠍ⹜ߺࠆޕຠಽ㘃ߪᱜ㗄⋡એᄖࠍኻ
⽎ߣߔࠆޕᦨೋߪ1ᩴࡌ࡞ಽ㘃ࠦ࠼ߦ߇mdcc ಽ㘃ࠦ࠼߆ߤ߁߆ࠍ⺞ߴࠆߚޔk 1ߣߔࠆޕ
3ߦ߅ߡC(1)ߩⷐ⚛ߪ㨧0㨩ߩ1߇ሽߔ ࠆߩߢߎࠇࠍc {0}ߣߔࠇ߫ޔv(c,W) v(0,W)
0
12z ߢࠆޕ1ᩴࡌ࡞߇㨧0㨩ߣߥࠆ2ᩴ
ࡌ࡞ಽ㘃ࠦ࠼ߩ㓸߹ࠅߪ㧔2-1㧕ᑼࠃࠅޔ )
2 ( } 02 , 01 , 00 { ) 0
( C
DS ߣߥࠅޔ3ߩⷐ⚛߇ሽ
ߔࠆޕC(2) ߩⷐ⚛ߩ㧝ߟߢࠆ㨧00㨩ߪ 0
3 ) , 00
( W z
v ߥߩߢޔc {0}M ߣߥࠆޕ
) 1 ( C
c ߦ߅ߡZDS(c)߇v(Z,W)z0ߣߥࠆ
߽ߩ߇㧝ߟߢ߽ሽߔࠇ߫㧔2-4㧕ᑼࠍḩ⿷ߒߥ
߆ࠄߢࠆޕ໑৻ߩC(1)ߩⷐ⚛ߢࠆ㨧0㨩ߪ M
} 0
{ ߣߥࠆߚޔ1 ᩴࡌ࡞ಽ㘃ࠦ࠼ߢM ߦዻߔࠆ߽ߩߪሽߒߥޕ
หߓࠃ߁ߦߒߡޔ2ᩴࡌ࡞ಽ㘃ࠦ࠼ߢߪM ߦዻߔࠆ߽ߩߪሽߖߕޔ3 ᩴࡌ࡞ಽ㘃ࠦ࠼
ߩਛߢMߦዻߔࠆ߽ߩߪ㨧012㨩ߩߺߢࠆߎߣ ߇␜ߐࠇࠆ 2 ޕ4ᩴࡌ࡞ಽ㘃ࠦ࠼ߦߟߡߪޔ 㨧0118㨩એᄖߩ4ᩴࡌ࡞ಽ㘃ࠦ࠼ߪขᒁ㗵߇ 0ߢߪߥߊޔ5ᩴࡌ࡞ಽ㘃ࠦ࠼߇ሽߒߥߩ ߢ M ߦዻߒޔ5 ᩴࡌ࡞ಽ㘃ࠦ࠼ߪ㨧01181,
01189㨩ߪMߦዻߔࠆߎߣߦߥࠆ 3 ޕ
ᓧࠄࠇߚmdccಽ㘃ࠦ࠼ߩߔߴߡߩⷐ⚛ߪ1 ߦ߅ߌࠆ mdccಽ㘃ࠦ࠼ߩᱜߒߡߥ⾏ᤃ
࠺࠲ࠍࠊߔNߦ٤ߢ␜ߐࠇߡࠆޕ
2.2 mdccಽ㘃ࠦ࠼ߩ․ᓽ
ขᒁ㗵ࠍ⠨ᘦߒߚ⚦ಽ㘃ߣߒߡߩmdcc ಽ㘃
ࠦ࠼ߩ․ᓽߪ⇇ว⸘ࠍ⋧ᚻ࿖ࠍ࿕ቯ ߔࠇ߫ᢛวᕈ߇⸽ߐࠇߡࠆߣ߈ޔmdccಽ㘃ࠦ
࠼ߦኻᔕߔࠆขᒁ㗵ࠍว⸘ߔࠆߣຠ✚㗵ߩ )
, (T W
v ߦ৻⥌ߔࠆߎߣߢࠆޕຠಽ㘃߇SITC ฦᡷ⸓ ߢࠆߣ߈ޔਔ⠪߇৻⥌ߔࠆߎߣࠍએਅ ߦ߅ߡ␜ߔޕᩴࡌ࡞ಽ㘃ࠦ࠼ߦ߅ߡ1ᩴ
ࡌ࡞ಽ㘃ࠦ࠼ߩขᒁ㗵ߩߪv(T,W)ߦ৻⥌
ߔࠆߣቯߔࠆޕ1 ᩴࡌ࡞ಽ㘃ࠦ࠼ߩ㓸߹ࠅ ࠍޔC(1) N1ߣߔࠆޕ߹ߚޔkᩴࡌ࡞ಽ㘃ࠦ
࠼ߩcC(k)ߦኻߒߡޔDS(c)ߣߥࠆk1ᩴࡌ
࡞ಽ㘃ࠦ࠼ߩขᒁ㗵ߩࠍޔ
(2-7) ( , ) (( ( ) ), )
)) ( (
W k c v W v
k c DS
x
¦
u
Z
Z
ߣߔࠆޕᦨೋߩࠬ࠹࠶ࡊߣߒߡޔk 1ߣ߅ߊޕ mdccಽ㘃ࠦ࠼ߩ㓸߹ࠅߩMߪᩴࡌ࡞ಽ㘃ࠦ
࠼ߣߪή㑐ଥߥߩߢޔMߩਛߢkᩴࡌ࡞ಽ㘃
ࠦ࠼㓸߹ࠅࠍMkߣߔࠇ߫ޔ (2-8)
} 0 ) ), ) ( ((
, 0 ) ), ( ( , ) (
| ) ( {
x u
z
W k c v
W k c v N k c k c
