Excel Taller 3.1
29
N° Año N° Año N° Año 1 1941 3,25 21 1961 3,38 41 1981 3,06 2 1942 3,5 22 1962 3,5 42 1982 3,97 3 1943 3,57 23 1963 3,36 43 1983 3,97 4 1944 3,25 24 1964 2,52 44 1984 3,83 5 1945 2,24 25 1965 3,28 45 1985 2,81 6 1946 2,38 26 1966 2,75 46 1986 2,08 7 1947 2,47 27 1967 3,92 47 1987 2,09 8 1948 2,26 28 1968 3,74 48 1988 2,45 9 1949 3,36 29 1969 3,24 49 1989 2,3 10 1950 2,77 30 1970 4,45 50 1990 2,26 11 1951 2,72 31 1971 3,56 51 1991 2,16 12 1952 2,71 32 1972 4,05 52 1992 2,54 13 1953 3,07 33 1973 2,95 53 1993 3,17 14 1954 3,86 34 1974 2,89 54 1994 3,17 15 1955 3,77 35 1975 3,77 55 1995 2,28 16 1956 3,92 36 1976 4,87 56 1996 3,35 17 1957 3,56 37 1977 2,61 57 1997 3,05 18 1958 1,88 38 1978 3,15 58 1998 2,98 19 1959 3,47 39 1979 3,65 59 1999 3,47 20 1960 2,08 40 1980 3,62 60 2000 3,23 Evaluación de los eventos de creciente en la cuenca del rio Tunjuelo aguas debajo de la cantarrana-Acueducto, aguas y alcantarillado de Bogotá- 2004 Q Máx Anual [m3/s] Q Máx Anual [m3/s] Q Máx Anual [m3/s]
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Transcript of Excel Taller 3.1
N° Año N° Año N° Año
1 1941 3,25 21 1961 3,38 41 1981 3,062 1942 3,5 22 1962 3,5 42 1982 3,973 1943 3,57 23 1963 3,36 43 1983 3,974 1944 3,25 24 1964 2,52 44 1984 3,835 1945 2,24 25 1965 3,28 45 1985 2,816 1946 2,38 26 1966 2,75 46 1986 2,087 1947 2,47 27 1967 3,92 47 1987 2,098 1948 2,26 28 1968 3,74 48 1988 2,459 1949 3,36 29 1969 3,24 49 1989 2,3
10 1950 2,77 30 1970 4,45 50 1990 2,2611 1951 2,72 31 1971 3,56 51 1991 2,1612 1952 2,71 32 1972 4,05 52 1992 2,5413 1953 3,07 33 1973 2,95 53 1993 3,1714 1954 3,86 34 1974 2,89 54 1994 3,1715 1955 3,77 35 1975 3,77 55 1995 2,2816 1956 3,92 36 1976 4,87 56 1996 3,3517 1957 3,56 37 1977 2,61 57 1997 3,0518 1958 1,88 38 1978 3,15 58 1998 2,9819 1959 3,47 39 1979 3,65 59 1999 3,4720 1960 2,08 40 1980 3,62 60 2000 3,23
Evaluación de los eventos de creciente en la cuenca del rio Tunjuelo aguas debajo de la cantarrana-Acueducto, aguas y alcantarillado de Bogotá- 2004
Q Máx Anual [m3/s]
Q Máx Anual [m3/s]
Q Máx Anual [m3/s]
AÑO
1958 1.88 Q medio Anual (m3/s)
1960 2.08 Media Geometrica 3.05716575 Intervalo [m3/s]
1986 2.08 Media 3.12616667 1.88 -
1987 2.09 Error típico 0.08431917 2.179 -
1991 2.16 Mediana 3.2 2.478 -
1945 2.24 Moda 2.08 2.777 -1948 2.26 Desviación estándar 0.65313349 3.076 -
1990 2.26 Varianza de la muestra 0.42658336 3.375 -
1995 2.28 Curtosis -0.38600173 3.674 -1989 2.3 Coeficiente de asimetría 0.10202323 3.973 -1946 2.38 Rango 2.99 4.272 -1988 2.45 Mínimo 1.88 4.571 -1947 2.47 Máximo 4.87 2.991964 2.52 Suma 187.571992 2.54 Coeficiente de variación 0.208924721977 2.61 Cuenta 601952 2.711951 2.72 Intervalos 0.2991966 2.751950 2.77 1.881985 2.81 2.1791974 2.89 2.4781973 2.95 2.7771998 2.98 3.0761997 3.05 3.3751981 3.06 3.6741953 3.07 3.9731978 3.15 4.2721993 3.17 4.5711994 3.172000 3.231969 3.241941 3.251944 3.251965 3.281996 3.351949 3.361963 3.361961 3.381959 3.471999 3.471942 3.5
Q medio Anual (m3/s)
2.18 2.48 2.78 3.08 3.37 3.67 3.97 4.27 4.57 4.870.0%
5.0%
10.0%
15.0%
20.0%
Histograma
Frecuencia
Q medio Anual (m3/s)
Frec
uenc
ia
