Método de Distribución
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VALORES DE DESCARGA UTILES PARA CALCULOS CAUDALES MEDIOS ANUALES DE RIO SANTA (m3/seg.) caudales 30 valores caudales 30 valores ordenados de menor a mayor m Q m Q 1 95.05 1 95.05 2 105.21 2 101.76 3 108.75 3 105.21 4 146.08 4 105.81 5 158.48 5 106.40 6 177.00 6 108.75 7 193.78 7 110.77 8 212.48 8 114.31 9 105.81 9 116.69 10 110.77 10 119.52 11 134.10 11 128.15 12 153.64 12 134.10 13 182.53 13 146.08 14 193.09 14 153.64 15 106.40 15 153.97 16 114.31 16 154.80 17 153.97 17 158.48 18 183.11 18 169.04 19 197.58 19 169.18 20 239.07 20 177.00 21 116.69 21 182.53 22 154.80 22 183.11 23 169.18 23 183.49 24 183.49 24 184.98 25 101.76 25 193.09 26 119.52 26 193.78 27 128.15 27 197.58 28 169.04 28 212.48 29 184.98 29 239.07 30 266.54 30 266.54 m Q = x Ҳ - X (Ҳ - X)2 P(X) = m/N+1 Z=(Ҳ - X)/σ F(Z) (Z) - P(X) F(Z) - P(X) | 1 95.05 -60.46 3655.6454 0.0323 -1.38668 0.08277 0.05051 0.05051 2 101.76 -53.75 2889.2703 0.0645 -1.23279 0.10883 0.04431 0.04431 3 105.21 -50.30 2530.2845 0.0968 -1.15367 0.12432 0.02754 0.02754 4 105.81 -49.70 2470.2822 0.1290 -1.13990 0.12716 -0.00187 0.00187 5 106.40 -49.11 2411.9820 0.1613 -1.12637 0.13000 -0.03129 0.03129 6 108.75 -46.76 2186.6784 0.1935 -1.07248 0.14175 -0.05180 0.05180 7 110.77 -44.74 2001.8406 0.2258 -1.02615 0.15241 -0.07340 0.07340 8 114.31 -41.20 1697.5993 0.2581 -0.94496 0.17234 -0.08572 0.08572 9 116.69 -38.82 1507.1425 0.2903 -0.89037 0.18663 -0.10369 0.10369 10 119.52 -35.99 1295.4193 0.3226 -0.82547 0.20455 -0.11803 0.11803 11 128.15 -27.36 748.6754 0.3548 -0.62754 0.26515 -0.08969 0.08969 12 134.10 -21.41 458.4709 0.3871 -0.49108 0.31169 -0.07541 0.07541 13 146.08 -9.43 88.9614 0.4194 -0.21632 0.41437 -0.00499 0.00499 14 153.64 -1.87 3.5041 0.4516 -0.04293 0.48288 0.03126 0.03126 15 153.97 -1.54 2.3776 0.4839 -0.03536 0.48589 0.00202 0.00202 16 154.80 -0.71 0.5068 0.5161 -0.01633 0.49349 -0.02264 0.02264 17 158.48 2.97 8.8094 0.5484 0.06807 0.52714 -0.02125 0.02125 18 169.04 13.53 183.0086 0.5806 0.31026 0.62182 0.04117 0.04117 19 169.18 13.67 186.8160 0.6129 0.31347 0.62304 0.01014 0.01014 20 177.00 21.49 461.7370 0.6452 0.49282 0.68893 0.04377 0.04377 21 182.53 27.02 729.9759 0.6774 0.61965 0.73226 0.05484 0.05484 22 183.11 27.60 761.6533 0.7097 0.63296 0.73662 0.02694 0.02694 23 183.49 27.98 782.7722 0.7419 0.64167 0.73946 -0.00248 0.00248 24 184.98 29.47 868.3670 0.7742 0.67584 0.75043 -0.02376 0.02376 25 193.09 37.58 1411.9608 0.8065 0.86180 0.80560 -0.00085 0.00085 26 193.78 38.27 1464.4449 0.8387 0.87767 0.80994 -0.02877 0.02877 27 197.58 42.07 1769.7222 0.8710 0.96482 0.83268 -0.03828 0.03828 28 212.48 56.97 3245.3606 0.9032 1.30655 0.90432 0.00109 0.00109 29 239.07 83.56 6981.9505 0.9355 1.91639 0.97234 0.03686 0.03686 30 266.54 111.03 12327.2316 0.9677 2.54641 0.99456 0.02682 0.02682 SUMATORIA 4665.358 55132.4508 155.512 Δ= 0.11803 0.24 43.60182 N= 30 α= 0.05 PROMEDIO x ΔS-K = VARIANZA σ
description
excel de distribuciones
Transcript of Método de Distribución
VALORES DE DESCARGA UTILES PARA CALCULOS
CAUDALES MEDIOS ANUALES DE RIO SANTA (m3/seg.)
