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Funciones Continuas Vacacional (1)

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funciones continuas
34
AÑO PUENTE SANCHEZ CERRO 1926 1600 1927 1200 1928 720 1929 669 1930 580.1 1931 572.1 1932 502.1 1933 500 1934 483.6 1935 427.5 1936 360.5 1937 350.1 1938 349.1 1939 331 1940 325.1 1941 320.1 1942 303.8 1943 293.7 1944 273.2 1945 266.2 1946 264.4 1947 251.5 1948 250.2 1949 221.2 1950 205.2 1951 197.3 1952 188.1 1953 187.2 1954 183.1 1955 180.1 1956 175 1957 170.8 1958 169.5 1959 160.3 1960 159.9 1961 146.3 1962 146.1 1963 146 1964 145.3 1965 137.8 1966 132.9 1967 128.5 1968 119.3 1969 118.5 1970 100.2 1971 96.9 1972 90.3 1973 53.1 1974 45.5 1975 44.3 DESCARGAS MAXIMAS EXTREMAS (m 3 /s) 1926 1929 0 200 400 600 800 1000 1200 1400 1600 1800
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DescriptivaDESCARGAS MAXIMAS EXTREMAS (m3/s)AOPUENTE SANCHEZ CERRO1926160019271200192872019296691930580.11931572.11932502.119335001934483.61935427.51936360.51937350.11938349.119393311940325.11941320.11942303.81943293.71944273.21945266.21946264.41947251.51948250.2Herramientas / Anlisis de Datos / Estadstica Desciptiva1949221.2PUENTE SANCHEZ CERRO1950205.2Media300.81951197.3Mediana201.251952188.1Moda1953187.2Desviacin estndar883.41954183.1Varianza7804541955180.1Curtosis4.601956175Coeficiente de asimetra2.061957170.8Rango44241958169.5Mnimo44.31959160.3Mximo16001960159.9Suma49299.51961146.3Cuenta741962146.119631461964145.31965137.81966132.91967128.51968119.31969118.51970100.2197196.9197290.3197353.1197445.5197544.3

Descriptiva

PUENTE SANCHEZ CERRO

NDESCARGAS MAXIMAS EXTREMAS (m3/s)AOQQ ORDENADOSF(x)f(x)MEDIA300.8419261600.01600.001.00000.000000DESV.EST.280.0319271200.01200.000.99930.0000081928720.0720.000.93280.0004651929669.0669.000.90570.0006001930580.1580.100.84070.0008661931572.1572.100.83360.0008911932502.1502.100.76380.0011001933500.0500.000.76150.0011061934483.6483.600.74300.0011511935427.5427.500.67450.0012861936360.5360.500.58440.0013931937350.1350.100.56980.0014031938349.1349.100.56840.0014041939331.0331.000.54290.0014161940325.1325.100.53450.0014191941320.1320.100.52740.0014211942303.8303.800.50420.0014251943293.7293.700.48980.0014241944273.2273.200.46070.0014181945266.2266.200.45080.0014141946264.4264.400.44820.0014131947251.5251.500.43010.0014031948250.2250.200.42820.0014021949221.2221.200.38810.0013681950205.2205.200.36640.0013441951197.3197.300.35580.0013311952188.1188.100.34360.0013141953187.2187.200.34240.0013121954183.1183.100.33710.0013041955180.1180.100.33320.0012981956175.0175.000.32660.0012881957170.8170.800.32120.0012791958169.5169.500.31950.0012761959160.3160.300.30790.0012561960159.9159.900.30740.0012551961146.3146.300.29050.0012231962146.1146.100.29030.0012231963146.0146.000.29020.0012231964145.3145.300.28930.0012211965137.8137.800.28020.0012031966132.9132.900.27430.0011901967128.5128.500.26910.0011791968119.3119.300.25840.0011551969118.5118.500.25750.0011521970100.2100.200.23680.001102197196.996.900.23320.001093197290.390.300.22610.001074197353.153.100.18820.000963197445.545.500.18090.000940197544.344.300.17980.000936