1962 3.51957 3.561971 3.561943 3.571980 3.621979 3.651968 3.741955 3.771975 3.771984 3.831954 3.861956 3.921967 3.921982 3.971983 3.971972 4.051970 4.451976 4.87
Intervalo [m3/s] Frecuencia % relativa % acumulado [m3/s] Frecuencia
2.179 5 8.33% 8.33% 3.375 11 18.33%
2.478 8 13.33% 21.67% 3.674 10 35.00%
2.777 7 11.67% 33.33% 3.973 9 50.00%
3.076 7 11.67% 45.00% 2.478 8 63.33%3.375 11 18.33% 63.33% 2.777 7 75.00%
3.674 10 16.67% 80.00% 3.076 7 86.67%
3.973 9 15.00% 95.00% 2.179 5 95.00%4.272 1 1.67% 96.67% 4.272 1 96.67%4.571 1 1.67% 98.33% 4.571 1 98.33%4.87 1 1.67% 100.00% 4.87 1 100.00%
60
% acumulado
2.18 2.48 2.78 3.08 3.37 3.67 3.97 4.27 4.57 4.870.00%
10.00%20.00%30.00%40.00%50.00%60.00%70.00%80.00%90.00%
100.00%
Histograma frecuencias acumuladas
% acumulado
Q Máx.Anual [m3/s]
Frec
uenc
ia
2.18 2.48 2.78 3.08 3.37 3.67 3.97 4.27 4.57 4.870.0%
5.0%
10.0%
15.0%
20.0%
Histograma
Frecuencia
Q medio Anual (m3/s)
Frec
uenc
ia
3.3753.674
3.9732.478
2.7773.076
2.1794.272
4.5714.87
02468
1012
0.00%20.00%40.00%60.00%80.00%100.00%120.00%
Histograma
Frecuencia% acumulado
Q medio Anual (m3/s)
Frec
uenc
ia
2.18 2.48 2.78 3.08 3.37 3.67 3.97 4.27 4.57 4.870.00%
10.00%20.00%30.00%40.00%50.00%60.00%70.00%80.00%90.00%
100.00%
Histograma frecuencias acumuladas
% acumulado
Q Máx.Anual [m3/s]
Frec
uenc
ia
3.3753.674
3.9732.478
2.7773.076
2.1794.272
4.5714.87
02468
1012
0.00%20.00%40.00%60.00%80.00%100.00%120.00%
Histograma
Frecuencia% acumulado
Q medio Anual (m3/s)
Frec
uenc
ia
AJUSTE DE BONDAD DISTRIBUCIÓN NORMAL CON CHI CUADRADO
año Q (m3/s Intervalo Rango
1950 31000 4.49136169383 1 15000 - 16589.851951 30000 4.47712125472 2 16589.85 - 21265.021952 28000 4.44715803134 3 21265.02 - 24665.141953 26000 4.41497334797 4 24665.14 - 27533.991954 17000 4.23044892138 5 27533.99 - 30190.3321955 16000 4.20411998266 6 30190.33 - 32846.681957 16000 4.20411998266 8 35715.53 - 39115.651958 19000 4.27875360095 9 39115.65 - 43790.811959 24000 4.38021124171 10 43790.81 - 510001960 27000 4.431363764161960 31000 4.491361693831961 29000 4.46239799791962 26000 4.41497334797 AJUSTE DE BONDAD DISTRIBUCIÓN NORMAL CON CHI CUADRADO
1963 18000 4.2552725051 Intervalo Rango
1964 16400 4.21484384805 1 4.176091 - 4.22923921965 16300 4.2121876044 2 4.229 - 4.2823871966 17100 4.23299611039 3 4.282 - 4.33553491967 18000 4.2552725051 4 4.336 - 4.38868281968 23000 4.36172783602 5 4.389 - 4.44183071969 30000 4.47712125472 6 4.442 - 4.49497861970 40000 4.60205999133 7 4.495 - 4.54812651971 37000 4.56820172407 8 4.548 - 4.60127441972 32000 4.50514997832 9 4.601 - 4.65442231973 27000 4.43136376416 10 4.654 - 4.70757021974 25000 4.397940008671975 24000 4.380211241711976 23000 4.361727836021977 21000 4.322219294731978 20000 4.30102999566 Columna11979 19000 4.278753600951980 18000 4.2552725051 Media 4.4524571981 24000 4.38021124171 Error típico 0.021982 30000 4.47712125472 Mediana 4.469761983 31000 4.49136169383 Moda 4.4913621984 38000 4.57978359662 Desviación e 0.1574791985 45000 4.65321251378 Varianza de 0.02481986 47000 4.67209785794 Curtosis -1.177771987 50000 4.69897000434 Coeficiente d-0.1047951988 48000 4.68124123738 Rango 0.5314791989 44000 4.64345267649 Mínimo 4.1760911990 36000 4.55630250077 Máximo 4.70757
