af max - pruebas de ajuste
DESCRIPTION
Análisis de frecuencia para estimar caudales máximosTRANSCRIPT
Min 0 Max 10000
LINEAS PRINCIPALES LINEAS SECUNDARIAS
Tr P(x) Z Normal Z Gumbel Rango Tr
1.01 0.9900990 -2.330 -1.642 0.0 1.021.01 0.9900990 -2.330 -1.642 10000 1.02
1.1 0.9090909 -1.335 -1.132 0 1.031.1 0.9090909 -1.335 -1.132 10000 1.03
1.5 0.6666667 -0.431 -0.523 0 1.041.5 0.6666667 -0.431 -0.523 10000 1.04
2.33 0.4291845 0.178 0.001 0 1.052.33 0.4291845 0.178 0.001 10000 1.05
5 0.2000000 0.842 0.719 0 1.065 0.2000000 0.842 0.719 10000 1.06
10 0.1000000 1.282 1.305 0 1.0710 0.1000000 1.282 1.305 10000 1.07
25 0.0400000 1.751 2.044 0 1.0825 0.0400000 1.751 2.044 10000 1.08
50 0.0200000 2.054 2.592 0 1.0950 0.0200000 2.054 2.592 10000 1.09
100 0.0100000 2.326 3.137 0 1.2100 0.0100000 2.326 3.137 10000 1.2
200 0.0050000 2.576 3.679 0 1.3200 0.0050000 2.576 3.679 10000 1.3
500 0.0020000 2.878 4.395 0 1.4500 0.0020000 2.878 4.395 10000 1.4
1000 0.0010000 3.090 4.936 0 1.61000 0.0010000 3.090 4.936 10000 1.6
10000 0.0001000 3.719 6.731 0 1.710000 0.0001000 3.719 6.731 10000 1.7
100000 0.0000100 4.265 8.527 0 1.8100000 0.0000100 4.265 8.527 10000 1.8
1000000 0.0000010 4.753 10.322 0 1.9
1000000 0.0000010 4.753 10.322 10000 1.9
22
33
44
66
77
88
99
1515
2020
3030
3535
4040
4545
6060
7070
80
80
9090
125125
150150
175175
300300
400400
625625
750750
875875
25002500
50005000
75007500
2500025000
5000050000
7500075000
250000
LINEAS SECUNDARIAS
P(x) Z Normal Z Gumbel Rango
0.9803922 -2.062 -1.518 00.9803922 -2.062 -1.518 10000
0.9708738 -1.894 -1.435 00.9708738 -1.894 -1.435 10000
0.9615385 -1.769 -1.371 00.9615385 -1.769 -1.371 10000
0.9523810 -1.668 -1.318 00.9523810 -1.668 -1.318 10000
0.9433962 -1.584 -1.273 00.9433962 -1.584 -1.273 10000
0.9345794 -1.511 -1.232 00.9345794 -1.511 -1.232 10000
0.9259259 -1.446 -1.196 00.9259259 -1.446 -1.196 10000
0.9174312 -1.388 -1.163 00.9174312 -1.388 -1.163 10000
0.8333333 -0.967 -0.905 00.8333333 -0.967 -0.905 10000
0.7692308 -0.736 -0.748 00.7692308 -0.736 -0.748 10000
0.7142857 -0.566 -0.626 00.7142857 -0.566 -0.626 10000
0.6250000 -0.319 -0.435 00.6250000 -0.319 -0.435 10000
0.5882353 -0.223 -0.357 00.5882353 -0.223 -0.357 10000
0.5555556 -0.140 -0.287 00.5555556 -0.140 -0.287 10000
0.5263158 -0.066 -0.223 0
0.5263158 -0.066 -0.223 10000
0.5000000 0.000 -0.164 00.5000000 0.000 -0.164 10000
0.3333333 0.431 0.254 00.3333333 0.431 0.254 10000
0.2500000 0.674 0.521 00.2500000 0.674 0.521 10000
0.1666667 0.967 0.877 00.1666667 0.967 0.877 10000
0.1428571 1.068 1.008 00.1428571 1.068 1.008 10000
0.1250000 1.150 1.120 00.1250000 1.150 1.120 10000
0.1111111 1.221 1.218 00.1111111 1.221 1.218 10000
