统计建模与Ｒ软件(上册).pdf

?R?R?R?R?R?R?R?R?R?R?SAS?SPSS?R?R?R?R?R?R?R?R?(1)?(2)?R?R?R?iii?R?(3)?R?R?R?R?R?R?R?I?II?Monte Carlo?R?R?R?R-2.1.1?(?R-2.3.1,?3?4?),?R?.?iii?(?);(?).?2006?7?iv?i?11.1?.11.1.1?.11.1.2?.31.1.3?.51.1.4?.61.1.5?.71.1.6?Bayes?.81.1.7?.91.1.8n?Bernoulli?.101.2?.111.2.1?.111.2.2?.111.2.3?.121.2.4?.141.2.5?.181.3?.221.3.1?.221.3.2?.241.3.3?.251.3.4?.251.3.5?.271.4?.291.4.1?.30iii?1.4.2?.311.5?.321.5.1?.331.5.2?.341.5.3?.351.5.4?.42?.43?R?472.1R?.472.1.1R?.482.1.2?R.492.1.3R?.552.2?.662.2.1?.662.2.2?.692.2.3?.702.2.4?.712.2.5?.722.2.6?.732.2.7?.732.3?.762.3.1?mode?length.762.3.2?.772.3.3attributes()?attr()?.782.3.4?class?.792.4?.792.4.1factor()?.80?iii2.4.2tapply()?.812.4.3gl()?.812.5?.822.5.1?.822.5.2?.832.5.3?.862.5.4?.872.5.5?(?)?.942.6?.972.6.1?(list).972.6.2?(data.frame).992.6.3?.1022.7?.1032.7.1?.1032.7.2?.1062.7.3?.1082.7.4?.1092.8?.1102.8.1?.1112.8.2?.1122.8.3?.1122.9?.1142.9.1?.1142.9.2?.1172.9.3?.1172.9.4?.120?.121iv?1253.1?.1253.1.1?.1253.1.2?.1313.1.3?.1333.2?.1353.2.1?.1363.2.2?QQ?.1393.2.3?.1443.2.4?.1513.3R?.1523.3.1?.1533.3.2?.1603.3.3?.1623.4?.1643.4.1?.1643.4.2?.1663.4.3?.1693.4.4?.1733.5?.1803.5.1?.1813.5.2?.1833.5.3?.186?.187?1914.1?.1914.1.1?.192?v4.1.2?.1964.2?.2054.2.1?.2054.2.2?.2074.2.3?(?).2084.3?.2084.3.1?.2094.3.2?.2144.3.3?.2234.3.4?.224?.235?2395.1?.2395.1.1?.2395.1.2?.2415.1.3?.2425.2?.2425.2.1?.2425.2.2?.2535.2.3?.2595.3?.2615.3.1Pearson?2?.2615.3.2Kolmogorov-Smirnov?.2685.3.3?.2705.3.4?.2775.3.5?.2815.3.6?.2825.3.7Wilcoxon?.286?.293vi?R?R?1.1?1.1.1?1.?1?0?1?2?;?(random experi-ment),?E.?(1)?(2)?(3)?(sample space),?.?(sample point),?.12?(random event),?A,B,C,?(?).?(certain event).?(impossible event).2.?A?B?A?B,?B?A,?A B,?(contain)?A B?B A,?A?B?(equivalent),?A=B.?A?B?(union),?AB.?n?A1,A2,An?n?A1 A2 An?nSi=1Ai.?A1A2An?Si=1Ai,?A?B?A?B?AB.?A?B?A?B?(intersection),?AB?AB.?n?A1,A2,An?n?A1 A2 An?nTi=1Ai.?A1A2An?Ti=1Ai,?A?B?A?B?(mutuallyexclusive event)?(incompatiable event),?AB=.?A?A?A?(oppositeevent)?(complementary event),?A.?1.1?3?A A=,AA=.?3.?(1)?A B=B A,AB=BA.(1.1)(2)?(A B)C=A (B C),(A B)C=A (B C).(1.2)(3)?(A B)C=(AC)(BC),A (BC)=(A B)(A C).(1.3)(4)?A1 A2=A1 A2,A1 A2=A1 A2.(1.4)?n?nk=1Ak=nk=1Ak,nk=1Ak=nk=1Ak,k=1Ak=k=1Ak,k=1Ak=k=1Ak.(1.5)(5)?A B=AB?A B=A B.(1.6)1.1.2?1.?4?1.1?E?,F?(1)F;(2)?A F,?A F;?(3)?Ai F,i=1,2,?Si=1Ai F.?F?-?F?(,F)?1.2?E?,(,F)?A F,?P(A)?P()?(1)?A,?0 P(A)1;(2)P()=1;(3)?A1,A2,?i,j=1,2,i 6=j,AiAj=?P(A1 A2)=P(A1)+P(A2)+,?P(A)?A?(probability),?(,F,P)?2.?1:P()=0,?P(A)=0 6 A=.?2:?A1,A2,An?P(A1 A2 An)=P(A1)+P(A2)+P(An),(1.7)?3:?A,?P(A)=1 P(A).?4:?A?B,?A B,?P(B A)=P(B)P(A),P(B)P(A).