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1 * ( ) ( ) 20
2 2 X f( ) (pdf: probability density function) F( ) X (cdf: cumulative distribution function) (2.1) X ( ) p ( ) W( ) 1 F( ) p p 1(p) W( p) ( p) X 1/T T ( ) T p T T T p 1 1/T p F( ) cdf N [F( )] (2.2) 1 1/ T N 1 (3.1) (3.2) (3.1) (3.2) (1) T 100,N 10 (3.2) 10% T Nª0.7T (2) 109 (3.2)
3 (3)T N N (3.1) e N N N 37% 63% (4) (3.1) (cdf) (3.1) cdf (3.1) F( ) 4. N :0 1 Weibull( ) ; =0 Hazen( ) ; =1/2 Gringorten( ) ; =0.44 Blom( ) ; =3/8 Cunnane( ) ; 2/5 Cunnane 12) pi (4.1) F( ) ( ) N
4 r r 5.2 X (pdf: probability density function)
5 r ( ) r ( ) 6 (2.1) pdf T T ( ) (1) (2.1) cdf ( ) cdf (2) 2 3 (3) L PWM
6 ( ) ( ) ( ) 6.1 (PWM) L 14),15) ( ) (bias) L (L Moments) PWM(Probability Weighted Moments) L PWM L (L linear combinations ) L 1 L E( ): N 2 L L PWM E( ): F(X): X (cdf) 0 E(X)( ) r PWM r F PWM (6.5) PWM
7 2 F ( ) ( ) 2 (r+ ) (r+ ) N (r+ ) (6,8) b0, b1 b2 b0 L (L Moments) PWM r L PWM PWM r (r=0,1,2, ) (6.6) (6.9) L PWM L PWM L 2/ 1 L (L CV) X>0 (pdf) 0< 2/ 1<1 3/ 2 L ( ) 3/ 2 <1
8 6.2 (N ) (pdf) (cdf) 2 (6.11) N(, 2 ) 0, 2 1 (0,1) (pdf) (cdf) (6.14) 1 17) (6.14) cdf p 1(p) p>0.5 (6.15) (6.16) graphic display (6,15) (6.16) PWM L 14) 18) PWM L (6.6) (6.9) 0 1 (6.17)
9 6.3 (LN3 ) Y X a (LN3 ) pdf cdf ( ) N(0,1) cdf (6.14) p ( ) Zp N(0,1) (6.16) 3 (6.23) (6.25) S
10 (6.28), LN3 7) 20) (6.30) (6.31) (6.29) PWM 18),21) ( ) N(0,1) cdf
11 (6.32) (6.34) PWM PWM <0.3 (6.20) 3 (LN3) 2 (LN2) LN2 (6.23) (6.25) (6.36) LN3 LN3 LN2 LN III (P3 ) III III 22),23) Y III (P3 ) P3 pdf >0 c (b): P3 >0 0<b<1 J b 1 b 1 P 3 P3 (i)c 0, 1 (6.38) 1 (6.39) c 0, 1 (ii) c 0 (6.38) 2
12 P3 (6.39) (5.6) (5.8) b<1( >2) P3 PWM 18),21) B(, ): B 1/3(, ): P3 PWM (6.42) (6.43) b 18),21) P3 cdf p (6.44) P3 ( ) (6.45) <0 (6.44) ( ) 1 (6.39) K 0 1 (6.47) (6.46) (6.48) P3
13 b (6.44) (6.44) Wilson-Hilferty( - ) :N(0,1) 0 (6.49) (6.50) (1 p) b 0.44 ( >3) (6.49) (6.50) III (LP3 ) P3 III (LP3 ) pdf >0 exp(c)< < <0 0< <exp(c) LP3 r ( ) ( ) ( ) LP3 cdf (6.44) LP3 LP3
14 (1) P3 (6.39) LP3 (6.57) Water Resources Council (6.39) <0 (2) PWM PWM (6.6) (6.9) (6.41) (6.43) PWM, 0, 1 2,, LP3 (6.57) (3) (6.52) r a,b,c (6.52) 1, 2 3 (6.59) B 6.1 (6.59) B Kite Leeyavanija
15 B < B< (c 0 c6) B B b c (6.60) (6.61) P3 ( ) (6.39)
16 Kp (6.57) (6.54) (6.55) Newton- Raphson( - ) a b (6.53) c 0 0 exp(c) 0 exp(c) LP3 ( ) >0 < pdf cdf c a (6.68)
