应用统计学5new

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1、H0:F(x)=F0(x;θ),F0(x;θ)θ(1)θ=θ0 H0.(2)θ F0(x;θ)H0
.F0(x;θ),x1,···,xnF0(x;θ)Δ(x1,···,xn;F)Δ0,ΔΔ0,x1,···,xn!"!H0,#"H0.Δ$$%%&(GoodnessofFit),'$%%'&2χ%(%'1.F(x).(X1,···

2、,Xn)&)'*H0:F(x)=F0(x;θ0),θ0+(1)(&r−1−∞

3、Pearson22:χ∼χ(r−1),n;<8;22<=>α,'!W={χ≥χ1−α(r−1)}.2.
H0:F(x)=F0(x;θ),θs?θ=(θ1,···,θs)(1)MLE=>θˆ?@(2)ˆpi=F0(yi;θˆ)−F0(yi−1;θˆ),i=1,2,···,r22r(ni−npˆi)2(3)χ=∼χ(r−s−1)i=1npˆi3.'@(1),23()rA:A/0B*ni,C/0D5)/0B%-+(2)H04MLEC7=EC7F+(3)H047BGpi=

4、F(yi)−F(yi−1),i=21,···,r,17Bnpi.22r(ni−npi)(4)7Bχ=i=1npi(5)8;<=>α,'!W={χ2≥χ2(r−s−1)}1−αE>Hs+(6)22χ>χ1−α,!H0,#"H0+2:(1)χ%(%'FI<)4JK+(2)5npi≥5(3)'/0G/0G:L+M1.!I
O20OJK"0,1,···,9,C"P8OK*'Q#

5、T:!20O#Q#P(α=0.05)1U:H0:!20OQ#pi=P(x=i)=,i=100,1,···,9,npi=8032"ninpini−npi(ni−npi)07480-6361928012144283803937980-11480800057380-74767780-3977580-52587680-41699180111218004102210(ni−npi)1χ==∗410=5.125,8α=0.05,Ei=1npi80χ2(10−1)=16.9,220.95χ<χ0.95(9),F"H0,!20OQ#+M2.&QV

6、RR78%'M'MWSXYZ-T[]:U^V^_!R"Z^_I&QWF,fFÆ((F,F)X?YZU^(F,f)X?V^_(f,f)!R1`PW+-aU^V^_!RYMÆ1:2:1.b4JKc93MF>4OaZU^V^_!R235020p1=P{X?ZU^},p2=P{X?ZV^_},p3=P{X?Z!R},'111H0:p1=p10=,p2=p20=,p3=p30=424↔H1:Dpi=pi0.121212(23−93×)(50−93×)(20−93×)2424χ=++=0.72,11

7、193×93×93×4242228α=0.05,χ0.95(2)=5.991χ=0.72<χ0.95(2),.!)Z^_[%&QW(F,F),(F,f)((f,f)FÆ(dQV*>+M3.]^_`e6f"abcdMeC,7cgMni0123456≥72ni81617106210T:]^C,cgM#fghhP(α=0.05)5λˆ=X¯,U:MLE>)23>x¯=(0∗8+1∗16+···+6∗1)/60=22ie−2H0:ˆpi=P(X=i)=,i=0,1,···i!H04