0.0666667 1.501 1.635 00.0666667 1.501 1.635 10000
0.0500000 1.645 1.866 00.0500000 1.645 1.866 10000
0.0333333 1.834 2.189 00.0333333 1.834 2.189 10000
0.0285714 1.902 2.311 00.0285714 1.902 2.311 10000
0.0250000 1.960 2.416 00.0250000 1.960 2.416 10000
0.0222222 2.010 2.509 00.0222222 2.010 2.509 10000
0.0166667 2.128 2.736 00.0166667 2.128 2.736 10000
0.0142857 2.189 2.857 00.0142857 2.189 2.857 10000
0.0125000 2.241 2.962 0
0.0125000 2.241 2.962 10000
0.0111111 2.287 3.054 00.0111111 2.287 3.054 10000
0.0080000 2.409 3.311 00.0080000 2.409 3.311 10000
0.0066667 2.475 3.454 00.0066667 2.475 3.454 10000
0.0057143 2.529 3.575 00.0057143 2.529 3.575 10000
0.0033333 2.713 3.996 00.0033333 2.713 3.996 10000
0.0025000 2.807 4.221 00.0025000 2.807 4.221 10000
0.0016000 2.948 4.569 00.0016000 2.948 4.569 10000
0.0013333 3.004 4.711 00.0013333 3.004 4.711 10000
0.0011429 3.050 4.831 00.0011429 3.050 4.831 10000
0.0004000 3.353 5.650 00.0004000 3.353 5.650 10000
0.0002000 3.540 6.191 00.0002000 3.540 6.191 10000
0.0001333 3.646 6.507 00.0001333 3.646 6.507 10000
0.0000400 3.944 7.446 00.0000400 3.944 7.446 10000
0.0000200 4.107 7.986 00.0000200 4.107 7.986 10000
0.0000133 4.200 8.302 00.0000133 4.200 8.302 10000
0.0000040 4.465 9.241 0
0.0000040 4.465 9.241 10000
0.0000020 4.611 9.781 00.0000020 4.611 9.781 10000
0.0000013 4.695 10.098 00.0000013 4.695 10.098 10000
ANÁLISIS DE FRECUENCIAS MÁXIMOS
ESTACIÓN: La Joya
Año Tr Z Normal Z Gumbel1981 1.41 0.710 -0.212 -0.552 -0.6161982 1.19 0.839 -0.601 -0.989 -0.9191983 1.24 0.806 -0.496 -0.865 -0.8371984 1.55 0.645 -0.035 -0.372 -0.4781985 1.15 0.871 -0.717 -1.131 -1.0091986 2.21 0.452 0.510 0.122 -0.0531987 1.72 0.581 0.140 -0.204 -0.3411988 1.41 0.710 -0.212 -0.552 -0.6161989 2.38 0.419 0.610 0.204 0.0251990 2.58 0.387 0.714 0.287 0.1071991 1.11 0.903 -0.848 -1.300 -1.1111992 1.07 0.935 -1.008 -1.518 -1.2361993 1.48 0.677 -0.123 -0.460 -0.5461994 1.63 0.613 0.052 -0.287 -0.4091995 3.44 0.290 1.070 0.552 0.3841996 1.29 0.774 -0.397 -0.753 -0.7601997 1.03 0.968 -1.234 -1.849 -1.4121998 1.82 0.548 0.230 -0.122 -0.2711999 7.75 0.129 1.979 1.131 1.0932000 7.75 0.129 1.979 1.131 1.0932001 4.43 0.226 1.363 0.753 0.6132002 2.07 0.484 0.413 0.040 -0.1282004 2.82 0.355 0.825 0.372 0.1932005 3.10 0.323 0.943 0.460 0.2852006 3.88 0.258 1.209 0.649 0.4932007 5.17 0.194 1.537 0.865 0.7482008 10.33 0.097 2.285 1.300 1.3322009 31.00 0.032 3.418 1.849 2.2152010 15.50 0.065 2.708 1.518 1.6612011 1.94 0.516 0.320 -0.040 -0.200
n 300.5471.139
Cs 0.691
P(X>xTR) YTR (Gumbel)
m s
Ajuste a distribucion Gumbel (ó Tipo I de valores extremos)
Factor de frecuencia acorde con el numero de datos