17 p F( ) 2 L L ( ) a a 6.7 (GEV : Generalized Extreme Value ) Jenkinson A B 1 (GEV ) Natural Environment Research Council GEV GEV cdf >0 <0 c a =0 GEV pdf (6.72) f( ) GEV (6.72) p F( ) ( ) ( ) ( ) ( ) sign( ) k k 1/3 k 1/3 GEV 3
18 GEV r PWM( ) L GEV L (6.80) (6.81) (6.80) 1/2 k 1/ k a c L (6.78) (6.79)
19 6.8 (SQRT ET ) (cdf) a b pdf (6.83) (SQRT exponential-type distribution of maximum SQRT ET ) 2 cdf pdf SQRT-ET (6.84) N L b a a b (6.87) (6.85) b b (6.87) a a, b (6.85) L b a SQRT ET (6.83)
20 (6.89) tp 6.9 (pdf) pdf pdf r r 0 (6.90) r (6.92) (6.92) 1
21 (6.95) ar( ) 100(1 )% N(0,1) (1 /2) =0.05(95% ) =1.96 ar( ) ar( ) ar( ) (3.1) 7.2 SLSC(Standard Least-Squares Criterion: )
22 si: ( ) (7.2) SLSC 0.02 SLSC>0.03 (7.1) AIC( ) AIC (, ) pdf (7.5) MLL MLL (7.4) 2 1 AIC 7.3 (Resampling) N N (7.1) jackknife bootstrap (1)jackknife N ( ) (N 1) ( ) ( ) N ( ) ( ) (2) bootstrap N N M ) M
23 ( ) 8.2 z ( 1) ( ) =1 2
24 9. ( ) ( ) 2 ( ) 2 ( ) Box-Jenkins( ) = _1 (autoregressive-integrated-moving average, ARIMA) 9.1 (9.1) (autoregressiv movingaverage) ARMA (p,q) ARMA(p,q) 2 1 (autoregressive) (9.1) 1 3 AR(p) 1 (moving average) 2 3 MA(q) AR(p) AR 9.2 AR(p) p (9.1)
25 0 1 AR(1) 1 ( ) AR = 1 ) AR(1) t N(0,1) 9.3 ARMA(1,1) (9.1) ARMA(1,1) 1 =, 1 = ARMA(1,1) (9.7) (9.8) 1< <1 1< <1 AR(1) ARMA (1,1) AR(1) ARMA(1,1) ARMA(1,1) Hurst 10. (data generation) (Operational Hydrology)
26 10.1 AR(1) 1 p1 (9.5) ) 2 (1) (LN3) :3 (LN3) (1): ( ) 1 (1): 1 t:n(0,1) LN3 (1) (10.3) (1) (1) (10.1) (10.2) (1) ln( a) 1 (2) III (P3) (9.5) AR(1), : t 0 1 (10,4) -1 t 3 t t (7.5.52) Wilson Hilferty
27 t N(0,1) t P3 ( 2/ ) 10.2 AR(1) (9.5) AR(1) Thomas Fiering( ) Thomas Fiering 2 (1) (LN3) : LN3 ( 1) (, : (2) III (P3) Wilson Hilferty : 0 1 : :N(0,1)
28 10.3 Disaggregation( ) Thomas-Fiering 1 Disaggregation AR(1) ARMA(1,1) 1 LN3 N(0,1) (10.10) Disaggregation Z:(12 1) Y:(1 1) E:(12 1) A:(12 1) B:(12 12) A B S ZY (12x1) S YY S YY 1 S (12 12) BB T B LN3 (10.11) BB T B :LN3 (10.16) P3 E (10.16) 1 Disaggregation
29 10.4 AR(1) AR(1) 1 LN3 P3 2 LN3 N(0,1) Z t : ( 1) E t :( 1) A,B:( ) M 0 lag 0 M 1 lag 1 BB T Disaggregation (10.20) M 0 M 1 1,,,,No.233,pp23 31, ,,No.243,pp.33 46, Hoshi,K.and Q.A.Romano:Approximate skew of the sum of skewed and correlated variates, J. Hydrosci.and Hydrau.Eng.,Vol.3,No.1,pp.75 88, , 642,,59pp., : 11 (A ),A-3,A-4,A-5,A-6,1975, 6 :,, 26,,275PP, pp.31-35, No.178, pp.1-18, ( ),, 6,pp , ,,,,,No,369/II-5,pp , ,,No.4,pp , Cunnane,C. Unbiased plotting position-a review,j.hydrol.,no.37,pp ,1978.