Mk k
ߣߔߎߣ߇ߢ߈ࠆޕMk NkߢࠅޔMkߩⷐ
⚛ߩᢙࠍ m(k)ߣߔࠇ߫ޔ )}
( )
(
{c1 k c ( ) k
Mk " mk
ߢࠆޕNkߪmdccಽ㘃ߣߘ߁ߢߪߥಽ㘃ߦಽ
ഀߔࠆߎߣ߇ߢ߈ޔNk Mk(Nk \Mk)ߢࠅޔ หᤨߦMk(Nk \Mk) Iߣߥࠆޕmdcc ಽ㘃ߢ ߪߥ߽ߩߩᢙࠍm('k)ߣߔࠆޕNkߩⷐ⚛ߩ
ᢙߪm(k)m('k)ߣߥࠅޔ
)}
( )
(
{c1 k c ( ) (' ) k
Nk " mkm k
ߣߥࠆޕ߹ߚޔᢛวᕈ߇㓚ߐࠇߡࠆߚޔk
ᩴࡌ࡞ಽ㘃ࠦ࠼ߩߔߴߡߩขᒁ㗵ߩߪޔ (2-9) ( ( ), ) ( , )
) (
W T v W k c v
Nk
k
c
¦
ߢࠆޕ
Nkߦ߅ߡޔm('k)!0ߩߣ߈ޔmdccಽ㘃ࠦ
࠼ߢߪߥಽ㘃ࠦ࠼ߩ㓸߹ࠅߪޔ
(2-10)
)}
(
) ( {
\
) (' ) (
1 ) (
k c
k c M N
k m k m
k m k k
"
ߣߥࠅޔNk\Mkߩⷐ⚛ࠍkᩴࡌ࡞ߣߔࠆk1
ᩴࡌ࡞ಽ㘃ࠦ࠼ߢขᒁ㗵ߩ0ߢߪߥ߽ߩ߇ ሽߔࠆޕNkߪMkߣNk \Mkߦࠃࠅಽഀߐࠇࠆ ߚޔ
(2-11)
) ), ( (
) ), ( ( )
), ( (
\
W k c v
W k c v W
k c v
k k
k k
M N c
M c N
c
¦
¦
¦
ߣߥࠅޔขᒁ㗵ߩࠍ2ߟߦಽߌࠆߎߣ߇ߢ߈ࠆޕ Nkߩߔߴߡߩⷐ⚛߇ mdcc ಽ㘃ࠦ࠼ߢࠆ
0 ) ('k
m ߩߣ߈ߪޔNk Mkߣߥࠆޕ 0
) ('k !
m ߩߣ߈ߪᒁ߈⛯߈ޔk ᩴࡌ࡞߇
k
k M
N \ ߦዻߔࠆk1ᩴࡌ࡞ಽ㘃ࠦ࠼ࠍ
1 k
N ߣߒߡޔ
(2-12)
))}
( (
),
\ ( ) (
|
1 { k c D
M N k c N
S
k k k
Z
Z
ߣߔࠆޕߘߩⷐ⚛ߩᢙࠍޔm(k1) m('k1) ߣߔࠆޕNk1ߪޔ
)}
1 ( )
1 (
{ 1 ( 1) (' 1)
1
c k c k
Nk " mk m k
ߣߥࠆޕkᩴࡌ࡞ಽ㘃ࠦ࠼ߢࠊߐࠇࠆ㧔2-10㧕 ᑼߪk1ᩴࡌ࡞ಽ㘃ࠦ࠼߇ሽߒޔߘࠇࠍ
ࠊߖ߫㧔2-12㧕ᑼߣߥࠆޕ
ᩴࡌ࡞ಽ㘃ࠦ࠼㑆ߦᢛวᕈ߇⸽ߐࠇߡ
ࠇ߫ޔkᩴࡌ࡞ಽ㘃ࠦ࠼ߩߔߴߡߩcC(k) ߩขᒁ㗵ߪޔ
(2-13) v(c(k),W) v((c(k)ux),W)
ߢࠆޕߒߚ߇ߞߡޔkᩴࡌ࡞ಽ㘃ࠦ࠼c(k) ߩขᒁ㗵ߦኻߔࠆߔߴߡߩߪ
(2-14)
) ), 1 ( (
) ), ) ( ((
) ), ( (
) 1 ( ) 1 (
) ( ) ( )