Log (Q medio Anual) (m3/s)
1991 37000 4.56820172407 Suma 276.05231992 39000 4.59106460703 Cuenta 621993 40000 4.602059991331994 42000 4.62324929041995 45000 4.653212513781996 48000 4.681241237381997 51000 4.70757017611998 48000 4.681241237381999 46000 4.662757831682000 44000 4.643452676492001 37000 4.568201724072002 31000 4.491361693832003 37000 4.568201724072004 36000 4.556302500772005 31000 4.491361693832006 28000 4.447158031342007 24000 4.380211241712008 20000 4.301029995662009 19000 4.278753600952010 16000 4.20411998266
AJUSTE DE BONDAD DISTRIBUCIÓN NORMAL CON CHI CUADRADO
Frecuencia z= (X-x)/s F(z) P(X) Xc^2 1.886 9.68% 9.68% -1.280 0.100 10.04% 0.008 2.179
11 17.74% 27.42% -0.840 0.201 10.02% 3.696 2.4786 9.68% 37.10% -0.520 0.301 10.07% 0.010 2.7775 8.06% 45.16% -0.250 0.401 10.00% 0.233 3.0766 9.68% 54.84% 0.000 0.500 9.87% 0.002 3.3756 9.68% 64.52% 0.250 0.599 9.87% 0.002 3.6748 12.90% 77.42% 0.840 0.799 10.07% 0.492 4.2723 4.84% 82.26% 1.280 0.900 10.02% 1.659 4.571
11 17.74% 100.00% 1.958 0.975 7.55% 8.524 4.8762 1 20.828
AJUSTE DE BONDAD DISTRIBUCIÓN NORMAL CON CHI CUADRADO
Frecuencia z= (X-x)/s F(x) P(X) Xc^2
6 0.0968 0.0968 -1.417 0.078 0.078 0.2758 0.1290 0.2258 -1.080 0.140 0.062 4.4613 0.0484 0.2742 -0.742 0.229 0.089 1.1306 0.0968 0.3710 -0.405 0.343 0.114 0.1555 0.0806 0.452 -0.067 0.473 0.131 1.193
11 0.1774 0.6294 0.270 0.606 0.133 0.9131 0.0161 0.6455 0.608 0.728 0.122 5.6998 0.1290 0.7745 0.945 0.827 0.099 0.5617 0.1129 0.8874 1.282 0.900 0.073 1.3917 0.1129 1.0003 1.620 0.948 0.048 5.578
62 21.355
Clase Frecuencia Clase Frecuencia4.2292391508 6 4.4949786093 114.2823870425 8 4.2823870425 84.3355349342 3 4.6012743927 84.3886828259 6 4.6544222844 74.4418307176 5 4.2292391508 64.4949786093 11 4.3886828259 6
4.548126501 1 4.7075701761 64.6012743927 8 4.4418307176 54.6544222844 7 4.3355349342 34.7075701761 6 4.548126501 1
Frecuencia relativa %
Frecuencia acumulada %
Frecuencia relativa %
Frecuencia acumulada %
L3
z= variable estandarizada x = Media de los dato s= Desv estandar
L18
z= variable estandarizada x = Media de los dato s= Desv estandar
y mayor... 1 y mayor... 1
Q medio Anual (m3/s)
Media Geometrica 28343.7107Media 30190.3226
Mediana 29500Moda 31000Desviación estándar 10625.375Varianza de la muestra 111077648Coeficiente de asimetría 0.33947745Coeficiente de variación 1.15077E-05
Log(Q medio Anual) (m3/s)
Media 4.45245671Error típico 0.01999985Mediana 4.46975963Moda 4.49136169Desviación estándar 0.157479Varianza de la muestra 0.02479964Curtosis -1.17776952Coeficiente de asimetría -0.10479473Rango 0.53147892Mínimo 4.17609126Máximo 4.70757018Suma 276.052316Cuenta 62
16,589.85
21,265.02
24,665.14
27,533.99
30,190.33
32,846.68
39,115.65
43,790.81
51,000.000.0%
2.0%
4.0%
6.0%
8.0%
10.0%
12.0%
14.0%
16.0%
18.0%
20.0%
Frecuenc...
Q Máx. Anual [m3/s]
HISTROGRAMA FRECUENCIAS RELATIVAS
1.88 2.179 2.478 2.777 3.076 3.375 3.674 4.272 4.5710.0%
20.0%
40.0%
60.0%
80.0%
100.0%
120.0%
HISTOGRAMA DE FRE-CUENCIA ACUMULADA
Axis Title
Axis
Title
16,589.85
21,265.02
24,665.14
27,533.99
30,190.33
32,846.68
39,115.65
43,790.81
51,000.000.0%
2.0%
4.0%
6.0%
8.0%
10.0%
12.0%
14.0%
16.0%
18.0%
20.0%
Frecuenc...