(1.8)?5:(?)?A?B,?P(A B)=P(A)+P(B)P(AB).(1.9)1.1?5?5?P(A1 A2 A3)=P(A1)+P(A2)+P(A3)P(A1A2)P(A1A3)P(A2A3)+P(A1A2A3),(1.10)P(A1 A2 An)=S1 S2+S3 S4+(1)n1Sn,(1.11)?S1=nPi=1P(Ai),S2=P1ijnP(AiAj),S3=P1ijknP(AiAjAk),Sn=P(A1A2An).1.1.3?E?=1,2,n,?n?i(i=1,2,n)?(classical probabilitymodel).?A?m?A?P(A)=mn=?A?.(1.12)?1.1?k?1/l?l?(l k)?A?B?A:?k?B:?k?l?k?l?l?k?lk?A?k?k?k!,?P(A)=k!lk.?B?k?l?k?Ckl?6?k?k!?B?Cklk!?P(B)=Cklk!lk=l!(l k)!lk.?k?k?1.1?k?365?l=365,?P(B)?k=40?P(B)=0.109.?40?P(B)=10.109=0.891,?1.1.4?(?)?A?P(A)=SAS=?A?.(1.13)?(geometric probability model).?1.2(Buffon(?)?).?a?l(l 0,?P(A|B)=P(AB)P(B)(1.16)?B?A?(conditional probability).?N?M?n?m?A?B?P(A)=MM+N,P(B)=m+nM+N,P(AB)=mM+N.?(?A?),?(?)?P(B|A)=mM=P(AB)P(A).8?(1)?A,?0 P(A|B)1;(2)P(|B)=1;(3)?A1,A2,?i,j=1,2,i 6=j,AiAj=?P(A1 A2)|B)=P(A1|B)+P(A2|B)+,?A1,A2,?P(A1 A2)|B)=P(A1|B)+P(A2|B)P(A1A2|B).1.1.6?Bayes?P(AB)=P(A|B)P(B)=P(B|A)P(A).(1.17)?(1.17)?(multiplication formula).?n 2,?P(A1A2An1)0?P(A1A2An1An)=P(A1)P(A2|A1)P(A3|A1A2)P(An|A1A2An1).(1.18)?1.3?B1,B2,?(1)B1,B2,?BiTBj=,i 6=j,i,j=1,2,?P(Bi)0,i=1,2,.(2)B1 B2 =,?B1,B2,?B1,B2,?A?P(A)=Xi=1P(Bi)P(A|Bi).(1.19)?(1.19)?(formula of total probability).1.1?9?B1,B2,?A(P(A)0),?P(Bi|A)=P(BiA)P(A)=P(Bi)P(A|Bi)Pj=1P(Bj)P(A|Bj),i=1,2,(1.20)?(1.20)?Bayes(?)?(Bayes formula),?P(Bi)(i=1,2,)?P(Bi|A)(i=1,2,)?B1,B2,Bn?B?B?Bi?A?P(Bi)?P(Bi|A)?A?1.3?C?A?P(A|C)=0.95,P(A|C)=0.90.?P(C)=0.0004,?P(C|A).?Bayes?P(C|A)=P(C)P(A|C)P(C)P(A|C)+P(C)P(A|C)=0.0004 0.950.0004 0.95+0.9996 0.10=0.0038.1.1.7?A,B?P(AB)=P(A)P(B),?A?B?(mutually independent).?A?B?A?B,A?B,A?B?A1,A2,An?n?n 2.?k(k 2)?Ai1,Ai2,Aik,1 i1 i2 ik n,?P(Ai1Ai2Aik)=P(Ai1)P(Ai2)P(Aik)10?n?A1,A2,An?(1)?A1,A2,An?A1,A2,An?k(k 2)?Ai1,Ai2,Aik,1 i1 i2 ik n,?(2)?A1,A2,An?B1,B2,Bn?Bi?Ai?Ai,i=1,2,n.?A1,A2,An?A1,A2,An?A1,A2,An?A1,A2,An?n?C2n+C3n+Cnn=2n n 1?C2n=n(n1)2?1.4?4?3?A?B,B?C,A?C,?4?A,(B?C)?“?A,(B?C)”,?P(A)=P(B)=P(C)=12,P(AB)=P(AC)=P(BC)=14,P(ABC)=0 6=P(A)P(B)P(C).?A,B,C?1.1.8n?Bernoulli?A?A,?P(A)=p,P(A)=1 p=q,?0 p 1,?Bernoulli(?)?(Bernoulli trial).Bernoulli?n?n?Bernoulli?n?“?”,?“?”,?n?Bernoulli?Ak=n?Bernoulli?A?k?,1.2?11?P(Ak)=Cknpk(1 p)nk,k=0,1,2,n.(1.21)?B(n,k).1.2?1.2.1?1.4?E?,?X()?x R,?:X()x F,?X()?(random variable).?1.2.2?1.5?X?x,?F(x)=PX x,x (,+),(1.22)?F(x)?X?(distribution function),?(probability cumulative function).?F(x)?(,+)?F(x)?x?X?(,x?(1)0 F(x)1;(2)F(x)?x1 x2?F(x1)F(x2);(3)F()=limxF(x)=0,F(+)=limx+F(x)=1;(4)F(x)?limxx+0F(x)=F(x0),x0 R?12?(5)Pa a=1 PX a=1 F(a).?1.2.3?1.?1.6?X?X?1.7?X