( ) (
W k c v
W k c v W
k c v
k C k c
k C k c k
C k c
x u
¦
¦
¦
ߣߥࠅޔk1ᩴࡌ࡞ಽ㘃ࠦ࠼ߩߔߴߡߩขᒁ 㗵ߣ৻⥌ߔࠆޕߐࠄߦޔ㧔2-12㧕ᑼࠃࠅޔ
(2-15)
) , (
) , (
) ), ((
) , (
1
) (
\
\
\
W v
W v
W c v W
c v
k S k k
k k k
k
N
c D M N c
M N c M
N c
Z Z
Z Z
¦
¦
¦
¦
¦
x u
ߣߥࠆޕ㧔2-11㧕ᑼߩฝㄝߩ╙2㗄⋡ߦ㧔2-15㧕ᑼ ࠍઍߔࠇ߫ޔ
(2-16)
) , (
) , ( )
, (
1
W c v
W c v W
c v
k
k k
N c
M c N
c
¦
¦
¦
ߣߥࠆޕkࠍ2߆ࠄ4߹ߢ㗅ߦ⟎߈឵߃ߡޔߎߩ ᠲࠍ➅ࠅߔߎߣߦࠃࠅޔM1߆ࠄM4ࠍᚑ ߔࠆߎߣ߇ߢ߈ࠆޕk 5ߩߣ߈ߪޔߔߴߡߩ
N5
c ߦኻߒߡޔ6ᩴࡌ࡞ಽ㘃ࠦ࠼ߪሽߒ ߥߩߢޔm('6) 0ߢࠅޔN5 M5ߣߥࠆޕ ߎࠇࠄߩ৻ㅪߩᠲߦࠃࠅM1߆ࠄM5߇ᚑߐ ࠇࠆޕMߪ㧔2-4㧕ᑼߢ␜ߐࠇࠆmdccಽ㘃ࠦ࠼
ߩ㓸߹ࠅߢࠅޔM M1"M5ߣࠊߐࠇ ࠆޕએߩߎߣ߆ࠄޔ
(2-17)
¦
¦
¦
¦
¦
Mk
c k M
c
N c M
c
W k c v W
c v
W c v W
c v W
T v
) ), ( ( )
), 1 ( (
) ), 2 ( ( )
), 1 ( ( )
, (
5
1 1
2 1
"
ߣߥࠆޕ
ᩴࡌ࡞ಽ㘃ࠦ࠼㑆ߦᢛวᕈ߇⸽ߐࠇߡ
ࠆߎߣࠍቯߔࠇ߫ޔmdccಽ㘃ࠦ࠼ߦኻᔕߔࠆ ขᒁ㗵ࠍว⸘ߔࠆߣຠ✚㗵ߩv(T,W)ߦ৻⥌ߔ ࠆߎߣࠍ⏕߆ࠄࠇࠆޕຠಽ㘃߇HSߩOriginal ߅ࠃ߮ฦᡷ⸓ ߢ߽หߓࠃ߁ߦߔࠆߎߣߢਔ⠪ߩ
৻⥌ࠍ␜ߔߎߣ߇ߢ߈ࠆޕᢛวᕈ߇ᰳᅤߒߡࠆ
⾏ᤃ࠺࠲ߦߟߡߩmdcc ಽ㘃ࠦ࠻ߦߟߡ ߪᰴ▵ߦߡ⚫ߔࠆޕ
3 㧚ຠಽ㘃ߦ߅ߌࠆᢛวᕈߩ⹏ଔ
⾏ᤃ࠺࠲ߩ⛔⸘୯ߩਛߢขᒁ㗵ࠍኻ⽎ߣߒߚ ߣ߈ޔಽ㘃ࠞ࠹ࠧߩຠಽ㘃߅ࠃ߮⋧ᚻ࿖ߦ
2 kᩴࡌ࡞ಽ㘃ࠦ࠼ߣ⋧ᚻ࿖ߩ⾏ᤃࡑ࠻ࠢࠬߦ߅ߌࠆขᒁ㗵
P )
(k C
p1 pj pn Error of P World
)
1(k
c v(c1(k),1) ̖ v(c1(k),j) ̖ v(c1(k),n) ep(c1(k)) v(c1(k),W)
㧦 㧦 : :
) (k
ci v(ci(k),1) ̖ v(ci(k),j) ̖ v(ci(k),n) ep(ci(k)) v(ci(k),W)
㧦 㧦 : :
)
)(
( k
