某大学工程水文及水利计算课件水文统计原理

WuhanUniversityXPWuhanUniversityXPWuhanUniversityXP1.WuhanUniversityXP2.PxpF(x)Pxp)()(ppxFPxXP==≥xpWuhanUniversityXP3.WuhanUniversityXP4.„„WuhanUniversityXP.1.2.123WuhanUniversityXP.1.2.P(A)AkAn3.4.1046ABCDP(A)=4/10=0.4;P(B)=0.6;P(C)=0.0;P(D)=1.05.1001nkAP=)(WuhanUniversityXP.1.2.P(A)Anm3.nnA4.404020480.50801200060190.50160.524000120140.50055.nmAP=)(WuhanUniversityXP.1.A+BABA*BABABABABAB2.P(AB)=P(A)·P(BA)=P(B)·P(AB)P(AB)ABA3.P(A+B)=P(A)+P(B)-P(AB)ABABABWuhanUniversityXP.4.0.10.20.3ABC.C=A+BP(C)=P(A+B)=P(A)+P(B)-P(AB)=P(A)+P(B)-P(A)P(BA)=0.1+0.2-0.10.3=0.27P(A)P(BA)=P(B)P(AB)15.02.03.01.0P(B))ABP(A)P()BAP(=×==WuhanUniversityXP.1.A,B,C……2.WuhanUniversityXP3.1123456200WuhanUniversityXP4.Xx1,x2,……,xn5.WuhanUniversityXP.XxXxP(Xx)xP(Xx)xXFxF(x)=P(Xx)XxWuhanUniversityXP1Xx1,x2,…,xn…p1,p2,…,pn…XPi0∑Pi=1P(X=xi)=Pii=1,2,…XXX,,,,,,,,2121nnpppxxx∑≥=≥=xxiipxXPxF)()(WuhanUniversityXP20XxXxXxX()xxx∆+,)()()()()(xxFxFxxXPxXPxxXxP∆+−=∆+≥−≥=∆+≤≤xx+xP(Xx)P(Xx+x))()()(lim)('0xFxxFxxFxfx−=∆−∆+−=→∆WuhanUniversityXPx,f(x)F(x)∫∞=xdxxfxF)()(f(x)F(x)00xxf(x)F(x)xpxppF(xp)F(xp)WuhanUniversityXP.WuhanUniversityXP.„„;„WuhanUniversityXP.x1x2……,xn1956~1979475.9mm1070.5mm,∑=⋅⋅⋅⋅⋅⋅++==niinxnnxxxx1211WuhanUniversityXPkxk1k11121==⋅⋅⋅⋅⋅⋅++=∑=niinkkkknnk,xxkii=WuhanUniversityXPMe1/2Mof(x)x0Mo∫∞=eMdxxf21)(f(x)x1/20Me0)(==oMxdxxdfWuhanUniversityXP1/21/2Moxf(x)x0MoMef(x)x0MexWuhanUniversityXP.5101511019105~151~19WuhanUniversityXP()Dxxxσxσ4.087.35)(xx−2)(1∑−=xxnDixnxxi∑−=2)(σxxWuhanUniversityXP5101510995100010051000σ4.08,,,10,1000,WuhanUniversityXPCvCvkCv1=4.08/10=0.408;Cv2=4.08/1000=0.00408nxkCiV∑−==2)1(σWuhanUniversityXPCS3333)()(σσnxnxxxciiS∑∑−=−=x33)1(ViSnCkc∑−=WuhanUniversityXP„CS0„CS≠0CS0„CS0WuhanUniversityXP.XkE(Xk)Xkk=0k=1n),0,1,2,(k)(==kkXEvkv∑===niikikkpxXEv1)(∫∞∞−==dxxfxXEvkkk)()(1)(00==XEvxXEv==)(11vx=WuhanUniversityXPXE(X)kXkk=0k=1k=2[]{}n),0,1,2,(k)((=−=kkXEXEµ[]∑=−=niikikpXEx1)(µ[]∫∞∞−−=dxxfXExkk)()(µ10=µ212µσ=[]{}kXEXE)(−kµ01=µ22σµ=1212vxCvµσ==2323µµ=SCWuhanUniversityXP2122ννµ−=31123323ννννµ+−=WuhanUniversityXP.„„„()WuhanUniversityXP.„,WuhanUniversityXP10„N„P„LP-„KM„„LN2„LN3„IEVI„GEV„Weibull„Exp„PV„GambleWuhanUniversityXPPLPP1993“”PWuhanUniversityXPXX.eCs=0xxy()22221)(σπσxxexf−−=xσxxy−=2221)(xexf−=πf(x)x-+-3+3xWuhanUniversityXPx123xf(x)x-+-3+3%7.99)33(%4.95)22(%3.68)(=+−=+−=+−σσσσσσxxxpxxxpxxxpxxxxxxWuhanUniversityXPS“”P=50%xpWuhanUniversityXPPerson133P—a0()P—0)(10,)()()(0axeaxxfax≥−Γ=−−−βαααβf(x)x0a0WuhanUniversityXPa0CvCsCs0Cs=0P—Pxpxx)21(,2,402svsvsCCxaCCxC−===βαvssvCCCCxa20)21(0≥∴≥−=∵PxXPxFp=≥=)()(WuhanUniversityXPx01PCs∫∞+−−−−Γ=pxaxdxeaxP)(100)()(βαααβ[]∫∞+Φ−Φ−−Φ+ΦΓ=pdeP)(1)()(αααααααvCxxXxX−=−=Φσ24sC=α)1(pvpCxxΦ⋅+=WuhanUniversityXP=1000mmCv=0.5Cs=1.0P—P=1%xp2000mmPxCs=1.0P=1%=3.02x1%=(1+pCv)=1000(1+3.020.5)=2510(mm)x=2000Cs=1.0=2P=4.238%x25.0100010002000=×−=−=ΦvCxxXWuhanUniversityXPP—CvCsPpxpP,xp=1000mmCv=0.5Cs=1.0xxWuhanUniversityXP„„WuhanUniversityXP.WuhanUniversityXPn…21iP1=1nx1P2=2nx2……Pn=nn=1xnPi=inP(Xxi)xiWuhanUniversityXPWuhanUniversityXPpinninp100100%ipn=×WuhanUniversityXP%1001×+=nmp%1004.03.0×+−=nmp%1005.0×−=nmpWuhanUniversityXPxipiWuhanUniversityXPnp=10.1%0.01%WuhanUniversityXP.(X1,X2,……,Xn)Xnn11lim1=−∑=∞→ενknikinXnPl,1,2,k,1),,,(121=≈∑=nikilkXnθθθν()lkXXXnkk,,2,1,,,,21==∧∧θθWuhanUniversityXP.(x1,x2,……,xn)∑==niixnx11∑=−=niixnSx12)(1∑=−==niivknxSC12')1(1()()3'13313'1vniiniisnCknSxxC∑∑==−=−=WuhanUniversityXP.’E(’)=’,WuhanUniversityXP.n∑−−≈−−=issknCnnC33')1()3()2)(1(∑=−−==−=niivvknnnCC12')1(111=nivCn121WuhanUniversityXP.kkxxx,,,21x),,2,1(kixxxii⋅⋅⋅⋅⋅⋅=−=∆ix∆ix∆WuhanUniversityXP.,,68.3%95,99.7%xσxσxσxσxσxσ2xσ3WuhanUniversityXP.,ncvcscs,n100csnxσσ=csn24312+=σσσsvsvcccnCccvv24321222−++=σ)165231(642ccsscns++=σWuhanUniversityXP.„„„WuhanUniversityXP.cscs1984P—csP—csWuhanUniversityXP.f(x)cscs∫∫∫∞∞∞−−−=000)()(')()()(')()()(22aaasdxxfxxxdxxfxdxxfxxxCϕϕσϕσ∑∑∑===−−−=niininiisxxxxxxxC1112)(')()(')()(2ϕϕσϕσ)(xϕ)(xϕWuhanUniversityXP.„„CsCs)(xϕ1)(0=∫∞adxxϕ222)(21)(σσπϕxxex−−=GEcsσ4−=)()(1)()()(10iniaxxxndxxfxxxEϕϕ∑∫=∞−≈−=)()(1)()()(2120iniaxxxndxxfxxxGϕϕ∑∫=∞−≈−=WuhanUniversityXP.„cscsCv„cs„WuhanUniversityXP.„„WuhanUniversityXPpm=i(n+1)cscscvcvcspxpxppxWuhanUniversityXP.cvcscv=0.5,cs=1.0,50751003cvkcs=1.0cv=0k=1cvcskcv=0.1csWuhanUniversityXP.“”“”pT1P50Tpp1%T1002P50p80T5102102…pT1=pT−=11WuhanUniversityXP.2410pm=m(n+1)CvCv0.3,Cs3Cv0.9,pxppxpCsCv0.3,Cs2Cv0.6,pxp(=666.4,Cv=0.3,Cs=0.6)p=10%932mm4.66624/5.159931==∑=ixnx26.023592.11)1(2==−∑−=nkCiVWuhanUniversityXP.5.GrapherWuhanUniversityXP.pixiWuhanUniversityXP.OLS„Xnxi,,i=1,2,…,nxi,pi„cvcspixi,xMinxxCCxSniiisv→−=∑=12,,)(),,(WuhanUniversityXP.ABSWLSMinxxCCxSniiisv→−=∑=1,,),,(MinxxxCCxSniiiisv→−=∑=12,,,),,(WuhanUniversityXP.Genetic“”mmmmmWuhanUniversityXPSimplexSplendy1962NelderMead1965Enn+1nXEnf[X]f[X]f[X]Complexn2n+1‘’‘’WuhanUniversityXPRosenbrockRosenbrock1960Genetic(Rosenbrock)SimplexWuhanUniversityXP.OLSABSOLSOLSWLSOLSABSOLSABSWuhanUniversityXP.„„WuhanUniversityXP.,„(),,;„(),„,,,“”,,,WuhanUniversityXP.(,),,„,,;„,,,,,WuhanUniversityXP.(),i(pixi),,,i=0;,1;,i