Q Máx. Anual [m3/s]
HISTROGRAMA FRECUENCIAS RELATIVAS
1.88 2.179 2.478 2.777 3.076 3.375 3.674 4.272 4.5710.0%
20.0%
40.0%
60.0%
80.0%
100.0%
120.0%
HISTOGRAMA DE FRE-CUENCIA ACUMULADA
Axis Title
Axis
Title
Kolgomorov - Smirnov Datos Pearson lll β1 1.1976
ᾳ 0.05n 60
Media 3.126 ᾳ1 0.5968
d 0.1756 S 0.653 δ1 2.4114
DATOS Distribución Pearson Tipo lll
N° AÑO F(0) ɤ y F(x) |F(x) - F(0)|
1 1976 4.87 0.688 0.984 0.3172 4.119 0.993993 0.0104
2 1970 4.45 0.648 0.967 0.1388 3.416 0.991209 0.0240
3 1972 4.05 0.607 0.951 0.0472 2.745 0.987334 0.0365
4 1982 3.97 0.599 0.934 0.0359 2.611 0.986370 0.0519
5 1983 3.97 0.599 0.918 0.0359 2.611 0.986370 0.0683
6 1956 3.92 0.593 0.902 0.0299 2.528 0.985730 0.0841
7 1967 3.92 0.593 0.885 0.0299 2.528 0.985730 0.1005
8 1954 3.86 0.587 0.869 0.0236 2.427 0.984921 0.1161
9 1984 3.83 0.583 0.852 0.0209 2.377 0.984499 0.1320
10 1955 3.77 0.576 0.836 0.0160 2.276 0.983619 0.1476
11 1975 3.77 0.576 0.820 0.0160 2.276 0.983619 0.1639
12 1968 3.74 0.573 0.803 0.0138 2.226 0.983160 0.1799
13 1979 3.65 0.562 0.787 0.0086 2.075 0.981702 0.1948
14 1980 3.62 0.559 0.770 0.0072 2.025 0.981188 0.2107
15 1943 3.57 0.553 0.754 0.0052 1.941 0.980298 0.2262
16 1957 3.56 0.551 0.738 0.0049 1.924 0.980115 0.2424
17 1971 3.56 0.551 0.721 0.0049 1.924 0.980115 0.2588
18 1942 3.5 0.544 0.705 0.0031 1.824 0.978979 0.2741
19 1962 3.5 0.544 0.689 0.0031 1.824 0.978979 0.2905
20 1959 3.47 0.540 0.672 0.0024 1.774 0.978386 0.3063
21 1999 3.47 0.540 0.656 0.0024 1.774 0.978386 0.3226
22 1961 3.38 0.529 0.639 0.0010 1.623 0.976502 0.3372
23 1949 3.36 0.526 0.623 0.0008 1.589 0.976061 0.3531
24 1963 3.36 0.526 0.607 0.0008 1.589 0.976061 0.3695
25 1996 3.35 0.525 0.590 0.0007 1.573 0.975838 0.3857
26 1965 3.28 0.516 0.574 0.0002 1.455 0.974211 0.4004
27 1941 3.25 0.512 0.557 0.0001 1.405 0.973480 0.4161
28 1944 3.25 0.512 0.541 0.0001 1.405 0.973480 0.4325
29 1969 3.24 0.511 0.525 0.0001 1.388 0.973231 0.4486
30 2000 3.23 0.509 0.508 0.0001 1.372 0.972980 0.4648
31 1993 3.17 0.501 0.492 0.0000 1.271 0.971423 0.4796
32 1994 3.17 0.501 0.475 0.0000 1.271 0.971423 0.4960
33 1978 3.15 0.498 0.459 0.0000 1.238 0.970884 0.5119
34 1953 3.07 0.487 0.443 0.0000 1.103 0.968620 0.5260
Q máx. (m3/s)
Log(Q medio) (m3/s)
35 1981 3.06 0.486 0.426 0.0000 1.087 0.968324 0.5421
36 1997 3.05 0.484 0.410 0.0000 1.070 0.968026 0.5582
37 1998 2.98 0.474 0.393 -0.0002 0.953 0.965855 0.5724
38 1973 2.95 0.470 0.377 -0.0003 0.902 0.964878 0.5878
39 1974 2.89 0.461 0.361 -0.0008 0.802 0.962837 0.6022
40 1985 2.81 0.449 0.344 -0.0019 0.668 0.959923 0.6157
41 1950 2.77 0.442 0.328 -0.0027 0.601 0.958378 0.6305
42 1966 2.75 0.439 0.311 -0.0032 0.567 0.957583 0.6461
43 1951 2.72 0.435 0.295 -0.0040 0.517 0.956360 0.6613
44 1952 2.71 0.433 0.279 -0.0043 0.500 0.955944 0.6773
45 1977 2.61 0.417 0.262 -0.0082 0.333 0.951555 0.6893
46 1992 2.54 0.405 0.246 -0.0120 0.215 0.948213 0.7023
47 1964 2.52 0.401 0.230 -0.0133 0.182 0.947215 0.7177
48 1947 2.47 0.393 0.213 -0.0169 0.098 0.944631 0.7315