cmk v(cm(k),1) ̖ v(cm(k),j) ̖ v(cm(k),n) ep(cm(k)) v(cm(k),W) Error of C(k) ec(k)(1) ec(k)(j) ec(k)(n) ec,p(k) b
Total v(T1,) v(T, j) v(T,n) a v(T,W)
㧔ᚲ㧕㊁↰ኈഥޟ⇇⾏ᤃࡑ࠻ࠢࠬᚑߦ߅ߌࠆᢛวᕈߩ⹏ଔߣᱜޠ㧔ޡᡷ⸓ ⇇⾏ᤃࡑ࠻ࠢࠬ̆࿖㓙↥ᬺ
ㅪ㑐24ㇱ㐷ಽ㘃ߦ߽ߣߠߡ̆ޢSDS No.84 ᡷ⸓ 㧕ߩ1ߦ߽ߣߠ߈╩⠪ᚑޕ
㧔ᵈ㧕k ᩴࡌ࡞ಽ㘃ࠦ࠼߆ࠄ᭴ᚑߐࠇࠆຠಽ㘃ߩ㓸߹ࠅࠍޔC(k) {c1(k),",cm(k)(k)}ߢࠊߒޔ⋧ᚻ࿖ߩ 㓸߹ࠅࠍP {World, p1,",pn}ߣߔࠆޕຠ✚㗵ߪTotal߹ߚߪTޔ⋧ᚻ࿖⇇ߪWorld߹ߚߪWߢࠆޕcm(k)(k) ߢࠊߔߣߎࠈޔ⚕㕙ߩㇺวߦࠃࠅޔcm(k)ߣߒߡ␜ߐࠇߡࠆޕ⋧ᚻ࿖ߦࠃࠆ⺋Ꮕߪޔa ep(cx(k))ec,p(k)ޔ
ຠಽ㘃ߦࠃࠆ⺋Ꮕߪޔb ec(k)(x)ec,p(k)ߢࠆޕᓇߩㇱಽߪUN Comtrade⾏ᤃ࠺࠲߆ࠄᓧࠄࠇࠆㇱಽߢࠆޕ
ߟߡߪߘࠇߙࠇߩຠಽ㘃ࠦ࠼ߩߺߥࠄ ߕߘࠇࠄว⸘୯ߢࠆຠ✚㗵߅ࠃ߮⋧ᚻ࿖⇇
߇߹ࠇߡࠆޕߘߩߚޔຠ✚㗵ߣ⋧ᚻ࿖
⇇ߩ⾏ᤃ࠺࠲ߩv(T,W)ࠍၮḰ୯ߣߔࠆߎߣߦ ࠃࠅຠಽ㘃ࠦ࠼ࠆߪ⋧ᚻ࿖ߩ࠺
࠲ࠍว⸘ߒߚ୯߇ၮḰ୯ߦ৻⥌ߔࠆ߆ߤ߁߆ߢ ߘࠇߙࠇຠಽ㘃߅ࠃ߮⋧ᚻ࿖ߩᢛวᕈࠍᬌ⸛ߔ ࠆߎߣ߇ߢ߈ࠆޕᧄ▵ߪ⾏ᤃࡑ࠻ࠢࠬߦߟߡ ႎ๔࿖ޔャಽޔᐕߏߣߦຠ✚㗵ߣ⋧ᚻ࿖
⇇ߩ⾏ᤃ࠺࠲ࠍၮḰ୯ߣߒߚߣ߈ߩຠಽ㘃 ߅ࠃ߮⋧ᚻ࿖ߩขᒁ㗵ߩᢛวᕈࠍᬌ⸛ߒߡࠆޕ
ຠಽ㘃ߦߟߡߪᩴࡌ࡞ಽ㘃ࠦ࠼ޔmdcc ಽ㘃ࠦ࠼ߦ߅ߌࠆᩴࡌ࡞ಽ㘃ࠦ࠼ౝߩᢛว ᕈࠍᬌ⸛ߔࠆߣหᤨߦ⇣ߥࠆᩴࡌ࡞ಽ㘃ࠦ࠼
㑆ߩᢛวᕈߦߟߡ߽ᬌ⸛ߔࠆޕ
3.1 ᩴࡌ࡞ಽ㘃ࠦ࠼ߩขᒁ㗵
ᩴࡌ࡞ಽ㘃ࠦ࠼ߩ⾏ᤃࡑ࠻ࠢࠬߩขᒁ㗵
ߪห৻ᩴࡌ࡞ಽ㘃ࠦ࠼㑆ߦ߅ߌࠆขᒁߢ
ࠆޕk ᩴࡌ࡞ಽ㘃ࠦ࠼ߣ⋧ᚻ࿖ߩ⾏ᤃ ࡑ࠻ࠢࠬߦ߅ߌࠆขᒁ㗵߇2ߦ␜ߐࠇߡ
ࠆޕຠಽ㘃߇SITCฦᡷ⸓ ߩߣ߈ߪޔk 1,2,3,4 ߦኻߔࠆkᩴࡌ࡞ಽ㘃ࠦ࠼ߣ⚦ಽ㘃ߣߒߡ ߩmdcc ಽ㘃ࠦ࠼߇ኻ⽎ߣߥࠆޕ೨ㅀߒߚࠃ߁ ߦၮᧄ㗄⋡ߢߪᔅߕߒ߽ߘࠇࠄߩว⸘ߪຠ✚㗵 ߣߪ৻⥌ߔࠆߣߪ㒢ࠄߥߚޔၮᧄ⊛ߦຠ✚
㗵ߣ৻⥌ߔࠆmdccಽ㘃ࠦ࠼ࠍ⚦ಽ㘃ߣߔࠆޕ
ຠಽ㘃߇HSߩOriginal߅ࠃ߮ฦᡷ⸓ ߩߣ߈ ߪᩴࡌ࡞ߩಽ㘃ࠦ࠼ߪk 2,4,6ߣߒߚߣ߈ ߩkᩴࡌ࡞ಽ㘃ࠦ࠼ߣ⚦ಽ㘃ࠦ࠼ߣߒߡ ߩmdccಽ㘃ࠦ࠼߇ኻ⽎ߣߥࠆޕ