N

histograma

LN2ANALISIS CON DISTRIBUCION LOG - NORMAL DE 2 PARAMETROSAOQQ ORDENADOSy = ln (x)F(x)f(x)MEDIA300.84MEDIA5.420219261600.01600.007.37780.99580.0167DESV.EST.280.03DESV.EST.0.742919271200.01200.007.09010.98770.04291928720.0720.006.57930.94060.15901929669.0669.006.50580.92800.1846C.ASIMETRIA0.20411930580.1580.106.36320.89780.23991931572.1572.106.34930.89450.2457Si quiero conocer el caudal para Tr = 100 aos,1932502.1502.106.21880.85880.30131933500.0500.006.21460.85750.3032sabiendo que Tr = 1 / P exc1934483.6483.606.18130.84720.31771935427.5427.506.05800.80470.3715--> Pexc = 1 / 100 =0.011936360.5360.505.88750.73530.4406--> Pno exc = 1-P exc =0.991937350.1350.105.85820.72230.45131938349.1349.105.85540.72100.4524z = f ( Pno exc)=DISTR.NORM.ESTAND.INV(0,99)1939331.0331.005.80210.69640.47051940325.1325.105.78410.68790.4763z =2.3263478741941320.1320.105.76860.68050.48111942303.8303.805.71640.65490.4960y =m + z s1943293.7293.705.68260.63800.50461944273.2273.205.61020.60090.5197y =5,435 + 2,326 * 1,8051945266.2266.205.58420.58740.52411946264.4264.405.57750.58380.5251y =7.14841947251.5251.505.52740.55740.53151948250.2250.205.52230.55460.5320y =ln (x)1949221.2221.205.39910.48870.53681950205.2205.205.32400.44850.5325x =e (y)1951197.3197.305.28470.42770.52821952188.1188.105.23700.40260.5209x =1272.11953187.2187.205.23220.40010.52011954183.1183.105.21000.38860.51601955180.1180.105.19350.38010.51261956175.0175.005.16480.36550.50621957170.8170.805.14050.35330.50031958169.5169.505.13290.34950.49831959160.3160.305.07700.32210.48271960159.9159.905.07450.32090.48191961146.3146.304.98570.27930.45261962146.1146.104.98430.27870.45211963146.0146.004.98360.27840.45181964145.3145.304.97880.27620.45011965137.8137.804.92580.25290.43031966132.9132.904.88960.23750.41611967128.5128.504.85590.22380.40241968119.3119.304.78160.19500.37121969118.5118.504.77490.19250.36831970100.2100.204.60720.13690.2951197196.996.904.57370.12720.2806197290.390.304.50310.10850.2507197353.153.103.97220.02560.0803197445.545.503.81770.01550.0524197544.344.303.79100.01410.0485

