P ordenados N° orden Tr (años)Año P max 24 h1988 34.00 225.50 1.00 28.00 0.96431989 116.80 131.60 2.00 14.00 0.92861990 46.50 120.00 3.00 9.33 0.89291991 96.90 116.80 4.00 7.00 0.85711992 69.50 108.00 5.00 5.60 0.82141993 45.20 96.90 6.00 4.67 0.78571994 42.30 96.80 7.00 4.00 0.75001995 60.00 82.00 8.00 3.50 0.71431996 72.50 79.00 9.00 3.11 0.67861997 108.00 76.00 10.00 2.80 0.64291998 120.00 74.30 11.00 2.55 0.60711999 60.00 72.50 12.00 2.33 0.57142000 76.00 71.20 13.00 2.15 0.53572001 82.00 69.50 14.00 2.00 0.50002002 79.00 68.40 15.00 1.87 0.46432003 225.50 67.50 16.00 1.75 0.42862004 44.60 65.20 17.00 1.65 0.39292005 65.20 62.10 18.00 1.56 0.35712006 56.50 60.00 19.00 1.47 0.32142007 74.30 60.00 20.00 1.40 0.28572008 62.10 57.90 21.00 1.33 0.25002009 68.40 56.50 22.00 1.27 0.21432010 57.90 46.50 23.00 1.22 0.17862011 131.60 45.20 24.00 1.17 0.14292012 96.80 44.60 25.00 1.12 0.10712013 71.20 42.30 26.00 1.08 0.07142014 67.50 34.00 27.00 1.04 0.0357

Parametros de la funcion Error cuadratico mínimo

78.90

38.33

P(X≤x)

𝜇=1/(𝑛−1) ∑24_(𝑖=1)^𝑛▒𝑥_1 =𝜎=[1/( −1) ∑_( =1)^ ( _ − ̅ )^2 𝑛 𝑖 𝑛▒ 𝑥 𝑖 𝑥 ]^(1/2)=𝐶=[∑24_(𝑖=1)^𝑛▒( _( _ )− _( _ ) )𝑥 𝑒 𝑖 𝑥 𝑜 𝑖 ^2 ]^(1/2)=

0 20 40 60 80 100 1200.00

50.00

100.00

150.00

200.00

250.00

Ph de campoPh etimadas

Probabilida en %

Prec

ipita

cione

s, m

m

0 20 40 60 80 100 1200.00

50.00

100.00

150.00

200.00

250.00

Ph de campoPh etimadas

Probabilida en %

Prec

ipita

cione

s, m

m

Z P calculado(P-Pc)2 Probabilidad

1.80 148.00 6006.4658 96.4285714291.47 135.06 11.9852814 92.8571428571.24 126.50 42.2550136 89.2857142861.07 119.82 9.11835506 85.7142857140.92 114.19 38.3764324 82.1428571430.79 109.24 152.356387 78.5714285710.67 104.75 63.2500816 750.57 100.59 345.68665 71.4285714290.46 96.67 312.362518 67.8571428570.37 92.93 286.717956 64.2857142860.27 89.32 225.632842 60.7142857140.18 85.80 176.885231 57.1428571430.09 82.34 124.00971 53.5714285710.00 78.90 88.36 50-0.09 75.46 49.9005945 46.428571429-0.18 72.00 20.2516135 42.857142857-0.27 68.48 10.7513168 39.285714286-0.37 64.87 7.65768348 35.714285714-0.46 61.13 1.26837031 32.142857143-0.57 57.21 7.79889636 28.571428571-0.67 53.05 23.5515313 25-0.79 48.56 63.095585 21.428571429-0.92 43.61 8.38028078 17.857142857-1.07 37.98 52.1235109 14.285714286-1.24 31.30 176.900258 10.714285714-1.47 22.74 382.670925 7.1428571429-1.80 9.80 585.572618 3.5714285714