49 1988 2.45 0.389 0.197 -0.0185 0.065 0.943561 0.7468
50 1946 2.38 0.377 0.180 -0.0249 -0.053 0.939641 0.7593
51 1989 2.3 0.362 0.164 -0.0337 -0.187 0.934811 0.7709
52 1995 2.28 0.358 0.148 -0.0362 -0.220 0.933541 0.7860
53 1948 2.26 0.354 0.131 -0.0389 -0.254 0.932246 0.8011
54 1990 2.26 0.354 0.115 -0.0389 -0.254 0.932246 0.8175
55 1945 2.24 0.350 0.098 -0.0416 -0.287 0.930924 0.8326
56 1991 2.16 0.334 0.082 -0.0540 -0.421 0.925358 0.8434
57 1987 2.09 0.320 0.066 -0.0665 -0.539 0.920100 0.8545
58 1960 2.08 0.318 0.049 -0.0685 -0.555 0.919318 0.8701
59 1986 2.08 0.318 0.033 -0.0685 -0.555 0.919318 0.8865
60 1958 1.88 0.274 0.016 -0.1158 -0.890 0.901842 0.8854
-1.8276 D 0.8865
Hipotesis Nula
Datos LogPearson lll β1 6.8842 Datos Gumbel n 60
Media 0.485 ᾳ1 0.0357 Media 3.126 μy 0.5521
S 0.094 δ1 0.2394 S 0.653 σy 1.1747
β1 [m^3/s] 2.8192 ᾳ1 [m^3/s]^-1 1.7986
Distribución Log-Pearson Tipo lll Distribución Tipo Gumbel
ɤ y F(x) |F(x) - F(0)| F(X) |F(0)-F(x)|
0.4016 12.545 0.936 0.04755 -3.688 0.975 0.008
0.2105 11.448 0.934 0.03294 -2.933 0.948 0.019
0.0885 10.303 0.932 0.01854 -2.214 0.896 0.054
0.0710 10.061 0.932 0.00258 -2.070 0.881 0.053
0.0710 10.061 0.932 0.01381 -2.070 0.881 0.037
0.0611 9.906 0.932 0.02992 -1.980 0.871 0.031
0.0611 9.906 0.932 0.04631 -1.980 0.871 0.014
0.0504 9.719 0.931 0.06236 -1.872 0.857 0.011
0.0455 9.624 0.931 0.07858 -1.818 0.850 0.002
0.0366 9.432 0.931 0.09461 -1.710 0.835 0.002
0.0366 9.432 0.931 0.11100 -1.710 0.835 0.015
0.0326 9.335 0.930 0.12721 -1.656 0.826 0.023
0.0222 9.039 0.930 0.14303 -1.494 0.799 0.012
0.0192 8.939 0.930 0.15923 -1.440 0.789 0.019
0.0148 8.769 0.929 0.17529 -1.350 0.772 0.018
0.0140 8.735 0.929 0.19161 -1.332 0.768 0.030
0.0140 8.735 0.929 0.20801 -1.332 0.768 0.047
0.0098 8.529 0.929 0.22398 -1.224 0.745 0.040
0.0098 8.529 0.929 0.24038 -1.224 0.745 0.057
0.0081 8.424 0.929 0.25656 -1.171 0.733 0.061
0.0081 8.424 0.929 0.27295 -1.171 0.733 0.078
0.0040 8.105 0.928 0.28869 -1.009 0.694 0.055
0.0034 8.032 0.928 0.30493 -0.973 0.685 0.062
0.0034 8.032 0.928 0.32133 -0.973 0.685 0.079
0.0030 7.996 0.928 0.33764 -0.955 0.680 0.090
0.0014 7.740 0.927 0.35349 -0.829 0.646 0.072
0.0009 7.628 0.927 0.36965 -0.775 0.631 0.073
0.0009 7.628 0.927 0.38604 -0.775 0.631 0.090
0.0008 7.590 0.927 0.40235 -0.757 0.626 0.101
0.0007 7.553 0.927 0.41867 -0.739 0.620 0.112
0.0002 7.325 0.926 0.43456 -0.631 0.587 0.096
0.0002 7.325 0.926 0.45096 -0.631 0.587 0.112
0.0001 7.248 0.926 0.46718 -0.595 0.576 0.117
0.0000 6.935 0.925 0.48287 -0.451 0.529 0.086
F(x) exponente
0.0000 6.895 0.925 0.49918 -0.433 0.523 0.097
0.0000 6.856 0.925 0.51548 -0.415 0.517 0.107
-0.0001 6.573 0.925 0.53122 -0.289 0.473 0.079
-0.0002 6.450 0.924 0.54733 -0.235 0.454 0.077
-0.0007 6.201 0.924 0.56313 -0.127 0.415 0.054
-0.0024 5.859 0.923 0.57869 0.017 0.362 0.018
-0.0038 5.685 0.923 0.59465 0.088 0.335 0.008
-0.0047 5.597 0.922 0.61083 0.124 0.322 0.011
-0.0063 5.464 0.922 0.62688 0.178 0.303 0.008