LN2

x (Caudales)histograma de los x

LN3

y = ln xhistograma de los y

GumbelANALISIS CON DISTRIBUCION LOG - NORMAL DE 3 PARAMETROSAOQQ ORDENADOSy = ln (x-a)F(x)f(x)MEDIA300.8419261600.01600.007.393300.997400.01219DESV.EST.280.0319271200.01200.007.110750.991010.03683MEDIA5.42021928720.0720.006.613480.946510.16497DESV.EST.0.74291929669.0669.006.542570.933770.195061930580.1580.106.405510.902620.260961931572.1572.106.392200.899100.26782C.ASIMETRIA0.20411932502.1502.106.267520.861580.33487Si quiero conocer el caudal para Tr = 100 aos,1933500.0500.006.263530.860240.337071934483.6483.606.231800.849260.35466sabiendo que Tr = 1 / P exc1935427.5427.506.114940.804030.419281936360.5360.505.954720.730120.50120--> Pexc = 1 / 100 =0.011937350.1350.105.927370.716240.51366--> Pno exc = 1-P exc =0.991938349.1349.105.924700.714870.514851939331.0331.005.875120.688820.53578z = f ( Pexc)=DISTR.NORM.ESTAND.INV(0,99)1940325.1325.105.858410.679810.542331941320.1320.105.844030.671970.54775z =2.3263478741942303.8303.805.795660.645060.564421943293.7293.705.764460.627300.57379y =m + z s1944273.2273.205.697990.588600.589881945266.2266.205.674240.574540.59427y =5,731 + 2,326 * 1,367MEDIA5.55031946264.4264.405.668040.570850.59529DESV.EST.0.65961947251.5251.505.622460.543560.60125y =7.0847a(25.0680)1948250.2250.205.617750.540730.601701949221.2221.205.506420.473490.60352y =ln (x - a)C.ASIMETRIA4.73E-011950205.2205.205.439240.433150.596351951197.3197.305.404330.412430.59023x - a =e (y)1952188.1188.105.362080.387690.580731953187.2187.205.357850.385230.57965x - a =1193.51896455191954183.1183.105.338350.373980.574421955180.1180.105.323830.365670.57024x =7413,477 - 25,0681956175.0175.005.298660.351410.562401957170.8170.805.277440.339550.55526x =1168.51958169.5169.505.270780.335870.552911959160.3160.305.222340.309520.534531960159.9159.905.220180.308360.533651961146.3146.305.143810.268860.500241962146.1146.105.142650.268270.499701963146.0146.005.142060.267980.499421964145.3145.305.137960.265940.497501965137.8137.805.092940.244030.475601966132.9132.905.062390.229730.460081967128.5128.505.034140.216940.445321968119.3119.304.972370.190460.412041969118.5118.504.966810.188170.408991970100.2100.204.830460.137550.33343197196.996.904.803760.128850.31876197290.390.304.748130.111950.28871197353.153.104.358860.035430.11833197445.545.504.256580.024910.08835197544.344.304.239430.023440.08393

Gumbel

LN3; C.A.=0

parm Gumb0.01667897280.04293209480.15899828450.18462040790.23993325120.24565176450.30133250010.30316082620.31774936720.37149374430.44062662530.45133442530.45235691690.47054168620.47629548930.48108407880.49599483260.50455413840.51974068680.52408627620.52512246610.53145523950.53197780120.5368052510.53253747180.52816692750.52093462220.52009493330.51595642780.51259383760.5062024150.50027554810.49831569380.48268079540.48192879840.45257988610.4520918880.45184726070.45012312270.43034540540.41611632420.40244858360.37115165090.36825825570.29505203790.28056324810.25065699360.08034638390.05242786650.0484814267

LN2; C.A.=-0,8

GammaANALISIS CON DISTRIBUCION GUMBELVar. ReducidaAOQQ ORDENADOSy = (x - u)/aTr19261600.01600.005.93377.9519271200.01200.004.2872.411928720.0720.002.2910.341929669.0669.002.078.471930580.1580.101.716.021931572.1572.101.675.841932502.1502.101.384.511933500.0500.001.374.471934483.6483.601.314.211935427.5427.501.073.451936360.5360.500.802.751937350.1350.100.752.661938349.1349.100.752.651939331.0331.000.672.501940325.1325.100.652.461941320.1320.100.632.421942303.8303.800.562.301943293.7293.700.522.231944273.2273.200.432.101945266.2266.200.402.051946264.4264.400.402.041947251.5251.500.341.971948250.2250.200.341.961949221.2221.200.221.811950205.2205.200.151.731951197.3197.300.121.701952188.1188.100.081.661953187.2187.200.081.661954183.1183.100.061.641955180.1180.100.051.631956175.0175.000.031.611957170.8170.800.011.591958169.5169.500.001.591959160.3160.30(0.03)1.551960159.9159.90(0.04)1.551961146.3146.30(0.09)1.501962146.1146.10(0.09)1.501963146.0146.00(0.09)1.501964145.3145.30(0.10)1.501965137.8137.80(0.13)1.471966132.9132.90(0.15)1.461967128.5128.50(0.17)1.441968119.3119.30(0.20)1.421969118.5118.50(0.21)1.411970100.2100.20(0.28)1.36197196.996.90(0.30)1.35197290.390.30(0.32)1.33197353.153.10(0.48)1.25197445.545.50(0.51)1.23197544.344.30(0.51)1.23P exc = F (x > X)Si quiero conocer el caudal para Tr = 100 aos,sabiendo que:0.021 - e(-e(-y))=0.02e(-e(-y))=0.98-e(-y)=-0.0202027073e(-y)=0.0202027073-y =-3.9019386579x medio300.840.5485179.0000y =3.9019386579desv. Est x (Sx)280.031.160713.3000y =x-un = nmero de datos5032ayn medio =0.54850.538Sn =1.16071.1193x =u + a.yparmetros, segn nx =1109.9219.0a = Sx / Sn =241.2611.88u = x-yn*a=168.51172.61