96.29841868𝐶=[∑24_(𝑖=1)^𝑛▒( _( _ )− _( _ ) )𝑥 𝑒 𝑖 𝑥 𝑜 𝑖 ^2 ]^(1/2)=

0 20 40 60 80 100 1200.00

50.00

100.00

150.00

200.00

250.00

Ph de campoPh etimadas

Probabilida en %

Prec

ipita

cione

s, m

m

0 20 40 60 80 100 1200.00

50.00

100.00

150.00

200.00

250.00

Ph de campoPh etimadas

Probabilida en %

Prec

ipita

cione

s, m

m

Precipitaciones de diseño de la distribución normal estandarTr (años) P(X≤x) Z Precipitaciones

2 0.5 0 78.95 0.8 0.84162123 111.1590921604410 0.9 1.28155157 128.0214912505825 0.96 1.75068607 146.0032776546850 0.98 2.05374891 157.61958636453

100 0.99 2.32634787 168.06822374755250 0.996 2.65206981 180.55304882558500 0.998 2.87816174 189.21908546314

1000 0.999 3.09023231 197.3476873743110000 0.9999 3.71901649 221.4487983961520000 0.99995 3.89059189 228.02523260569

P ordenados N° orden Tr (años) In (P)Año P max 24 h1988 34.00 225.50 1.00 28.00 5.421989 116.80 131.60 2.00 14.00 4.881990 46.50 120.00 3.00 9.33 4.791991 96.90 116.80 4.00 7.00 4.761992 69.50 108.00 5.00 5.60 4.681993 45.20 96.90 6.00 4.67 4.571994 42.30 96.80 7.00 4.00 4.571995 60.00 82.00 8.00 3.50 4.411996 72.50 79.00 9.00 3.11 4.371997 108.00 76.00 10.00 2.80 4.331998 120.00 74.30 11.00 2.55 4.311999 60.00 72.50 12.00 2.33 4.282000 76.00 71.20 13.00 2.15 4.272001 82.00 69.50 14.00 2.00 4.242002 79.00 68.40 15.00 1.87 4.232003 225.50 67.50 16.00 1.75 4.212004 44.60 65.20 17.00 1.65 4.182005 65.20 62.10 18.00 1.56 4.132006 56.50 60.00 19.00 1.47 4.092007 74.30 60.00 20.00 1.40 4.092008 62.10 57.90 21.00 1.33 4.062009 68.40 56.50 22.00 1.27 4.032010 57.90 46.50 23.00 1.22 3.842011 131.60 45.20 24.00 1.17 3.812012 96.80 44.60 25.00 1.12 3.802013 71.20 42.30 26.00 1.08 3.742014 67.50 34.00 27.00 1.04 3.53

Parametros

4.28239634

0.40319459

𝛼=∑24_(𝑖=1)^𝑛▒〖〖 ln 𝑥〗 _𝑖/𝑛=〗𝛽=[∑24_(𝑖=1)^𝑛▒(〖 ln 𝑥〗 _𝑖−𝛼)^2/𝑛]^(1/2)=

𝐶=[∑24_(𝑖=1)^𝑛▒( _( _ )− _( _ ) )𝑥 𝑒 𝑖 𝑥 𝑜 𝑖 ^2 ]^(1/2)=

1 10 10010.00

100.00

1000.00

Ph de campoPh estimadas

Probabilidad en %

Prec

ipita

cion,

mm

Z P calculado(P-Pc)2 Probabilidad

0.9643 1.80 149.79 5731.58926 96.42857140.9286 1.47 130.73 0.74860814 92.85714290.8929 1.24 119.48 0.27522764 89.28571430.8571 1.07 111.37 29.5127132 85.71428570.8214 0.92 104.97 9.18561553 82.14285710.7857 0.79 99.64 7.51691482 78.57142860.7500 0.67 95.04 3.08119448 750.7143 0.57 90.97 80.5491548 71.42857140.6786 0.46 87.30 68.9049762 67.85714290.6429 0.37 83.93 62.9186144 64.28571430.6071 0.27 80.80 42.2919445 60.71428570.5714 0.18 77.86 28.7830537 57.14285710.5357 0.09 75.08 15.0459174 53.57142860.5000 0.00 72.41 8.48999835 500.4643 -0.09 69.84 2.08288639 46.42857140.4286 -0.18 67.34 0.02428323 42.85714290.3929 -0.27 64.90 0.09281879 39.28571430.3571 -0.37 62.48 0.14145837 35.71428570.3214 -0.46 60.07 0.00426078 32.14285710.2857 -0.57 57.64 5.57175937 28.57142860.2500 -0.67 55.17 7.44495193 250.2143 -0.79 52.63 15.0072075 21.42857140.1786 -0.92 49.96 11.9380243 17.85714290.1429 -1.07 47.09 3.55379279 14.28571430.1071 -1.24 43.89 0.50435798 10.71428570.0714 -1.47 40.11 4.79674681 7.142857140.0357 -1.80 35.01 1.01348738 3.57142857