-0.0070 5.419 0.922 0.64316 0.196 0.296 0.017
-0.0157 4.962 0.921 0.65836 0.376 0.233 0.029
-0.0253 4.631 0.920 0.67386 0.502 0.192 0.054
-0.0287 4.535 0.920 0.68999 0.538 0.180 0.049
-0.0386 4.291 0.919 0.70571 0.628 0.154 0.060
-0.0432 4.193 0.919 0.72182 0.664 0.143 0.053
-0.0625 3.840 0.918 0.73719 0.790 0.110 0.070
-0.0917 3.425 0.916 0.75233 0.934 0.079 0.085
-0.1004 3.318 0.916 0.76840 0.970 0.072 0.076
-0.1097 3.211 0.916 0.78446 1.006 0.065 0.066
-0.1097 3.211 0.916 0.80085 1.006 0.065 0.050
-0.1197 3.103 0.915 0.81690 1.042 0.059 0.040
-0.1668 2.661 0.914 0.83186 1.186 0.038 0.044
-0.2189 2.261 0.912 0.84689 1.312 0.024 0.041
-0.2273 2.202 0.912 0.86308 1.329 0.023 0.026
-0.2273 2.202 0.912 0.87947 1.329 0.023 0.010
-0.4573 0.973 0.908 0.89123 1.689 0.004 0.012
-0.7623 D 0.89123 D 0.117
Hipotesis Nula Hipotesis Se acepta
Análisis gráfico. Método de BlomDatos Blom n 60 Media 0.48532 Desv. Est 0.09373
N° AÑO W Z
1 1976 4.87 0.688 0.0104 3.0227 2.3130 0.70212 1970 4.45 0.648 0.0270 2.6881 1.9277 0.66603 1972 4.05 0.607 0.0436 2.5034 1.7111 0.64574 1982 3.97 0.599 0.0602 2.3709 1.5537 0.63095 1983 3.97 0.599 0.0768 2.2658 1.4274 0.61916 1956 3.92 0.593 0.0934 2.1777 1.3205 0.60917 1967 3.92 0.593 0.1100 2.1013 1.2269 0.60038 1954 3.86 0.587 0.1266 2.0333 1.1429 0.59249 1984 3.83 0.583 0.1432 1.9717 1.0663 0.5853
10 1955 3.77 0.576 0.1598 1.9153 0.9954 0.578611 1975 3.77 0.576 0.1763 1.8630 0.9293 0.572412 1968 3.74 0.573 0.1929 1.8140 0.8669 0.566613 1979 3.65 0.562 0.2095 1.7679 0.8078 0.561014 1980 3.62 0.559 0.2261 1.7243 0.7514 0.555715 1943 3.57 0.553 0.2427 1.6827 0.6972 0.550716 1957 3.56 0.551 0.2593 1.6429 0.6451 0.545817 1971 3.56 0.551 0.2759 1.6047 0.5946 0.541118 1942 3.5 0.544 0.2925 1.5679 0.5456 0.536519 1962 3.5 0.544 0.3091 1.5323 0.4979 0.532020 1959 3.47 0.540 0.3257 1.4978 0.4513 0.527621 1999 3.47 0.540 0.3423 1.4642 0.4057 0.523322 1961 3.38 0.529 0.3589 1.4315 0.3609 0.519123 1949 3.36 0.526 0.3755 1.3996 0.3168 0.515024 1963 3.36 0.526 0.3921 1.3684 0.2734 0.510925 1996 3.35 0.525 0.4087 1.3377 0.2305 0.506926 1965 3.28 0.516 0.4253 1.3076 0.1880 0.502927 1941 3.25 0.512 0.4419 1.2780 0.1458 0.499028 1944 3.25 0.512 0.4585 1.2488 0.1040 0.495129 1969 3.24 0.511 0.4751 1.2200 0.0623 0.491230 2000 3.23 0.509 0.4917 1.1915 0.0207 0.487331 1993 3.17 0.501 0.5083 1.1633 -0.0207 0.483432 1994 3.17 0.501 0.5249 1.1354 -0.0622 0.479533 1978 3.15 0.498 0.5415 1.1076 -0.1038 0.475634 1953 3.07 0.487 0.5581 1.0800 -0.1455 0.471735 1981 3.06 0.486 0.5747 1.0525 -0.1875 0.467736 1997 3.05 0.484 0.5913 1.0251 -0.2297 0.463837 1998 2.98 0.474 0.6079 0.9978 -0.2724 0.459838 1973 2.95 0.470 0.6245 0.9704 -0.3154 0.4558
Q máx. anual (m3/s)
Log(Q medio) (m3/s)
P(x) Excedencia de Bolm
Log Q de la distribucion Log normal