Tr Ym Kf Z Normal
1.01 0.990 -1.529 -1.823 -2.3302.33 0.429 0.579 0.027 0.178
5 0.200 1.500 0.836 0.84210 0.100 2.250 1.495 1.28220 0.050 2.970 2.128 1.64525 0.040 3.199 2.328 1.75130 0.033 3.384 2.491 1.83450 0.020 3.902 2.946 2.054
100 0.010 4.600 3.559 2.326500 0.002 6.214 4.975 2.878
1000 0.001 6.907 5.585 3.090
Ajuste a distribucion Normal de dos parametros
Tr Kf Z Normal Z Gumbel
1.01 0.990 -2.330 -2.330 -1.642
2.33 0.429 0.178 0.178 0.001
5 0.200 0.842 0.842 0.719
10 0.100 1.282 1.282 1.305
20 0.050 1.645 1.645 1.866
25 0.040 1.751 1.751 2.044
30 0.033 1.834 1.834 2.189
50 0.020 2.054 2.054 2.592
100 0.010 2.326 2.326 3.137
500 0.002 2.878 2.878 4.395
1000 0.001 3.090 3.090 4.936
Ajuste a distribucion Pearson Tipo III
TrKf
Z NormalArit Log
1.01 0.990 -1.784 -2.191 -2.3302.33 0.429 0.055 0.148 0.178
5 0.200 0.784 0.831 0.84210 0.100 1.332 1.300 1.28220 0.050 1.825 1.696 1.64525 0.040 1.976 1.814 1.75130 0.033 2.098 1.906 1.83450 0.020 2.428 2.153 2.054
100 0.010 2.857 2.464 2.326500 0.002 3.800 3.108 2.878
1000 0.001 4.188 3.361 3.090
P(X>xTR)
P(X>xTR)
P(X>xTR)
Orden442 6.091 22379 5.938 26415 6.028 25480 6.174 20356 5.874 27573 6.351 14538 6.288 18442 6.091 22615 6.422 13623 6.435 12356 5.874 28324 5.782 29449 6.107 21512 6.239 19810 6.697 9439 6.083 24287 5.660 30548 6.305 17
1065 6.971 41065 6.971 4920 6.824 7571 6.347 15723 6.583 11795 6.678 10904 6.807 8945 6.851 6
1082 6.987 31308 7.176 11141 7.040 2562 6.332 16
655.600 6.400280.674 0.418
0.742 0.188
QMaxIns (m3/s) Ln QMaxIns (m3/s)
Ajuste a distribucion Gumbel (ó Tipo I de valores extremos)
Z GumbelGumbel Log Gumbel
-1.642 143.800 280.6680.001 663.310 608.9140.719 890.383 854.2331.305 1075.330 1125.4401.866 1252.735 1466.1742.044 1309.011 1594.4902.189 1354.792 1707.1182.592 1482.369 2064.7343.137 1654.447 2668.5654.395 2052.092 4827.6734.936 2223.046 6229.073
Normal Log Normal
1.607 227.054705.686 648.624891.821 856.067
1015.298 1029.0931117.268 1198.0521146.972 1252.2991170.332 1296.6801232.034 1421.6161308.545 1593.3841463.425 2007.2391522.948 2193.500
Z GumbelPearson Log Pearson
-1.642 154.797 240.6590.001 671.075 640.3580.719 875.531 852.2841.305 1029.352 1036.9951.866 1167.932 1224.2082.044 1210.332 1285.7262.189 1244.331 1336.5602.592 1336.951 1482.0713.137 1457.584 1687.8564.395 1722.061 2210.1544.936 1831.166 2457.097
Valor esperado (m3/s)
Valor esperado (m3/s)
Valor esperado (m3/s)
PRUEBAS DE BONDAD DE AJUSTE
ESTACIÓN: La Joya
NORMAL LOGNORMAL GUMBEL
m 655.600 6.400 a
s 280.674 0.418 b
Cs 0.742 0.188
Tr Q observadoGUMBEL
