DISTRIBUCION GAMMA DE 2 PARAMETROS

PRUEBA DE SMIRNOV-KOLMOGOROV

m F(Z)

1 0 0.0455 -0.52 0.30153 0.25612 0.072 0.0909 -0.52 0.30153 0.21063 0.121 0.1364 -0.51 0.30503 0.16874 0.203 0.1818 -0.50 0.30954 0.12775 0.261 0.2273 -0.49 0.31207 0.08486 0.268 0.2727 -0.49 0.31207 0.03937 0.28 0.3182 -0.49 0.31207 -0.00618 0.355 0.3636 -0.48 0.31918 -0.04459 0.915 0.4091 -0.42 0.33724 -0.0719

10 1.083 0.4545 -0.41 0.3409 -0.113611 2.035 0.5000 -0.30 0.38209 -0.117912 2.25 0.5455 -0.28 0.38974 -0.155713 2.348 0.5909 -0.27 0.39358 -0.197314 3.448 0.6364 -0.15 0.44038 -0.196015 4.692 0.6818 -0.01 0.49202 -0.189816 5.235 0.7273 0.05 0.51994 -0.207317 6.848 0.7727 0.22 0.58706 -0.185718 7.768 0.8182 0.32 0.62552 -0.192719 9.6 0.8636 0.52 0.69497 -0.168720 11.113 0.9091 0.69 0.7549 -0.154221 42.133 0.9545 4.06 0.99997 0.0454

m= numero de orden n+1= 22n= numero de datos

= 4.8109

= 9.19

F(z) TABLA DE DISTRIBUCION NORMAL

Q=X m3/s

P(X) m3/s

Δ IF(Z)-P(X)I

𝑍=(𝑋−𝑋 ̅�)/𝑆

aa2

-4.8109 23.14-4.7389 22.46-4.6899 21.99-4.6079 21.23-4.5499 20.70-4.5429 20.64-4.5309 20.53-4.4559 19.85-3.8959 15.18-3.7279 13.90-2.7759 7.71-2.5609 6.56-2.4629 6.07-1.3629 1.86-0.1189 0.010.4241 0.182.0371 4.152.9571 8.744.7891 22.946.3021 39.72

37.3221 1392.94

n-1 20

Δ = Max I F(Z)-P(X)I = 0.2561

hallamos Δ0 critico : tabla

(𝑋−𝑋 ̅�)/

DISTRIBUCION GAMMA

Q Max. Anuales A Ln(A)

0.355 -1.035637490.121 -2.111964730.203 -1.59454930.28 -1.27296568

42.133 3.740831284.692 1.545858932.25 0.81093022

3.448 1.237794359.6 2.2617631

0.915 -0.088831210 0

1.083 0.079734972.035 0.710495820.072 -2.631089166.848 1.923956647.768 2.050012735.235 1.655366840.268 -1.3167683

11.113 2.408115590.261 -1.343234872.348 0.8535639

n= 21

calculamos parametros de distribucion Gamma

(𝐿𝑛𝑋) ̅�=1/𝑛 ∑▒𝐿𝑛𝑖

ENTONCES

0.05n= 21

Δ0= 0.28724

Δ < Δ00.2561 0.28724

cumple para realizar con distribucion gamma ENCONTRAMOS

=

tomando α=

DISTRIBUCION GAMMA

= 4.81 = 1.57

= 0.38

calculamos parametros de distribucion Gamma

= 1.20

(𝐿𝑛𝑋) ̅�=1/𝑛 ∑▒𝐿𝑛𝑖

= 0.5253

9.1583

HALLAMOS CALCULO DE DISEÑOS PARA LOS SIGUIENTES AÑOS DE RETORNO

T F(X) 1-F(X)2 0.5 0.55 0.8 0.2

10 0.9 0.125 0.96 0.0450 0.98 0.02

100 0.99 0.01200 0.995 0.005

1000 0.999 0.001

= 1.0506V = 1

EN TABLA TENEMOS los siguientes caudalesV=1 1-F(x)=0.5 X2= 0.3 V=1 1-F(x)=0.2

q= 1.374 m3/s q= 7.327

V=1 1-F(x)=0.04 X2= 4.2 V=1 1-F(x)=0.02

q= 19.232 m3/s q= 24.727

V=1 1-F(x)=0.005 X2= 7.9 V=1 1-F(x)=0.001

q= 36.175 m3/s q= 48.081

X2= 1.6 V=1 1-F(x)=0.1 X2= 2.6

m3/s q= 11.906 m3/s

X2= 5.4 V=1 1-F(x)=0.01 X2= 5.8

m3/s q= 26.559 m3/s

X2= 10.5

m3/s

𝑄=(𝐶.𝐼.𝐴)/3.6