ຠ✚㗵ࠍၮḰߣߔࠆߎߣߦࠃࠅ⾏ᤃࡑ࠻ࠢ
ࠬߩขᒁ㗵ߦ߅ߌࠆᢛวᕈߩ⹏ଔ߇น⢻ߣߥࠆޕ ᓟㅀߔࠆࠃ߁ߦߎߩ⾏ᤃࡑ࠻ࠢࠬߦߪᢛวᕈࠍ
ߟߚߦߪ⋧ᚻ࿖߅ࠃ߮ຠಽ㘃ߦߟߡߘࠇ ߙࠇߩ⺋ᏅߩޔError of P㧔Partner countriesߦ㑐ߔ ࠆ⺋Ꮕ㗄⋡㧕ߣError of C(k)㧔kᩴࡌ࡞ಽ㘃ࠦ
࠼ߩCommoditiesߦ㑐ߔࠆ⺋Ꮕ㗄⋡㧕߇ᔅⷐߣ
ߥࠆޕUN Comtrade⾏ᤃ࠺࠲ࠍ߽ߣߦߒߡᚑ
3 kᩴࡌ࡞ಽ㘃ࠦ࠼ߣ⋧ᚻ࿖ߩ⾏ᤃࡑ࠻ࠢࠬߦ߅ߌࠆขᒁ㗵ⷐ⚂
P )
(k C
P㧦⋧ᚻ࿖ߩว⸘ Error of P World )
(k
C :ຠಽ㘃ߩว⸘
Error of C(k)
) ), ( (cx k x v
)
)(
(k x ec
)) ( (c k ep x
)
, (k
ecp
) ), ( (c k W v x
) ( )
( ,
)
( e k
eck x cp
Total v(T,x) ep(cx(k))ec,p(k) v(T,W)
㧔ᚲ㧕㊁↰ኈഥ㧔2003㧕ޟ⇇⾏ᤃࡑ࠻ࠢࠬᚑߦ߅ߌࠆᢛวᕈߩ⹏ଔߣᱜޠ㧔ޡᡷ⸓ ⇇⾏ᤃࡑ࠻ࠢࠬ̆࿖
㓙↥ᬺㅪ㑐24ㇱ㐷ಽ㘃ߦ߽ߣߠߡ̆ޢSDS No.84 ᡷ⸓ 㧕ߩ2ߦၮߠ߈⪺⠪ᚑޕ
㧔ᵈ㧕k߇0ߩߣ߈ߪຠ✚㗵ߩߺߒ߆ሽߒߥߚ⺋Ꮕߩep(0),ec(0),ec,p(0)ߪߔߴߡ0ߣߥࠆޕ
ߐࠇߚ⾏ᤃࡑ࠻ࠢࠬߩขᒁ㗵ߦ߅ߡޔຠ
ಽ㘃ࠍci(k)ߦ࿕ቯߒߡ⋧ᚻ࿖ࠍว⸘ߒߡ߽ᔅߕ ߒ߽⋧ᚻ࿖⇇ߦ৻⥌ߔࠆߣߪ㒢ࠄߥޕ৻⥸⊛
ߦߪᓧࠄࠇߚ⾏ᤃ࠺࠲ߦ㑐ߒߡ⋧ᚻ࿖j ߦߟ
ߡޔj 1"nࠍว⸘ߒߡޔ
(3-1) ( ( ), ) ( ( ), )
1
¦
n v ci k j v ci k xj
ߣߔࠆޕߎߎߢޔ i 1"m(k)ߢࠅޔ৻⥸⊛ߦ ߪᔅߕߒ߽ޔv(ci(k),W) v(ci(k),x)ߢࠆߣߪ㒢 ࠄߥޕߎߩේ࿃ߣߒߡߪ⾏ᤃ࠺࠲࿕ߩ⺋Ꮕޔ ਣ⺋Ꮕޔຠಽ㘃߿⋧ᚻ࿖ਇߩขࠅᛒߦࠃ ࠆ⺋Ꮕ╬߇⠨߃ࠄࠇࠆޕຠಽ㘃ࠦ࠼ci(k)ߩ
⋧ᚻ࿖⇇ߩขᒁ㗵v(ci(k),W)ࠍၮḰߣߒߡߎ ߩ⺋Ꮕࠍ⋧ᚻ࿖ߦࠃࠆ⺋Ꮕep(k:i)ߣߔࠆߣޔ
) (
1 m k
i " ߦኻߒߡޔ
(3-2) v(ci(k),W)v(ci(k),x) ep(ci(k)) ߣࠊߐࠇࠆޕ2ߦ߅ߡ⋧ᚻ࿖ߦ㑐ߔࠆ⺋Ꮕ
ߪerror of Pߩ㗄⋡ߦኻᔕߔࠆޕหߓߎߣ߇ຠಽ
㘃ߦߟߡ߽߃ࠆޕ⋧ᚻ࿖ࠍpjߣ࿕ቯߒߚߣ߈
ຠಽ㘃ci(k)ߦኻߔࠆขᒁ㗵ߩv(ci(k),j)ࠍ )
(
1 mk
i " ߦߟߡว⸘ߒߡޔ
(3-3) ( ) ( ( ), ) ( ( ), )