39 1974 2.89 0.461 0.6411 0.9430 -0.3591 0.451740 1985 2.81 0.449 0.6577 0.9155 -0.4033 0.447541 1950 2.77 0.442 0.6743 0.8878 -0.4483 0.443342 1966 2.75 0.439 0.6909 0.8600 -0.4942 0.439043 1951 2.72 0.435 0.7075 0.8319 -0.5411 0.434644 1952 2.71 0.433 0.7241 0.8036 -0.5891 0.430145 1977 2.61 0.417 0.7407 0.7749 -0.6384 0.425546 1992 2.54 0.405 0.7573 0.7457 -0.6892 0.420747 1964 2.52 0.401 0.7739 0.7161 -0.7418 0.415848 1947 2.47 0.393 0.7905 0.6858 -0.7963 0.410749 1988 2.45 0.389 0.8071 0.6548 -0.8532 0.405350 1946 2.38 0.377 0.8237 0.6229 -0.9128 0.399851 1989 2.3 0.362 0.8402 0.5900 -0.9757 0.393952 1995 2.28 0.358 0.8568 0.5559 -1.0424 0.387653 1948 2.26 0.354 0.8734 0.5202 -1.1138 0.380954 1990 2.26 0.354 0.8900 0.4827 -1.1911 0.373755 1945 2.24 0.350 0.9066 0.4427 -1.2760 0.365756 1991 2.16 0.334 0.9232 0.3997 -1.3708 0.356857 1987 2.09 0.320 0.9398 0.3523 -1.4796 0.346658 1960 2.08 0.318 0.9564 0.2985 -1.6094 0.334559 1986 2.08 0.318 0.9730 0.2338 -1.7758 0.318960 1958 1.88 0.274 0.9896 0.1444 -2.0290 0.2951
-3.0 -2.0 -1.0 0.0 1.0 2.0 3.01.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
5.5
f(x) = 0.676428229107853 x + 3.11588199469285R² = 0.983608355053954
Análisis Distrib Log-Normal. Ec. Blom
Análisis Distrib Log-Normal. Blom
Variable normal estandar Z
Caun
al m
edio
anu
al [m
3/s]
Datos β 0.95 X 3.1262 X (log) 0.48532 L min 0.3467 Q min [m3/s] 2.2216
n 60 ᾳ 0.05 S 0.6531 S (log) 0.09373 L Máx 0.7549 Q máx [m3/s] 5.6868
Análisis de confiabilidad
N° AÑO F(0) Z (log) |F(x) - F(0)| Se Z (sin Log) Limite Min Limite Máx
1 1976 4.87 0.688 0.984 2.1573 0.9846 0.00100 0.03121 2.66995 0.6202 0.75492 1970 4.45 0.648 0.967 1.7394 0.9592 0.00797 0.02713 2.02690 0.6012 0.69553 1972 4.05 0.607 0.951 1.3030 0.9036 0.04721 0.02327 1.41446 0.5771 0.63784 1982 3.97 0.599 0.934 1.2106 0.8868 0.04763 0.02253 1.29198 0.5715 0.62615 1983 3.97 0.599 0.918 1.2106 0.8868 0.03124 0.02253 1.29198 0.5715 0.62616 1956 3.92 0.593 0.902 1.1519 0.8751 0.02654 0.02207 1.21542 0.5679 0.61877 1967 3.92 0.593 0.885 1.1519 0.8751 0.01015 0.02207 1.21542 0.5679 0.61878 1954 3.86 0.587 0.869 1.0804 0.8598 0.00906 0.02154 1.12356 0.5633 0.60999 1984 3.83 0.583 0.852 1.0443 0.8516 0.00087 0.02127 1.07763 0.5610 0.6054
10 1955 3.77 0.576 0.836 0.9711 0.8340 0.00202 0.02076 0.98576 0.5562 0.596511 1975 3.77 0.576 0.820 0.9711 0.8340 0.01437 0.02076 0.98576 0.5562 0.596512 1968 3.74 0.573 0.803 0.9341 0.8247 0.02140 0.02051 0.93983 0.5537 0.592013 1979 3.65 0.562 0.787 0.8212 0.7942 0.00727 0.01979 0.80203 0.5460 0.578514 1980 3.62 0.559 0.770 0.7830 0.7831 0.01266 0.01956 0.75610 0.5434 0.574015 1943 3.57 0.553 0.754 0.7185 0.7638 0.00974 0.01920 0.67954 0.5389 0.566516 1957 3.56 0.551 0.738 0.7055 0.7598 0.02212 0.01912 0.66423 0.5380 0.564917 1971 3.56 0.551 0.721 0.7055 0.7598 0.03852 0.01912 0.66423 0.5380 0.564918 1942 3.5 0.544 0.705 0.6268 0.7348 0.02984 0.01872 0.57237 0.5323 0.555819 1962 3.5 0.544 0.689 0.6268 0.7348 0.04623 0.01872 0.57237 0.5323 0.555820 1959 3.47 0.540 0.672 0.5869 0.7216 0.04942 0.01853 0.52644 0.5295 0.551221 1999 3.47 0.540 0.656 0.5869 0.7216 0.06582 0.01853 0.52644 0.5295 0.551222 1961 3.38 0.529 0.639 0.4651 0.6793 0.03997 0.01801 0.38864 0.5205 