f(x) F(X)0.29032 1.41 442.00 0.00153 0.225350.16129 1.19 379.00 0.00124 0.137080.19355 1.24 415.00 0.00143 0.185300.35484 1.55 480.00 0.00164 0.285760.12903 1.15 355.70 0.00111 0.109650.54839 2.21 573.00 0.00165 0.440900.41935 1.72 538.00 0.00168 0.382530.29032 1.41 442.00 0.00153 0.225350.58065 2.38 615.00 0.00157 0.508690.61290 2.58 623.10 0.00155 0.521340.09677 1.11 355.50 0.00111 0.109430.06452 1.07 324.40 0.00091 0.078050.32258 1.48 448.90 0.00156 0.236010.38710 1.63 512.40 0.00168 0.339520.70968 3.44 810.00 0.00096 0.757840.22581 1.29 438.50 0.00152 0.220000.03226 1.03 287.20 0.00067 0.048660.45161 1.82 547.50 0.00168 0.398460.87097 7.75 1065.00 0.00036 0.917160.87097 7.75 1065.00 0.00036 0.917160.77419 4.43 919.80 0.00065 0.845450.51613 2.07 570.90 0.00165 0.437440.64516 2.82 723.00 0.00125 0.661900.67742 3.10 795.00 0.00101 0.743080.74194 3.88 904.00 0.00069 0.834890.80645 5.17 945.00 0.00059 0.861030.90323 10.33 1082.00 0.00034 0.923110.96774 31.00 1308.00 0.00013 0.971920.93548 15.50 1141.00 0.00026 0.940730.48387 1.94 562.10 0.00166 0.42284
mLN
sLN
CsLN
Fs(x)=1-P(X>xTR) (Weibull)
PRUEBA SMIRNOV-KOLMOGOROV
Q observado Gumbel LogGumbel Normal LogNormal442.00 0.06498 0.05506 0.06700 0.06011379.00 0.02421 0.06285 0.00090 0.02685415.00 0.00825 0.02072 0.00211 0.00649480.00 0.06907 0.02980 0.08906 0.06060355.70 0.01938 0.06919 0.01362 0.02471573.00 0.10748 0.02793 0.16412 0.09528
538.00 0.03683 0.03348 0.08174 0.02517442.00 0.06498 0.05506 0.06700 0.06011615.00 0.07196 0.01046 0.13815 0.06021623.10 0.09157 0.00945 0.15899 0.08002355.50 0.01265 0.03722 0.04571 0.00731324.40 0.01354 0.04063 0.05448 0.00527448.90 0.08657 0.07099 0.09185 0.08097512.40 0.04757 0.01146 0.08214 0.03696810.00 0.04817 0.08801 0.00080 0.05129438.50 0.00581 0.00121 0.00619 0.00133287.20 0.01640 0.02785 0.06241 0.00623
547.50 0.05315 0.02036 0.10155 0.04125
1065.00 0.04620 0.03596 0.05670 0.042671065.00 0.04620 0.03596 0.05670 0.04267919.80 0.07126 0.08386 0.05253 0.07033
570.90 0.07869 0.00049 0.13472 0.06650723.00 0.01674 0.08084 0.05027 0.02410795.00 0.06566 0.10971 0.01287 0.06948904.00 0.09295 0.10898 0.06999 0.09249945.00 0.05458 0.06211 0.04230 0.05299
1082.00 0.01988 0.00791 0.03242 0.016221308.00 0.00417 0.01844 0.02221 0.000441141.00 0.00525 0.01152 0.02265 0.00129562.10 0.06103 0.01638 0.11435 0.04889
Dn 0.10748 0.10971 0.16412 0.09528
JERARQUIAAjusta Ajusta Ajusta Ajusta
3 4 6 2
N 30a 0.05
0.24830
JERARQUIA
Gumbel 3 4
LogGumbel 4 5Normal 6 6
LogNormal 2 1
Pearson 5 3LogPearson 1 2
Da
Smirnov-Kolmogorov
c2
PRUEBAS DE BONDAD DE AJUSTE
GUMBEL LOG-GUMBEL PEARSON LOG-PEARSON
218.841 a 0.326 q 104.16 q
529.285 b 6.212 k 7.26 k
-100.69
LOG-GUMBEL NORMAL LOG-NORMALf(x) F(X) f(x) F(X) f(x) F(X)