1
j k c v j k c v i
k n
i
¦
xߣߒߡ߽ᔅߕߒ߽⋧ᚻ࿖jߦኻߔࠆຠ✚㗵ߦ৻
⥌ߔࠆߣߪ㒢ࠄߥޕߎߎߢޔj 1"nߢࠆޕ ߎߩේ࿃߽⾏ᤃ࠺࠲࿕ߩ⺋Ꮕ߿ਣ⺋Ꮕ╬ߦ ࠃࠆ⺋Ꮕ╬߇⠨߃ࠄࠇࠆޕ㧔3-3㧕ᑼߪ1ߦ߅ߌ
ࠆkᩴࡌ࡞ಽ㘃ࠦ࠼ߩขᒁ㗵ว⸘ߩTotal(k,N) ߅ࠃ߮Total(k,C)ߦኻᔕߔࠆޕNߪᱜߐࠇߡߥ
⾏ᤃ࠺࠲ޔCߪᱜߐࠇߚ⾏ᤃ࠺࠲ߢࠆޕ
ຠಽ㘃ߩ✚㗵ࠍၮḰߣߒߡߎߩ⺋Ꮕࠍkᩴ
ࡌ࡞ಽ㘃ࠦ࠼ߩຠಽ㘃ߦࠃࠆ⺋Ꮕec(k)(j)ߣ
ߔࠆߣޔj 1"nߦኻߒߡޔ
(3-4) v(T,j)v(cx(k),j) ec(k)(j)
ߣߥࠆޕ2ߦ߅ߡkᩴࡌ࡞ಽ㘃ࠦ࠼ߦ߅ ߌࠆຠಽ㘃ߩ⺋Ꮕߪ Error of C(k)ߩ㗄⋡ߦኻ ᔕߔࠆޕߐࠄߦޔหߦ߅ߌࠆError of Pߩ㗄⋡
ߣError of C(k)ߩ㗄⋡ߩὐࠍ⋧ᚻ࿖߅ࠃ߮kᩴ
ࡌ࡞ಽ㘃ࠦ࠼ߩຠಽ㘃ߩㅢߩ⺋Ꮕߣߒߡ )
, (k
ecp ߣߔࠆޕએߩߎߣ߆ࠄޔkᩴࡌ࡞ಽ㘃
ࠦ࠼ߦ߽ߣߠߊᢛวᕈߩࠆ⾏ᤃࡑ࠻ࠢࠬߪ ቢᚑߔࠆޕ
ᰴߦ✚ว⺋Ꮕޔຠಽ㘃ߦࠃࠆ⺋Ꮕ߅ࠃ߮⋧ᚻ
࿖ߦࠃࠆ⺋Ꮕߩផቯ୯ࠍᓧࠆߚߦᓧࠄࠇߚ࠺
࠲ߩ⋧ᚻ࿖߅ࠃ߮ຠಽ㘃ߩi 1"m(k)ߣ⋧ᚻ
࿖ߩ j 1"nߦኻߔࠆߘࠇߙࠇߦኻߔࠆขᒁ㗵
ߩว⸘ࠍ㧔3-1㧕ᑼ߅ࠃ߮㧔3-3㧕ᑼߩ⸥ߦኻᔕ ߐߖߡv(cx(k),x)ߣߔࠆޕ㧔3-2㧕ᑼߦ߅ߡຠಽ 㘃ߢࠆci(k)ߩว⸘ࠍޔ
(3-5)
) (
) ), ( ( ) ), ( (
)) ( ( ))
(
( ( )
1
k e
k c v W k c v
k c e k
c e
p
i p k m
i p
x x
x
x
¦
ߣߔࠆߣޔߎߩ⺋Ꮕߪຠಽ㘃ߣߪή㑐ଥߥ⋧ᚻ
4 1ᩴࡌ࡞ಽ㘃ࠦ࠼ߣ⋧ᚻ࿖ߩ⾏ᤃࡑ࠻ࠢࠬߦ߅ߌࠆขᒁ㗵
P )
(k C
p1 p2 p3 Error of P World
0 16 16 16 0 48
Error of C(1) 0 0 0 0 0
Total 16 16 16 0 48
㧔ᚲ㧕1߆ࠄ1ᩴࡌ࡞ಽ㘃ࠦ࠼ߩ0ࠍขࠅߒޔ2ߦᓥߞߡ╩⠪ᚑޕ
㧔ᵈ㧕1ᩴࡌ࡞ಽ㘃ࠦ࠼ߢߪᢛวᕈ߇⸽ߐࠇߡࠆߚޔError of PߣError of C(1) ߪߦ0ߢࠆޕߔߥࠊ ߜޔ2ߦ߅ߌࠆaߪ0ޔbߪ0ߢࠆޕ
5 2ᩴࡌ࡞ಽ㘃ࠦ࠼ߣ⋧ᚻ࿖ߩ⾏ᤃࡑ࠻ࠢࠬߦ߅ߌࠆขᒁ㗵
P )
(k C
p1 p2 p3 Error of P World
00 01 02
4 9 2
4 9 2
4 9 2
0 0 0
12 27 6 Error of C(2) 1 1 1 0 3