30 13 Hirsch, R.M.,D.R.Helse1,T.A. Cohn and E.J.Gilroy: Statistical Analysis of Hydrologic Data, Chapter 17, Handbook of Hydrology, edited by D.J. Maidment,pp ,McGraw-Hil1,New York, Stedinger, J. R.,R. M.Vogel and E.Foufoula-Georgiou: Frequency Analysis of Extreme Events, Chapter 18,Handbook of Hydrology,edited by D.J. Maidment,pp ,McGraw-Hill,New York, Hosking,J. R.:L Moments:Analysis and estimation of distributions using linear combinations of order statistics,j. Royal Statistical Soc.,B,Vol.52,No.2,pp , Hosking,J. R. M., J. R. Wallis and E.F.Wood: Estimation of the generalized extreme-value distribution by the method of probability weighted moments, Technometrics,Vol.27,No.3,pp , Derenzo,S. E.: Approximations for hand calculators using small integer coefficients, Mathematics of Computation,Vol.31,No.137,pp , ,, III PWM,, No.393/II-9,PP , Bobee,B. and R.Robitaille: Correction of bias in the estimation of the coefficient of skewness, Water Resour. Res.,Vol.11,No.6,pp , Hoshi, K., J. R. Stedinger and S. J. Burges: Estimation of log-normal quantiles;monte Carlo results and first-order approximations, J. Hydrol.,No.71,pp.1 30, , : 3 PWM,,No.393/II-9,PP , Suzuki,E.:Hyper gamma distribution and its fitting to rainfall data,papers in Met.and Geo physics,vo1.15, No.1,PP.31 51, , :,,No.35, pp , Kirby, W.:Computer oriented Wilson Hilferty transformation that preserves the first three moments and the lower bound of the Pearson type 3 distribution,water Resour.Res.,Vol.8,No.5, pp , Hoshi,K. and S.J.Burges:Approximate estimation of the derivative of a standard gamma quantile for use in confidence interval estimates, J. Hydrol.,No.53,pp , Chowdhury,J. U. and J. R. Stedinger: Confidence intervals for design floods with estimated skew coefficent, Jour. Hydraul Eng.,Vol.117, No.7, pp , U.S. Water Resources Council: Guidelines for Detemining Flood Flow Frequency,Hydrol.Comm., Washington,D.C., Bul1.17A, Kite,G.W.:Frequency and Risk Analysis in Hydrology,Water Resour. Publication, Fort Collins, 224pp., Leeyavanija, U. :Parameter Estimates for Gamma Type Distributions by Quantile Method, Master Thesis,No.WA8-410,Asian Institute of Technology, Bangkok,Thailand,98pp , : 3, 34 (II), pp.7 8, Landwehr,J. M., N.C.Matalas and J. R. Wallis: Quantile estimation with more or less floodlike distributions,water Resour.Res.,Vol.16,No.3,pp , Jenkinson,A.F.:The frequency distribution of the annual maximum(or minimum) values of meteorological elements,quart. J.Roy. Meteor.Soc.,Vol.81,pp , Natural Environment Research Council: Flood Studies Report,Vol.I,Hydrological Studies,550pp., 1975.
31 34, : MEP,,No,335,pp.89-95, ,, :,,No.375/II-6,pp.89 98, ,,,No,393/ II-9,pp , :, 10B,pp.41-51, , :, 25,pp, , , : (1) (4),,(1); 13 B,pp ,1970,(2) (4); 14 B,pp.43-85, , :,,No.381/II-7,PP , ,,No.369/ 5 pp , Salas,J. D.: Analysis and Modeling of Hydrologic Time Series,Chapter 19, Handbook of Hydrology, edited by D. J. Maidment,pp ,McGraw-Hill, New York, 1993, 43 Box,G,E. P. and G. M. Jenkins: Time Series Analysis; Forecasting and Control, Holden Day, 553pp., :Box&Jenkins,,No.261,PP.59 66, , :,,254pp., O Connell, P. E.: Stochastic Modelling of Long Term Persistence in Streamflow Sequences, Ph.D. Thesis, Imperial College,Univ. of London,284pp., Lettenmaier, D. P. and S.J. Burges: Operational assesment of hydrologic models of long term persistence, Water Resour. Res.,Vol.13,No.1,pp , , J. W. Delleur: Hurst ARMA, 25,,pp , Hoshi, K., S. J. Burges and I. Yamaoka: Reservoir design capacities for various seasonal operational hydrology models, Proc. Of JSCE,. No.273,pp , Valencia, D. R. and J. C. Schaake:Disaggregation processes in stochastic hydrology, Water Resour. Res.,Vol.9, No.3,pp , :, 63, 2,pp.82-84, Grygier,J. C. and J. R. Stedinger: Condensed disaggregetion procedures and conservation corrections for stochastic hydrology, Water Resour.Res., Vol. 24,No.10, pp , ,, :,,No.203,PP.1 11,1972.
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