0.00236 0.23526 0.00106 0.22332 0.00164 0.230210.00185 0.09844 0.00087 0.16219 0.00137 0.134440.00224 0.17283 0.00098 0.19566 0.00155 0.187060.00233 0.32504 0.00117 0.26578 0.00172 0.294240.00145 0.05984 0.00080 0.14265 0.00122 0.104330.00182 0.52046 0.00136 0.38427 0.00165 0.453110.00204 0.45284 0.00130 0.33761 0.00171 0.394180.00236 0.23526 0.00106 0.22332 0.00164 0.230210.00155 0.59111 0.00141 0.44249 0.00155 0.520430.00150 0.60345 0.00141 0.45391 0.00152 0.532880.00145 0.05955 0.00080 0.14249 0.00121 0.104080.00084 0.02388 0.00071 0.11900 0.00099 0.069780.00237 0.25159 0.00108 0.23073 0.00166 0.241610.00219 0.39856 0.00125 0.30496 0.00173 0.350140.00068 0.79769 0.00122 0.70888 0.00092 0.760970.00235 0.22702 0.00105 0.21961 0.00163 0.224480.00026 0.00441 0.00060 0.09467 0.00069 0.038490.00198 0.47197 0.00132 0.35007 0.00170 0.410370.00025 0.90693 0.00049 0.92767 0.00035 0.913640.00025 0.90693 0.00049 0.92767 0.00035 0.913640.00044 0.85805 0.00091 0.82673 0.00062 0.844520.00183 0.51662 0.00136 0.38141 0.00166 0.449630.00099 0.72600 0.00138 0.59489 0.00120 0.669260.00073 0.78713 0.00126 0.69029 0.00096 0.746900.00047 0.85092 0.00096 0.81193 0.00066 0.834430.00040 0.86856 0.00084 0.84875 0.00056 0.859440.00024 0.91114 0.00045 0.93564 0.00033 0.919450.00012 0.94930 0.00010 0.98995 0.00013 0.968180.00020 0.92396 0.00032 0.95813 0.00026 0.936770.00189 0.50025 0.00134 0.36952 0.00167 0.43498
x0 x0
Pearson LogPearson N 300.05462 0.05592 IQR 438.5000.00554 0.02883 Ancho Clase 212.2300.00627 0.00500 Clases 70.06549 0.05297 a 0.050.00090 0.028560.12001 0.08300 Gumbel
0.04380 0.01393 Intervalo oi
0.05462 0.05592 287.2 500.2 110.08969 0.04778 500.2 713.2 80.11010 0.06768 713.2 926.2 50.03295 0.00344 926.2 1139.2 40.03447 0.00029 1139.2 1352.2 20.07738 0.07611 1352.2 1565.2 00.04999 0.02702 1565.2 1778.2 00.02882 0.05622 1778.2 1991.2 00.00512 0.00252 1991.2 2204.2 00.03593 0.00023 2204.2 2417.2 0
0.06172 0.02964
0.04456 0.03896 v 7
0.04456 0.038960.05993 0.07048 Log Gumbel
0.09091 0.05426 Intervalo oi
0.00587 0.03325 287.2 500.2 110.04545 0.07514 500.2 713.2 80.08041 0.09324 713.2 926.2 50.04518 0.05225 926.2 1139.2 40.01909 0.01224 1139.2 1352.2 20.00876 0.00466 1352.2 1565.2 00.00685 0.00338 1565.2 1778.2 00.07193 0.03685 1778.2 1991.2 0
1991.2 2204.2 02204.2 2417.2 0
v 7
Normal
0.12001 0.09324 Intervalo oi
Ajusta Ajusta 287.2 500.2 115 1 500.2 713.2 8
713.2 926.2 5926.2 1139.2 4
1139.2 1352.2 2
PRUEBA CHI CUADRADO c2
1352.2 1565.2 01565.2 1778.2 01778.2 1991.2 01991.2 2204.2 02204.2 2417.2 0
v 7
Log Normal
Intervalo oi
287.2 500.2 11500.2 713.2 8713.2 926.2 5926.2 1139.2 4
1139.2 1352.2 21352.2 1565.2 01565.2 1778.2 01778.2 1991.2 01991.2 2204.2 02204.2 2417.2 0
v 7
Pearson