Gamma

Tr (AOS)Q (m3/s))

Person IIIVALORES GUMBELMedia reducida Ynn0123456789100.49520.49960.50350.50700.51000.51280.51570.51810.52020.5220200.52300.52520.52680.52830.52960.53090.53200.53320.53430.5353300.53620.53710.53800.53880.53960.54020.54100.54180.54240.5430400.54360.54420.54480.54530.54580.54630.54680.54730.54770.5481500.54850.54890.54930.54970.55010.55040.55080.55110.55150.5518600.55210.55240.55270.55300.55330.55350.55380.55400.55430.5545700.55480.55500.55520.55550.55570.55590.55610.55630.55650.5567800.55690.55700.55720.55740.55760.55780.55800.55810.55830.5585900.55860.55870.55890.55910.55920.55930.55950.55960.55980.55991000.5600Desviacin tipica reducida Snn0123456789100.94960.96760.98330.99711.00951.02061.03161.04111.04931.0565201.06281.06961.07541.08111.08641.09151.09611.10041.10471.1086301.11241.11591.11931.22601.12551.12851.13131.13391.13631.3880401.14131.14301.14581.14801.14991.15191.15381.15571.15741.1590501.16071.16231.16381.16581.16671.16811.16961.17081.17211.1734601.17471.17591.17701.17821.17931.18031.18141.18241.18341.1844701.18541.18631.18731.18811.18901.18981.19061.19151.19231.1930801.19381.19451.19531.19591.19671.19731.19801.19871.19941.2001901.20071.20131.20201.20261.20321.20381.20441.20491.20551.20601001.2065

Bondad SKANALISIS CON DISTRIBUCION GAMMA DE 2 PARAMETROSAOSANCHEZ CERRODATOS ORDENADOSf(x)F(x)19261600.01600.001.176E-059.969E-0119271200.01200.005.218E-059.860E-011928720.0720.003.041E-049.172E-011929669.0669.003.657E-049.001E-011930580.1580.105.031E-048.618E-011931572.1572.105.177E-048.578E-011932502.1502.106.637E-048.166E-011933500.0500.006.687E-048.152E-011934483.6483.607.084E-048.039E-011935427.5427.508.620E-047.600E-011936360.5360.501.086E-036.950E-011937350.1350.101.125E-036.835E-01x (media)300.81938349.1349.101.129E-036.824E-01s2 (varianza)78416.21939331.0331.001.200E-036.613E-01a1.1541940325.1325.101.224E-036.542E-01b260.661941320.1320.101.245E-036.480E-011942303.8303.801.314E-036.271E-011943293.7293.701.359E-036.136E-01Si quiero conocer el caudal para Tr = 100 aos,1944273.2273.201.454E-035.848E-011945266.2266.201.488E-035.745E-01sabiendo que Tr = 1 / Pno exc1946264.4264.401.497E-035.718E-011947251.5251.501.560E-035.521E-01--> P exc = 1 / 100 =0.011948250.2250.201.567E-035.501E-01--> Pno exc = 1-P exc =0.991949221.2221.201.718E-035.025E-011950205.2205.201.806E-034.743E-01x = f ( Pno exc)=DISTR.GAMMA.INV(P;a;b)1951197.3197.301.850E-034.598E-011952188.1188.101.903E-034.426E-01x =1290.05916747421953187.2187.201.908E-034.409E-011954183.1183.101.932E-034.330E-011955180.1180.101.949E-034.272E-011956175.0175.001.979E-034.172E-011957170.8170.802.003E-034.088E-011958169.5169.502.011E-034.062E-011959160.3160.302.066E-033.874E-011960159.9159.902.068E-033.866E-011961146.3146.302.149E-033.579E-011962146.1146.102.150E-033.575E-011963146.0146.002.151E-033.573E-011964145.3145.302.155E-033.558E-011965137.8137.802.200E-033.394E-011966132.9132.902.229E-033.286E-011967128.5128.502.255E-033.187E-011968119.3119.302.310E-032.977E-011969118.5118.502.314E-032.959E-011970100.2100.202.419E-032.526E-01197196.996.902.438E-032.445E-01197290.390.302.473E-032.283E-01197353.153.102.628E-031.331E-01197445.545.502.642E-031.131E-01197544.344.302.644E-031.099E-01