caudales 30 valores caudales 30 valores ordenados de menor a mayor
m Q m Q1 95.05 1 95.052 105.21 2 101.763 108.75 3 105.214 146.08 4 105.815 158.48 5 106.406 177.00 6 108.757 193.78 7 110.778 212.48 8 114.319 105.81 9 116.69
10 110.77 10 119.5211 134.10 11 128.1512 153.64 12 134.1013 182.53 13 146.0814 193.09 14 153.6415 106.40 15 153.9716 114.31 16 154.8017 153.97 17 158.4818 183.11 18 169.0419 197.58 19 169.1820 239.07 20 177.0021 116.69 21 182.5322 154.80 22 183.1123 169.18 23 183.4924 183.49 24 184.9825 101.76 25 193.0926 119.52 26 193.7827 128.15 27 197.5828 169.04 28 212.4829 184.98 29 239.0730 266.54 30 266.54
m Q = x Ҳ - X (Ҳ - X)2 P(X) = m/N+1 Z=(Ҳ - X)/σ F(Z) F(Z) - P(X) |F(Z) - P(X) |1 95.05 -60.46 3655.6454 0.0323 -1.38668 0.08277 0.05051 0.050512 101.76 -53.75 2889.2703 0.0645 -1.23279 0.10883 0.04431 0.044313 105.21 -50.30 2530.2845 0.0968 -1.15367 0.12432 0.02754 0.027544 105.81 -49.70 2470.2822 0.1290 -1.13990 0.12716 -0.00187 0.001875 106.40 -49.11 2411.9820 0.1613 -1.12637 0.13000 -0.03129 0.031296 108.75 -46.76 2186.6784 0.1935 -1.07248 0.14175 -0.05180 0.051807 110.77 -44.74 2001.8406 0.2258 -1.02615 0.15241 -0.07340 0.073408 114.31 -41.20 1697.5993 0.2581 -0.94496 0.17234 -0.08572 0.085729 116.69 -38.82 1507.1425 0.2903 -0.89037 0.18663 -0.10369 0.10369
10 119.52 -35.99 1295.4193 0.3226 -0.82547 0.20455 -0.11803 0.1180311 128.15 -27.36 748.6754 0.3548 -0.62754 0.26515 -0.08969 0.0896912 134.10 -21.41 458.4709 0.3871 -0.49108 0.31169 -0.07541 0.0754113 146.08 -9.43 88.9614 0.4194 -0.21632 0.41437 -0.00499 0.0049914 153.64 -1.87 3.5041 0.4516 -0.04293 0.48288 0.03126 0.0312615 153.97 -1.54 2.3776 0.4839 -0.03536 0.48589 0.00202 0.0020216 154.80 -0.71 0.5068 0.5161 -0.01633 0.49349 -0.02264 0.0226417 158.48 2.97 8.8094 0.5484 0.06807 0.52714 -0.02125 0.0212518 169.04 13.53 183.0086 0.5806 0.31026 0.62182 0.04117 0.0411719 169.18 13.67 186.8160 0.6129 0.31347 0.62304 0.01014 0.0101420 177.00 21.49 461.7370 0.6452 0.49282 0.68893 0.04377 0.0437721 182.53 27.02 729.9759 0.6774 0.61965 0.73226 0.05484 0.0548422 183.11 27.60 761.6533 0.7097 0.63296 0.73662 0.02694 0.0269423 183.49 27.98 782.7722 0.7419 