0.537323 1949 3.36 0.526 0.623 0.4376 0.6694 0.04644 0.01791 0.35802 0.5185 0.534224 1963 3.36 0.526 0.607 0.4376 0.6694 0.06284 0.01791 0.35802 0.5185 0.534225 1996 3.35 0.525 0.590 0.4238 0.6644 0.07420 0.01786 0.34271 0.5175 0.532626 1965 3.28 0.516 0.574 0.3260 0.6279 0.05411 0.01756 0.23553 0.5101 0.521627 1941 3.25 0.512 0.557 0.2834 0.6116 0.05422 0.01745 0.18960 0.5069 0.516828 1944 3.25 0.512 0.541 0.2834 0.6116 0.07061 0.01745 0.18960 0.5069 0.516829 1969 3.24 0.511 0.525 0.2691 0.6061 0.08150 0.01742 0.17429 0.5059 0.515230 2000 3.23 0.509 0.508 0.2548 0.6005 0.09234 0.01739 0.15898 0.5048 0.513631 1993 3.17 0.501 0.492 0.1679 0.5665 0.07470 0.01723 0.06711 0.4982 0.504032 1994 3.17 0.501 0.475 0.1679 0.5665 0.09109 0.01723 0.06711 0.4982 0.504033 1978 3.15 0.498 0.459 0.1386 0.5549 0.09589 0.01719 0.03649 0.4959 0.500734 1953 3.07 0.487 0.443 0.0194 0.5077 0.06503 0.01711 -0.08600 0.4868 0.487535 1981 3.06 0.486 0.426 0.0043 0.5017 0.07546 0.01711 -0.10131 0.4856 0.485836 1997 3.05 0.484 0.410 -0.0109 0.4957 0.08588 0.01711 -0.11662 0.4845 0.484137 1998 2.98 0.474 0.393 -0.1185 0.4531 0.05964 0.01717 -0.22379 0.4763 0.472238 1973 2.95 0.470 0.377 -0.1653 0.4345 0.05748 0.01723 -0.26973 0.4727 0.467039 1974 2.89 0.461 0.361 -0.2605 0.3972 0.03658 0.01740 -0.36159 0.4654 0.456440 1985 2.81 0.449 0.344 -0.3906 0.3479 0.00359 0.01775 -0.48408 0.4556 0.441841 1950 2.77 0.442 0.328 -0.4570 0.3236 0.00428 0.01798 -0.54532 0.4507 0.434342 1966 2.75 0.439 0.311 -0.4906 0.3116 0.00014 0.01811 -0.57594 0.4482 0.430443 1951 2.72 0.435 0.295 -0.5414 0.2939 0.00120 0.01832 -0.62187 0.4445 0.424644 1952 2.71 0.433 0.279 -0.5585 0.2880 0.00935 0.01840 -0.63718 0.4432 0.422745 1977 2.61 0.417 0.262 -0.7327 0.2318 0.03046 0.01927 -0.79029 0.4308 0.402546 1992 2.54 0.405 0.246 -0.8587 0.1954 0.05052 0.02002 -0.89747 0.4220 0.3876
Q máx (m3/s)
Log(Q max) (m3/s)
F(x) Log-Normal
47 1964 2.52 0.401 0.230 -0.8953 0.1855 0.04404 0.02025 -0.92809 0.4195 0.383348 1947 2.47 0.393 0.213 -0.9882 0.1618 0.05136 0.02088 -1.00464 0.4133 0.372149 1988 2.45 0.389 0.197 -1.0258 0.1527 0.04401 0.02114 -1.03527 0.4109 0.367550 1946 2.38 0.377 0.180 -1.1601 0.1232 0.05712 0.02213 -1.14244 0.4023 0.350951 1989 2.3 0.362 0.164 -1.3186 0.0938 0.07018 0.02340 -1.26493 0.3926 0.330952 1995 2.28 0.358 0.148 -1.3590 0.0871 0.06042 0.02373 -1.29555 0.3902 0.325753 1948 2.26 0.354 0.131 -1.3999 0.0808 0.05035 0.02408 -1.32617 0.3878 0.320454 1990 2.26 0.354 0.115 -1.3999 0.0808 0.03396 0.02408 -1.32617 0.3878 0.320455 1945 2.24 0.350 0.098 -1.4410 0.0748 0.02360 0.02443 -1.35679 0.3855 0.315056 1991 2.16 0.334 0.082 -1.6095 0.0536 0.02838 0.02593 -1.47928 0.3762 0.292757 1987 2.09 0.320 0.066 -1.7622 0.0388 0.02678 0.02734 -1.58645 0.3683 0.272058 1960 2.08 0.318 0.049 -1.7844 0.0369 0.01223 0.02755 -1.60177 0.3672 0.268959 1986 2.08 0.318 0.033 -1.7844 0.0369 0.00416 0.02755 -1.60177 0.3672 0.268960 1958 1.88 0.274 0.016 -2.2528 0.0121 0.00429 0.03219 -1.90798 0.3467 0.2016