Bondad SK

f(x)

F(x)

Valores de "K", para la distribucin Pearson tipo IIICoeficiente de asimetraNivel de probabilidad, porcentaje9980502010421Periodo de retorno en aosg1.01011.25251025501003-0.667-0.636-0.3960.421.182.2783.1524.0512.8-0.714-0.666-0.3840.461.212.2753.1143.9732.6-0.769-0.696-0.3680.4991.2382.2673.0713.8892.4-0.832-0.725-0.3510.5371.2622.2563.0233.82.2-0.905-0.752-0.330.5741.2842.242.973.7052-0.99-0.777-0.3070.6091.3022.2192.9123.6051.8-1.087-0.7999-0.2820.6431.3182.1932.8483.4991.6-1.197-0.8177-0.2540.6751.3292.1632.783.3881.4-1.318-0.8332-0.2250.7051.3372.1282.7063.2711.2-1.449-0.844-0.1950.7321.342.0872.6263.1491-1.558-0.852-0.1640.7581.342.0432.5423.0220.8-1.733-0.856-0.1320.781.3361.9932.4532.8910.6-1.88-0.857-0.0990.81.3281.9392.3592.7550.4-2.029-0.855-0.0660.8161.3171.882.2612.6150.2-2.178-0.85-0.0330.831.3011.8182.1592.4720-2.326-0.84200.8421.2821.7512.0542.326-0.2-2.472-0.830.0330.851.2581.681.9452.178-0.4-2.615-0.8160.0660.8551.2321.6061.8342.029-0.6-2.755-0.80.0990.8571.21.5281.721.88-0.8-2.891-0.780.1320.8561.1661.4481.6061.733-1-3.022-0.7580.1640.8521.1281.3661.4921.588-1.2-3.149-0.7320.1950.8441.0861.2821.3791.449-1.4-3.271-0.7050.2250.8321.0411.1981.271.318-1.6-3.388-0.6750.2540.8170.9941.1161.1661.197-1.8-3.499-0.6430.2820.7990.9451.0351.0691.087-2-3.605-0.6090.3070.7770.8950.9580.980.99-2.2-3.705-0.5740.330.7520.8440.8880.90.905-2.4-3.8-0.5370.3510.7250.7950.8230.830.832-2.6-3.889-0.4990.3680.6960.7470.7640.7680.769-2.8-3.973-0.460.3840.6660.7020.7120.7140.714-3-4.051-0.420.3960.6360.660.6660.6660.667

Parmetros: Forma: x> 0Escala: x > 0

1.01011.2525102550100Coeficiente de asimetra, gcoeficiente KK versus g para diferentes TrK(Tr) = f (g)