0.64167 0.73946 -0.00248 0.0024824 184.98 29.47 868.3670 0.7742 0.67584 0.75043 -0.02376 0.0237625 193.09 37.58 1411.9608 0.8065 0.86180 0.80560 -0.00085 0.0008526 193.78 38.27 1464.4449 0.8387 0.87767 0.80994 -0.02877 0.0287727 197.58 42.07 1769.7222 0.8710 0.96482 0.83268 -0.03828 0.0382828 212.48 56.97 3245.3606 0.9032 1.30655 0.90432 0.00109 0.0010929 239.07 83.56 6981.9505 0.9355 1.91639 0.97234 0.03686 0.0368630 266.54 111.03 12327.2316 0.9677 2.54641 0.99456 0.02682 0.02682
SUMATORIA 4665.358 55132.4508155.512 Δ= 0.11803 0.24
43.60182 N= 30 α= 0.05PROMEDIO x ΔS-K =
VARIANZA σ
VALORES DE DESCARGA UTILES PARA CALCULOS
CAUDALES MEDIOS ANUALES DE LAMBAYEQUE (m3/seg.)
ESTACION : NIEPOS ALTITUD: 2464.3 m.s.n.m
m AÑOS Q m Q1 1999 37.5 1 17.202 2000 52.6 2 26.503 2001 52.4 3 33.504 2002 68.9 4 34.705 2003 34.7 5 37.506 2004 17.2 6 42.207 2005 55.8 7 47.908 2006 85.9 8 52.409 2007 26.5 9 52.60
10 2008 89.7 10 55.8011 2009 65.8 11 65.8012 2010 119.6 12 65.9013 2011 47.9 13 68.9014 2012 65.9 14 85.9015 2013 33.5 15 89.7016 2014 42.2 16 119.60
N15 0.3416 0.3320 0.29
m Q = x Ҳ - X (Ҳ - X)2 P(X) = m/N+1 Z=(Ҳ - X)/σ F(Z) F(Z) - P(X) |F(Z) - P(X) |1 37.5 -18.51 342.4813 0.0556 -0.97754 0.16415 0.10860 0.108602 52.6 -3.41 11.6025 0.1111 -0.17993 0.42861 0.31749 0.317493 52.4 -3.61 13.0050 0.1667 -0.19049 0.42446 0.25780 0.257804 68.9 12.89 166.2488 0.2222 0.68108 0.75209 0.52987 0.529875 34.7 -21.31 453.9563 0.2778 -1.12544 0.13020 -0.14758 0.147586 17.2 -38.81 1505.9250 0.3333 -2.04983 0.02019 -0.31314 0.313147 55.8 -0.21 0.0425 0.3889 -0.01089 0.49565 0.10676 0.106768 85.9 29.89 893.6363 0.4444 1.57905 0.94284 0.49839 0.498399 26.5 -29.51 870.6188 0.5000 -1.55858 0.05955 -0.44045 0.44045
10 89.7 33.69 1135.2688 0.5556 1.77978 0.96244 0.40689 0.4068911 65.8 9.79 95.9175 0.6111 0.51733 0.69754 0.08642 0.0864212 119.6 63.59 4044.1650 0.6667 3.35916 0.99961 0.33294 0.3329413 47.9 -8.11 65.7113 0.7222 -0.42819 0.33426 -0.38797 0.3879714 65.9 9.89 97.8863 0.7778 0.52261 0.69938 -0.07840 0.0784015 33.5 -22.51 506.5313 0.8333 -1.18883 0.11725 -0.71608 0.7160816 42.2 -13.81 190.6125 0.8889 -0.72928 0.23292 -0.65597 0.65597