Intervalo oi287.2 500.2 11500.2 713.2 8713.2 926.2 5926.2 1139.2 4
1139.2 1352.2 21352.2 1565.2 01565.2 1778.2 01778.2 1991.2 01991.2 2204.2 02204.2 2417.2 0
v 6
Log Pearson
Intervalo oi287.2 500.2 11500.2 713.2 8713.2 926.2 5926.2 1139.2 4
1139.2 1352.2 21352.2 1565.2 0
LOG-PEARSON
0.04
113.18
1.95
PEARSON LOG-PEARSONf(x) F(X) f(x) F(X)
0.00137 0.23570 0.00174 0.234400.00116 0.15575 0.00145 0.132460.00129 0.19982 0.00165 0.188550.00145 0.28935 0.00180 0.301870.00106 0.12993 0.00129 0.100470.00151 0.42838 0.00167 0.465380.00151 0.37556 0.00175 0.405430.00137 0.23570 0.00174 0.234400.00147 0.49095 0.00154 0.532870.00146 0.50281 0.00151 0.545230.00106 0.12972 0.00129 0.100210.00092 0.09899 0.00102 0.064230.00139 0.24520 0.00176 0.246470.00149 0.33711 0.00179 0.360080.00102 0.73850 0.00087 0.765900.00136 0.23093 0.00173 0.228320.00074 0.06819 0.00068 0.032490.00151 0.38990 0.00173 0.421980.00041 0.91553 0.00034 0.909920.00041 0.91553 0.00034 0.909920.00073 0.83413 0.00058 0.844670.00151 0.42521 0.00168 0.461870.00126 0.63929 0.00115 0.678410.00106 0.72287 0.00091 0.752560.00077 0.82234 0.00062 0.835180.00066 0.85163 0.00053 0.858700.00039 0.92232 0.00032 0.915460.00013 0.97650 0.00013 0.963080.00030 0.94234 0.00025 0.932100.00151 0.41194 0.00170 0.44703
Gumbel
ei8 1.03
10 0.376 0.173 0.601 0.730 0.430 0.160 0.060 0.020 0.01
3.58 Ajusta14.07 4
Log Gumbel
ei11 0.0010 0.534 0.102 2.381 1.290 0.490 0.280 0.180 0.110 0.08
5.44 Ajusta14.07 5
Normal
ei6 4.529 0.068 0.854 0.021 0.79
(oi-ei)2/ei
c2
c2a
(oi-ei)2/ei
c2
c2a
(oi-ei)2/ei
0 0.180 0.020 0.000 0.000 0.00
6.43 Ajusta14.07 6
Log Normal
ei
9 0.6010 0.356 0.093 0.711 0.700 0.460 0.190 0.080 0.030 0.02
3.23 Ajusta14.07 1
Pearson
ei8 1.619 0.176 0.293 0.271 0.540 0.390 0.110 0.030 0.010 0.00
3.42 Ajusta12.59 3
Log Pearson
ei9 0.36
10 0.355 0.042 0.901 0.730 0.49
c2
c2a
(oi-ei)2/ei
c2
c2a
(oi-ei)2/ei
c2
c2a
(oi-ei)2/ei
0
500
1000
1500
2000
2500
1.01 1.1 1.5 2.33 5 10 25 50 100 200 500 1000
La Joya Gumbel Pearson Normal
Período de Retorno (Años)
Ca
ud
al (
m3
/s)
*Papel probabilístico de distribución Gumbel
100
1000
10000
1.01 1.1 1.5 2.335 10 25 50 100 200 500 1000
La Joya Log Gumbel Log Normal Log Pearson
Período de Retorno (Años)
Ca
ud
al (
m3
/s)
*Papel probabilístico de distribución Log Gumbel
0
500
1000
1500
2000
2500
1.01 1.1 1.5 2.33 5 10 25 50 100 200 5001000
La Joya Normal Pearson Gumbel
Período de retorno (Años)
Ca
ud
al (
m3
/s)
*Papel probabilístico de distribución Normal
100
1000
10000
1.01 1.1 1.5 2.335 10 25 50 100 200 500 1000
La Joya Log Normal Log Pearson Log Gumbel
Período de retorno (Años)
Ca
ud
al (
m3
/s)
*Papel probabilístico de distribución Log Normal