Error cuadratico mínimo

78.3649745

P(X≤x)

𝐶=[∑24_(𝑖=1)^𝑛▒( _( _ )− _( _ ) )𝑥 𝑒 𝑖 𝑥 𝑜 𝑖 ^2 ]^(1/2)=

1 10 10010.00

100.00

1000.00

Ph de campoPh estimadas

Probabilidad en %

Prec

ipita

cion,

mm

Eventos de diseño de la distribución Log normalTr (años) P(X≤x) Z Precipitaciones

2 0.5 0.000 72.415 0.8 0.842 101.6710 0.9 1.282 121.4025 0.96 1.751 146.6850 0.98 2.054 165.75

100 0.99 2.326 185.00250 0.996 2.652 210.97500 0.998 2.878 231.10

1000 0.999 3.090 251.7310000 0.9999 3.719 324.3720000 0.99995 3.891 347.60

P ordenados N° orden Tr (años)Año P max 24 h1988 34.00 225.50 1 28.00 0.96431989 116.80 131.60 2 14.00 0.92861990 46.50 120.00 3 9.33 0.89291991 96.90 116.80 4 7.00 0.85711992 69.50 108.00 5 5.60 0.82141993 45.20 96.90 6 4.67 0.78571994 42.30 96.80 7 4.00 0.75001995 60.00 82.00 8 3.50 0.71431996 72.50 79.00 9 3.11 0.67861997 108.00 76.00 10 2.80 0.64291998 120.00 74.30 11 2.55 0.60711999 60.00 72.50 12 2.33 0.57142000 76.00 71.20 13 2.15 0.53572001 82.00 69.50 14 2.00 0.50002002 79.00 68.40 15 1.87 0.46432003 225.50 67.50 16 1.75 0.42862004 44.60 65.20 17 1.65 0.39292005 65.20 62.10 18 1.56 0.35712006 56.50 60.00 19 1.47 0.32142007 74.30 60.00 20 1.40 0.28572008 62.10 57.90 21 1.33 0.25002009 68.40 56.50 22 1.27 0.21432010 57.90 46.50 23 1.22 0.17862011 131.60 45.20 24 1.17 0.14292012 96.80 44.60 25 1.12 0.10712013 71.20 42.30 26 1.08 0.07142014 67.50 34.00 27 1.04 0.0357

PARAMÉTROS

2.330438694 0.73652014

78.90 44.6625118

P(X≤x)