SUMATORIA 896.100 10393.609456.006 Δmax= 0.71608 0.33
18.93146 N= 17 α= 0.05
α = 0.05
PROMEDIO x ΔS-K =
VARIANZA σ
3. . ANALISIS DE CONFIABILIDAD: "DISTRIBUCION GUMBELL”
m AÑOS Q1 1999 37.5
2 2000 52.6
3 2001 52.4
4 2002 68.9
5 2003 34.7
6 2004 17.2
7 2005 55.8
8 2006 85.9
9 2007 26.5
10 2008 89.7
11 2009 65.8
12 2010 119.6
13 2011 47.9
14 2012 65.9
15 2013 33.5
16 2014 42.2
m Q = x P(X) = m/N+1
1 17.20 -38.81 1505.9250 44.5370 19.8723 0.05562 26.50 -29.51 870.6188 44.5370 19.8723 0.11113 33.50 -22.51 506.5313 44.5370 19.8723 0.16674 34.70 -21.31 453.9563 44.5370 19.8723 0.22225 37.50 -18.51 342.4813 44.5370 19.8723 0.27786 42.20 -13.81 190.6125 44.5370 19.8723 0.33337 47.90 -8.11 65.7113 44.5370 19.8723 0.38898 52.40 -3.61 13.0050 44.5370 19.8723 0.44449 52.60 -3.41 11.6025 44.5370 19.8723 0.5000
10 55.80 -0.21 0.0425 44.5370 19.8723 0.555611 65.80 9.79 95.9175 44.5370 19.8723 0.611112 65.90 9.89 97.8863 44.5370 19.8723 0.666713 68.90 12.89 166.2488 44.5370 19.8723 0.722214 85.90 29.89 893.6363 44.5370 19.8723 0.777815 89.70 33.69 1135.2688 44.5370 19.8723 0.833316 119.60 63.59 4044.1650 44.5370 19.8723 0.8889
SUMATORIA 896.100 10393.609456.006
25.487
ESTADISTICOANALISIS DE CONFIABILIDAD
Ҳ - X (Ҳ - X)2 u= X - 0.45S
PROMEDIO x VARIANZA σ=S
𝜶= (√𝟔)/𝝅*S
15 0.34
16 0.3320 0.29
TIEMPOS DE RETORNO
ΔS-K= 0.32
(𝟏.𝟑𝟔)/√𝐍
3. . ANALISIS DE CONFIABILIDAD: "DISTRIBUCION GUMBELL”
m Q1 17.202 26.503 33.504 34.705 37.506 42.207 47.908 52.409 52.60
10 55.8011 65.8012 65.9013 68.9014 85.9015 89.7016 119.60
F(Y) - P(X) |F(Z) - P(X) |
-1.37563 0.01911 -0.03645 0.03645-0.90764 0.08387 -0.02724 0.02724-0.55539 0.17506 0.00839 0.00839-0.49501 0.19388 -0.02834 0.02834-0.35411 0.24053 -0.03725 0.03725-0.11760 0.32472 -0.00861 0.008610.16923 0.42985 0.04096 0.040960.39568 0.51006 0.06562 0.065620.40574 0.51351 0.01351 0.013510.56677 0.56702 0.01147 0.011471.06998 0.70963 0.09852 0.098521.07501 0.71085 0.04418 0.044181.22598 0.74567 0.02345 0.023452.08144 0.88272 0.10494 0.104942.27266 0.90209 0.06876 0.068763.77726 0.97737 0.08849 0.08849
Δmax= 0.10494 0.32N= 17 α= 0.05
ESTADISTICO ANALISIS DE CONFIABILIDAD CALCULADOS-K CRITICO |F(Z) - P(X)|max.