Total 16 16 16 0 48
㧔ᚲ㧕1߆ࠄ2ᩴࡌ࡞ಽ㘃ࠦ࠼ߩ00,01,02ࠍขࠅߒޔ2ߦᓥߞߡ╩⠪ᚑޕ
㧔ᵈ㧕⋧ᚻ࿖ߩError of P ߪᢛวᕈ߇⸽ߐࠇߡࠆߚ0ߢࠆ߇ޔ2ᩴࡌ࡞ಽ㘃ࠦ࠼ߢߪᢛวᕈ߇⸽ߐࠇߡ
ߥߚޔError of C(2) ߪ0ߢߪߥޕߔߥࠊߜޔ2ߦ߅ߌࠆaߪ0ޔbߪ3ߢࠆޕ
࿖ߩߺߩ⺋Ꮕߣߥࠆޕ߹ߚޔ㧔3-4㧕ᑼߦ߅ߡ⋧
ᚻ࿖ߢࠆjߩว⸘ࠍޔ
(3-6) ec(k)(x) v(T,x)v(cx(k),x) ec(k) ߣߔࠆߣޔߎߩ⺋Ꮕߪ⋧ᚻ࿖ߣߪή㑐ଥߥຠಽ 㘃ߩߺߦࠃࠆ⺋Ꮕߣߥࠆޕ⋧ᚻ࿖߅ࠃ߮ຠಽ㘃 ߦㅢߔࠆ⺋Ꮕߪޔ
(3-7)
) ), ( ( ) , (
) ), ( ( ) , ( )
, (
W k c v T v
k c v W T v k ecp
x
x
x
x
ߣࠊߐࠇࠆޕ㧔3-5㧕ᑼ߆ࠄ㧔3-7㧕ᑼ߹ߢߦࠃࠅޔ
⾏ᤃࡑ࠻ࠢࠬߩ✚ว⺋Ꮕࠍe(k)ߣߔࠇ߫ޔ (3-8)
) ), ( ( ) , (
) ( ) ( ) ( )
( ,
x
x k c v W T v
k e k e k e k
e c p cp
߇ᓧࠄࠇࠆޕ
ᧄ┨ߢߪႎ๔࿖ޔᐕޔャಽࠍ࿕ቯߒߚߣ ߈ߩ⚦ߥࠆຠಽ㘃ߣ⋧ᚻ࿖ࠍ߽ߣߦߒߚ
⾏ᤃࡑ࠻ࠢࠬߩ⺋Ꮕ␜ࠍ✚ว⺋Ꮕࠍ㧔3-8㧕ᑼޔ
ຠಽ㘃ߩߺ߆ࠄ↢ߓߚ⺋Ꮕࠍޔ
(3-9) ec(k)ec,p(k) v(T,W)v(cx(k),W)ߣ
ߒޔ⋧ᚻ࿖ߩߺ߆ࠄ↢ߓߚ⺋Ꮕࠍޔ (3-10) ep(k)ec,p(k) v(T,W)v(T,x) ߣߒߡࠊߔߎߣߦߔࠆޕ
ຠಽ㘃ߩkᩴࡌ࡞ಽ㘃ࠦ࠼ߩ⾏ᤃࡑ࠻
ࠢࠬߩขᒁ㗵߅ࠃ߮ⷐ⚂ߐࠇߚขᒁ㗵ߪ 2 ߅ࠃ߮3ߦ␜ߐࠇޔ⋧ᚻ࿖ߣຠಽ㘃ߩ⺋Ꮕߪ
) ( ), ( ),
(k e k e, k
ep c cp ߣߒߡ␜ߐࠇߡࠆޕk߇0 ߩߣ߈ߪຠ✚㗵ߩߺߒ߆ሽߒߥߚ⺋Ꮕߩ
) 0 ( ), 0 ( ), 0
( c c,p
p e e
e ߪߔߴߡ0ߣߥࠅޔ✚ว⺋Ꮕ
߽e(0)0 ߢࠆޕk ᩴࡌ࡞ಽ㘃ࠦ࠼ߦၮߠߊ
⾏ᤃࡑ࠻ࠢࠬߩ2ߣߘߩⷐ⚂ߢࠆ3ߪ
ߦຠ✚㗵ߦߪkᩴࡌ࡞ಽ㘃ࠦ࠼ߦኻߔࠆ
6 mdccಽ㘃ࠦ࠼ߣ⋧ᚻ࿖ߩ⾏ᤃࡑ࠻ࠢࠬߦ߅ߌࠆขᒁ㗵
P )
(k C
p1 p2 p3 Error of P World
0011 0012 0013 0111 0112 0113 0116 01181 01189 012 0221 0240
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
3
3
3
3
3
3