Probabilidad de excedencia F(x)Diferencia Delta DDATOSEmpricaNormalLN2LN3GumbelGammaNormalLN2LN3GumbelGamma11600.00.0200.0000.0040.0030.0030.0030.020410.016200.017810.017760.0172721200.00.0410.0010.0120.0090.0140.0140.040150.028520.031820.027010.026823720.00.0610.0670.0590.0530.0970.0830.005990.001870.007740.035460.021604669.00.0820.0940.0720.0660.1180.1000.012670.009670.015400.036420.018235580.10.1020.1590.1020.0970.1660.1380.057280.000110.004660.064010.036126572.10.1220.1660.1060.1010.1710.1420.043900.016930.021550.048700.019807502.10.1430.2360.1410.1380.2220.1830.093300.001670.004430.079040.040548500.00.1630.2380.1420.1400.2240.1850.075210.020810.023500.060340.021539483.60.1840.2570.1530.1510.2370.1960.073320.030870.032930.053630.0124110427.50.2040.3260.1950.1960.2900.2400.121440.008770.008110.085440.0359211360.50.2240.4160.2650.2700.3630.3050.191150.040170.045390.138660.0805012350.10.2450.4300.2780.2840.3760.3160.185280.032820.038860.130790.0715813349.10.2650.4320.2790.2850.3770.3180.166280.013710.019820.111600.0523014331.00.2860.4570.3040.3110.3990.3390.171400.017870.025470.113740.0529615325.10.3060.4650.3120.3200.4070.3460.159360.005980.014070.100860.0397016320.10.3270.4730.3200.3280.4130.3520.146050.007010.001500.086910.0254717303.80.3470.4960.3450.3550.4350.3730.148840.001880.008000.087970.0259118293.70.3670.5100.3620.3730.4490.3860.142820.005370.005350.081190.0190119273.20.3880.5390.3990.4110.4770.4150.151560.011310.023650.089130.0274320266.20.4080.5490.4130.4250.4870.4250.141060.004450.017300.078610.0173221264.40.4290.5520.4160.4290.4890.4280.123200.012400.000580.060760.0004122251.50.4490.5700.4430.4560.5080.4480.120950.006370.007460.058850.0011023250.20.4690.5720.4450.4590.5100.4500.102370.024030.010120.040330.0194824221.20.4900.6120.5110.5270.5520.4980.122150.021550.036720.062580.0077325205.20.5100.6340.5520.5670.5760.5260.123450.041320.056650.066180.0155126197.30.5310.6440.5720.5880.5880.5400.113600.041740.056950.057710.0095527188.10.5510.6560.5970.6120.6020.5570.105360.046390.061290.051260.0064128187.20.5710.6580.6000.6150.6040.5590.086130.028470.043340.032220.0122929183.10.5920.6630.6110.6260.6100.5670.071090.019540.034190.018050.0248230180.10.6120.6670.6200.6340.6140.5730.054580.007630.022090.002210.0394131175.00.6330.6730.6350.6490.6220.5830.040770.001850.015930.010430.0498032170.80.6530.6790.6470.6600.6290.5910.025750.006330.007380.024430.0618533169.50.6730.6800.6510.6640.6310.5940.007000.022920.009330.042860.0796534160.30.6940.6920.6780.6900.6450.6130.001750.015950.003400.049240.0813035159.90.7140.6930.6790.6920.6450.6130.021660.035150.022650.069040.1008836146.30.7350.7090.7210.7310.6660.6420.025210.013990.003550.068760.0926237146.10.7550.7100.7210.7320.6660.6430.045380.033780.023370.088860.1126038146.00.7760.7100.7220.7320.6660.6430.065660.053880.043490.109120.1327939145.30.7960.7110.7240.7340.6670.6440.085210.072120.061850.128460.1516940137.80.8160.7200.7470.7560.6790.6610.096530.069190.060350.137510.1557741132.90.8370.7260.7620.7700.6860.6710.111080.074270.066470.150520.1653342128.50.8570.7310.7760.7830.6930.6810.126280.080900.074090.164300.1758743119.30.8780.7420.8050.8100.7070.7020.135950.072560.068010.170940.1752844118.50.8980.7430.8070.8120.7080.7040.155430.090490.086130.190150.1938345100.20.9180.7630.8630.8620.7350.7470.155210.055250.055920.183560.170924696.90.9390.7670.8730.8710.7400.7550.172000.066020.067620.199170.183314790.30.9590.7740.8910.8880.7490.7720.185250.067700.071140.210040.187524853.10.9800.8120.9740.9650.8010.8670.167750.005230.015020.178790.112724945.51.0000.8190.9850.9750.8110.8870.180930.015500.024910.189180.113105044.31.0200.8200.9860.9770.8120.8900.200210.034560.043840.208020.130330.200210.090490.086130.210040.19383RechazadaAceptadaAceptadaRechazadaAceptada0.19230.1923330445

Tr = 100Tr = 1.01

MBD0036F04A.unknown


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