Y=(X - u)/α
ΔS-K =
F(Y) = 𝒆^( −〖 𝒆〗^(−𝒚) )
0.10494COMPARACOION
0.32984845 LA INFORMACION ES CONFIABLE
|F(Z) - P(X)|max. < ΔS-K
(𝟏.𝟑𝟔)/√𝐍
ANALISIS DE CONFIABILIDAD: "DISTRIBUCION LOG. NORMAL DE DOS PARAMETROS ”
m AÑOS Q1 1999 37.5
2 2000 52.6
3 2001 52.4
4 2002 68.9
5 2003 34.7
6 2004 17.2
7 2005 55.8
8 2006 85.9
9 2007 26.5
10 2008 89.7
11 2009 65.8
12 2010 119.6
13 2011 47.9
14 2012 65.9
15 2013 33.5
16 2014 42.2
m Q = x ln(x)
1 17.20 -38.81 1505.9250 2.8449 0.4551 3.9314 0.18822 26.50 -29.51 870.6188 3.2771 0.4551 3.9314 0.18823 33.50 -22.51 506.5313 3.5115 0.4551 3.9314 0.18824 34.70 -21.31 453.9563 3.5467 0.4551 3.9314 0.18825 37.50 -18.51 342.4813 3.6243 0.4551 3.9314 0.18826 42.20 -13.81 190.6125 3.7424 0.4551 3.9314 0.18827 47.90 -8.11 65.7113 3.8691 0.4551 3.9314 0.18828 52.40 -3.61 13.0050 3.9589 0.4551 3.9314 0.18829 52.60 -3.41 11.6025 3.9627 0.4551 3.9314 0.1882
10 55.80 -0.21 0.0425 4.0218 0.4551 3.9314 0.188211 65.80 9.79 95.9175 4.1866 0.4551 3.9314 0.188212 65.90 9.89 97.8863 4.1881 0.4551 3.9314 0.188213 68.90 12.89 166.2488 4.2327 0.4551 3.9314 0.188214 85.90 29.89 893.6363 4.4532 0.4551 3.9314 0.188215 89.70 33.69 1135.2688 4.4965 0.4551 3.9314 0.188216 119.60 63.59 4044.1650 4.7842 0.4551 3.9314 0.1882
SUMAT. 896.100 10393.609456.006 σy = 0.43384
25.487
ESTADISTICOANALISIS DE CONFIABILIDAD
15
1620
Ҳ - X (Ҳ - X)2 Cv = S/X Uy=1/2*ln(x^2/1+Cv^2) σ^2=ln(1+Cv^2)
PROM. x VARIANZA S
ΔS-K= 0.32
ANALISIS DE CONFIABILIDAD: "DISTRIBUCION LOG. NORMAL DE DOS PARAMETROS ”
m Q1 17.202 26.503 33.504 34.705 37.506 42.207 47.908 52.409 52.60
10 55.8011 65.8012 65.9013 68.9014 85.9015 89.7016 119.60
P(X) = m/N+1 F(Z) F(Y) - P(X) |F(Z) - P(X)|
0.0556 -2.50425 0.06393 0.00838 0.008380.1111 -1.50795 0.12350 0.01238 0.012380.1667 -0.96766 0.18861 0.02194 0.021940.2222 -0.88653 0.20159 -0.02063 0.020630.2778 -0.70766 0.23389 -0.04389 0.043890.3333 -0.43549 0.29402 -0.03932 0.039320.3889 -0.14346 0.37522 -0.01367 0.013670.4444 0.06351 0.44374 -0.00070 0.000700.5000 0.07229 0.44684 -0.05316 0.053160.5556 0.20842 0.49677 -0.05878 0.058780.6111 0.58838 0.64961 0.03850 0.038500.6667 0.59189 0.65106 -0.01561 0.015610.7222 0.69450 0.69353 -0.02869 0.028690.7778 1.20281 0.87958 0.10180 0.101800.8333 1.30259 0.90691 0.07358 0.073580.8889 1.96569 0.99370 0.10482 0.10482
Δmax= 0.10482 0.32N= 17 α= 0.05
ESTADISTICO ANALISIS DE CONFIABILIDAD CALCULADOANALISIS DE CONFIABILIDAD S-K CRITICO |F(Z) - P(X)|max.
0.34 0.104820.33 COMPARACOION0.29
Z=(ln(x) - Uy)/σy
ΔS-K =
|F(Z) - P(X)|max. < ΔS-K
(𝟏.𝟑𝟔)/√𝐍
0.329848450049413 LA INFORMACION ES CONFIABLE= 0.32