𝛾=∑24_(𝑖=1)^𝑛▒〖 ((𝑥_𝑖−𝑥)^3∕𝑛)/𝑆^3 =〗𝑥 ̅=1/(𝑛−1) ∑24_(𝑖=1)^𝑛▒𝑥_1 =

𝛽_1=(2/𝛾)^2=𝛼_1=𝑆/√( _1𝛽 )=

38.32970328 46.0051606

1.47304028

𝑆=[1/( −1) ∑_( =1)^ ( _ − ̅ )^2 𝑛 𝑖 𝑛▒ 𝑥 𝑖 𝑥 ]^(1/2)=

𝛼_1=𝑆/√( _1𝛽 )=𝛿_1=𝑥 ̅− _1 _1=𝛼 𝛽

𝜗=2𝛽_1=

0 20 40 60 80 100 1200.00

50.00

100.00

150.00

200.00

250.00

Ph de campoPh calculado

Axis Title

Axis

Title

INTERPOLACIÓN LINEAL

X Y0.99 7.92 1

0.99995 10.5468 1.50.995 9.24 2

y y/2 Ph calculada(P-Pc)2 Probabilidad

6.78 3.392 197.51 783.620306 96.63634795.40 2.699 166.56 1222.34429 93.27464664.51 2.257 146.83 719.605523 89.53758584.04 2.019 136.19 376.03154 86.72497473.56 1.781 125.56 308.269364 83.15624933.09 1.543 114.92 324.852677 78.62814332.61 1.305 104.29 56.0961833 72.88274652.44 1.218 100.40 338.476088 70.41365192.26 1.131 96.51 306.449559 67.71973992.09 1.044 92.61 276.014425 64.78054051.91 0.956 88.72 207.984363 61.57371951.74 0.869 84.83 152.020123 58.07490931.56 0.782 80.94 94.8213447 54.25752361.39 0.695 77.05 56.9361747 50.09255521.27 0.637 74.45 36.5494014 47.10099811.16 0.579 71.85 18.8843599 43.93012071.04 0.520 69.25 16.3670221 40.56917430.92 0.462 66.65 20.6626741 37.00676570.81 0.404 64.05 16.3670832 33.23081880.69 0.346 61.45 2.08984313 29.22853380.58 0.288 58.85 0.8942213 24.98634330.49 0.244 56.91 0.168311 21.66429360.40 0.201 54.97 71.8236202 18.19512380.32 0.158 53.04 61.4578576 14.57231860.23 0.114 51.10 42.3037161 10.78907410.15 0.075 49.34 49.5460863 7.192511750.07 0.036 47.62 185.400935 3.54286069

ERROR CUADRÁTICO MÍNIMO

E.C.M= 75.80261933

1.5

0 20 40 60 80 100 1200.00

50.00

100.00

150.00

200.00

250.00

Ph de campoPh calculado

Axis Title

Axis

Title

6.637.929.21

Eventos de diseño de la distribución Pearson IIITr (años) P(X≤x) y y/2 Precipitaciones

2 0.5 1.39 0.695 77.055 0.8 3.38 1.692 121.56

10 0.9 4.61 2.305 148.9525 0.96 6.55 3.273 192.1950 0.98 7.99 3.995 224.43100 0.99 9.21 4.605 251.68250 0.996 10.88 5.439 288.92500 0.998 11.43 5.717 301.34

1000 0.999 11.71 5.856 307.5510000 0.9999 11.96 5.981 313.1420000 0.99995 11.9761 5.98805 313.4465145485

1 0 0 0 46.00516059839

P ordenados N° orden Tr (años)Año P max 24 h1988 34.00 225.50 1 28.00 0.96431989 116.80 131.60 2 14.00 0.92861990 46.50 120.00 3 9.33 0.89291991 96.90 116.80 4 7.00 0.85711992 69.50 108.00 5 5.60 0.82141993 45.20 96.90 6 4.67 0.78571994 42.30 96.80 7 4.00 0.75001995 60.00 82.00 8 3.50 0.71431996 72.50 79.00 9 3.11 0.67861997 108.00 76.00 10 2.80 0.64291998 120.00 74.30 11 2.55 0.60711999 60.00 72.50 12 2.33 0.57142000 76.00 71.20 13 2.15 0.53572001 82.00 69.50 14 2.00 0.50002002 79.00 68.40 15 1.87 0.46432003 225.50 67.50 16 1.75 0.42862004 44.60 65.20 17 1.65 0.39292005 65.20 62.10 18 1.56 0.35712006 56.50 60.00 19 1.47 0.32142007 74.30 60.00 20 1.40 0.28572008 62.10 57.90 21 1.33 0.25002009 68.40 56.50 22 1.27 0.21432010 57.90 46.50 23 1.22 0.17862011 131.60 45.20 24 1.17 0.14292012 96.80 44.60 25 1.12 0.10712013 71.20 42.30 26 1.08 0.07142014 67.50 34.00 27 1.04 0.0357

Parametros

de la tabla 9.6 del libro de aparicio interpolando para 27 años se tiene que

0.53302 0.02869315

1.0998 60.323442

S= 38.3297033

P(X≤x)