3
3
3
3
3
3
Error of C(mdcc) 4 4 4 0 12 Total 16 16 16 0 48 㧔ᚲ㧕1߆ࠄmdccಽ㘃ࠦ࠼ߩNࠍขࠅߒޔ2ߦᓥߞߡ╩⠪ᚑޕ
㧔ᵈ㧕⋧ᚻ࿖ߩError of P ߪᢛวᕈ߇⸽ߐࠇߡࠆߚ0ߢࠆ߇ޔmdccಽ㘃ࠦ࠼ߢߪᢛวᕈ߇⸽ߐࠇߡߥ
ߚޔError of C(mdcc) ߪ0ߢߪߥޕߔߥࠊߜޔ2ߦ߅ߌࠆaߪ0ޔbߪ12ߢࠆޕ
ขᒁ㗵ߩว⸘ߩv(cx(k),x)ߢߪߥߊޔUN Comtrade
⾏ᤃ࠺࠲߆ࠄᓧࠄࠇࠆຠ✚㗵ߩv(T,W)ࠍណ
↪ߒߡࠆߎߣߦᵈᗧߔࠆᔅⷐ߇ࠆޕ⾏ᤃ࠺
࠲ߩᢛวᕈߩ⹏ଔߦ߅ߡv(T,W)ߪ⹏ଔၮḰߣ ߣߒߡᱜߒߣቯߐࠇߡ߅ࠅޔkᩴࡌ࡞ಽ㘃ࠦ
࠼ߦࠃࠆ⾏ᤃࡑ࠻ࠢࠬߩ✚ว⺋Ꮕߪ㧔3-8㧕ᑼ ߢ␜ߐࠇࠆ߆ࠄߢࠆޕ
1߆ࠄຠಽ㘃ߩᱜ㗄⋡એᄖࠍขࠅߒߡ
ᩴࡌ࡞ಽ㘃ࠦ࠼ߦࠃࠆขᒁ㗵ࠍᚑߔࠆޕ1
ᩴࡌ࡞ಽ㘃ࠦ࠼ߩขᒁ㗵ߪ4ߦ␜ߐࠇࠆޕ ߎߩࠍ2ߦኻᔕߐߖࠇ߫aߣbߪߦ0ߣߥ ࠅޔv(T,W) v(cx(1),x)ߣߥࠆޕߘߩᏅ߽0ߥߩ ߢޔ㧔3-8㧕ᑼ߆ࠄ✚ว⺋Ꮕߪޔe(1) 4848 0ߣ ߥࠅޔᢛวᕈߩ⸽ߐࠇߡࠆขᒁ㗵ߣߥࠆޕ2
ᩴࡌ࡞ಽ㘃ࠦ࠼ߩขᒁ㗵ߪ5ߦ␜ߐࠇࠆޕ ߎߩߩ✚ว⺋Ꮕߪޔe(2) 4845 3ߣߥࠅޔ ᢛวᕈߩᰳᅤߢࠆขᒁ㗵ߣߥࠆޕ㧔2-4㧕ᑼ߆ ࠄޔc{00,01,02}ߦኻߒߡޔError of C(2)ߩⷐ⚛ߪ
3 45 48 ) 2
(
ec ߢࠆޕ⋭⇛ߒߡࠆ߇ޔหߓ ࠃ߁ߦߒߡ3ᩴࡌ࡞߅ࠃ߮4ᩴࡌ࡞ಽ㘃ࠦ
࠼ߦࠃࠆขᒁ㗵߇ᚑߐࠇࠆޕmdccಽ㘃ࠦ࠼
ߩขᒁ㗵ߪ 6 ߦ␜ߐࠇࠆޕ✚ว⺋Ꮕߪޔ 12
36 48 )
(mdcc
e ߣߥࠅޔᢛวᕈߩᰳᅤߢ
ࠆขᒁ㗵ߣߥࠆޕc{0011,0012, 0013,̖,0240}
ߦኻߒߡޔec(2) 4836 12ߢࠆޕ
3.2 ⾏ᤃ࠺࠲ߦ߅ߌࠆᢛวᕈߩ⹏ଔ
⾏ᤃ࠺࠲ߦ߅ߡᢛวᕈߩࠆ⁁ᘒߢߪߔߴ ߡߩ⺋Ꮕߪሽߖߕޔk ᩴࡌ࡞ಽ㘃ࠦ࠼ߦኻ ߒߡޔec(k) 0ޔep(k) 0ޔec,p(k) 0ߢࠆޕ એਅޔkࠍ⋭⇛ߒߡ߽৻⥸ᕈࠍᄬࠊߥߩߢ⋭⇛
ߔࠆޕߘࠇߦኻߒߡ⾏ᤃ࠺࠲߇ᢛวᕈߦᰳߌࠆ ߣ߈ߩ⁁ᘒߪએਅߩㅢࠅ5ߟߩ⺋Ꮕߩ࠲ࠗࡊ߇⠨
߃ࠄࠇࠆޕ
㧔1㧕ຠಽ㘃ciߦ߅ߌࠆ⋧ᚻ࿖pjߦ⺋Ꮕ߇ࠆ
ߣߒߡޔᢛวᕈߩࠆ⾏ᤃ࠺࠲ߦኻߒߡ )
, (c j
v i ߇'v(ci,j)Ⴧടߒߚ⺋Ꮕߩ࠲ࠗࡊߢࠆޕ
⺋ Ꮕ ߪ ޔ ec 'v(ci,j) ޔ ep 'v(ci,j) ޔ )
,
, v(c j
ecp ' i ߣߥࠆߩߦኻߒߡޔຠಽ㘃ߦࠃ