𝜇_𝑦=𝜎_𝑦=

𝛼=𝜎_𝑦/𝑆=𝛽=𝑥 ̅− _𝜇 𝑦/𝛼=

78.90

Error cuadratico minimo

ECM= 73.2296114

𝑥 ̅=

In ln (1/F(x)) P calculado (P-Pc)2Probabilidad

-3.3141 175.82 2467.70 96.428571429-2.6022 151.02 376.95 92.857142857-2.1775 136.21 262.81 89.285714286-1.8698 125.49 75.51 85.714285714-1.6260 116.99 80.87 82.142857143-1.4223 109.89 168.80 78.571428571-1.2459 103.74 48.23 75-1.0892 98.29 265.20 71.428571429-0.9474 93.34 205.64 67.857142857-0.8168 88.79 163.61 64.285714286-0.6952 84.55 105.08 60.714285714-0.5805 80.55 64.88 57.142857143-0.4714 76.75 30.81 53.571428571-0.3665 73.10 12.94 50-0.2649 69.56 1.34 46.428571429-0.1657 66.10 1.96 42.857142857-0.0679 62.69 6.29 39.2857142860.0292 59.31 7.81 35.7142857140.1266 55.91 16.72 32.1428571430.2254 52.47 56.71 28.5714285710.3266 48.94 80.29 250.4321 45.27 126.22 21.4285714290.5439 41.37 26.35 17.8571428570.6657 37.12 65.26 14.2857142860.8036 32.32 150.89 10.7142857140.9704 26.50 249.55 7.14285714291.2036 18.37 244.14 3.5714285714

1 10 10010.00

100.00

1000.00

P estimado P campo

Probabilidad en %

Prec

ipita

ción,

mm

1 10 10010.00

100.00

1000.00

P estimado P campo

Probabilidad en %

Prec

ipita

ción,

mm

Eventos de diseño de la distribución GumbelTr (años) P(X≤x) In ln (1/F(x)) Precipitaciones

2 0.5 -0.3665 73.105 0.8 -1.4999 112.6010 0.9 -2.2504 138.7525 0.96 -3.1985 171.8050 0.98 -3.9019 196.31

100 0.99 -4.6001 220.65250 0.996 -5.5195 252.68500 0.998 -6.2136 276.881000 0.999 -6.9073 301.05

10000 0.9999 -9.2103 381.3220000 0.99995 -9.903462552 405.4741795411

1 10 10010.00

100.00

1000.00

P estimado P campo

Probabilidad en %

Prec

ipita

ción,

mm

1 10 10010.00

100.00

1000.00

P estimado P campo

Probabilidad en %

Prec

ipita

ción,

mm

Año P max 24 h P ordenados N° orden Tr (años)1988 34.00 225.50 1 28 0.96431989 116.80 131.60 2 14 0.92861990 46.50 120.00 3 9.33333333 0.89291991 96.90 116.80 4 7 0.85711992 69.50 108.00 5 5.6 0.82141993 45.20 96.90 6 4.66666667 0.78571994 42.30 96.80 7 4 0.75001995 60.00 82.00 8 3.5 0.71431996 72.50 79.00 9 3.11111111 0.67861997 108.00 76.00 10 2.8 0.64291998 120.00 74.30 11 2.54545455 0.60711999 60.00 72.50 12 2.33333333 0.57142000 76.00 71.20 13 2.15384615 0.53572001 82.00 69.50 14 2 0.50002002 79.00 68.40 15 1.86666667 0.46432003 225.50 67.50 16 1.75 0.42862004 44.60 65.20 17 1.64705882 0.39292005 65.20 62.10 18 1.55555556 0.35712006 56.50 60.00 19 1.47368421 0.32142007 74.30 60.00 20 1.4 0.28572008 62.10 57.90 21 1.33333333 0.25002009 68.40 56.50 22 1.27272727 0.21432010 57.90 46.50 23 1.2173913 0.17862011 131.60 45.20 24 1.16666667 0.14292012 96.80 44.60 25 1.12 0.10712013 71.20 42.30 26 1.07692308 0.07142014 67.50 34.00 27 1.03703704 0.0357

Población ciclónica 5Población no ciclónica 22

Probabilidad que en un año cualquiera sea no ciclonico=

Población ciclónica 5 datos

140.38 0.4776S2= 48.3278595

0.87860.01817999

P(X≤x)

𝑥 ̅2=𝛼2=𝜎_𝑦/𝑆=

𝛽2=𝑥 ̅− _𝜇 𝑦/𝛼=

𝜇_𝑦2=𝜎_𝑦2=

166.650642

Población no ciclónica 22 datos

64.93 0.52652S1= 16.4198249

1.074240.06542335

56.8793819

Error cuadratico minimo

EMC= 103.199329

𝛽2=𝑥 ̅− _𝜇 𝑦/𝛼=

𝑥 ̅1=𝛼1=𝜎_𝑦/𝑆=

𝛽1=𝑥 ̅− _𝜇 𝑦/𝛼=

𝜇_𝑦1=𝜎_𝑦1=

In ln (1/F(x)) P calculado (P-Pc)2 Probabilidad-3.3140758 251.396 670.60 96.43 x

-2.60223217 206.28 5577.10 92.86 f(x)-2.17746296 175.1 3036.01 89.30-1.86982471 147.3 930.25 85.72-1.62602322 121.29 176.62 82.15-1.42228614 103.89 48.86 78.58-1.24589932 94 7.84 75.01-1.08923964 87.5 30.25 71.44-0.94735442 82.66 13.40 67.86-0.81682386 78.79 7.78 64.30-0.69516689 75.1 0.64 60.22-0.58050482 72.68 0.03 57.15-0.47135765 70.14 1.12 53.58-0.36651292 67.829 2.79 50.02-0.26493587 65.669 7.46 46.44-0.16570298 63.64 14.90 42.87-0.06794781 61.7 12.25 39.300.02918924 59.82 5.20 35.720.12661497 57.986 4.06 32.150.22535149 56.161 14.74 28.570.32663426 54.33 12.74 25.000.43207136 52.46 16.32 21.440.54393149 50.501 16.01 17.860.66572981 48.41 10.30 14.300.80361115 46.067 2.15 10.720.97042178 43.28 0.96 7.141.2036341 39.45 29.70 3.57

0.81481481

se interpolo de la tabla 9.6

0.00 20.00 40.00 60.00 80.00 100.00 120.000.00

50.00

100.00

150.00

200.00

250.00

300.00

P de campoP estimado

Axis Title

Axis

Title

se interpolo de la tabla 9.6

0.00 20.00 40.00 60.00 80.00 100.00 120.000.00

50.00

100.00

150.00

200.00

250.00

300.00

P de campoP estimado

Axis Title

Axis

Title

funcion225.5 Eventos de diseño de la distribución Gumbel

0.9462074935 Tr (años) P(X≤x) Precipitaciones2 0.5 67.8175 0.8 109.59910 0.9 180.79125 0.96 244.4150 0.98 285.99

100 0.99 325.69250 0.996 377.01500 0.998 415.46

1000 0.999 453.710210000 0.9999 580.49920000 0.99995 630

0.00 20.00 40.00 60.00 80.00 100.00 120.000.00

50.00

100.00

150.00

200.00

250.00

300.00

P de campoP estimado

Axis Title

Axis

Title

0.00 20.00 40.00 60.00 80.00 100.00 120.000.00

50.00

100.00

150.00

200.00

250.00

300.00

P de campoP estimado

Axis Title

Axis

Title

Función Distribución normal estandarRango=

Año P max 24 h intervalo=1988 34.00 225.501989 116.80 131.601990 46.50 120.001991 96.90 116.80 intervalo1992 69.50 108.001993 45.20 96.90 11994 42.30 96.80 21995 60.00 82.00 31996 72.50 79.00 4

51997 108.00 76.00 61998 120.00 74.301999 60.00 72.502000 76.00 71.202001 82.00 69.502002 79.00 68.402003 225.50 67.50 Distribución Log Normal2004 44.60 65.202005 65.20 62.102006 56.50 60.002007 74.30 60.002008 62.10 57.902009 68.40 56.50 intervalo2010 57.90 46.502011 131.60 45.20 12012 96.80 44.60 22013 71.20 42.30 32014 67.50 34.00 4

65

Distribución Pearson III

intervalo

123465

Distribución Gumbel

intervalo

123465

Distribución Gumbel 2 poblaciones

intervalo

123

465

Función Distribución normal estandar191.50 Media= 78.90

10 Desv. Esta= 38.32970328419.15

F(Si) F(Ii) ei

0 40 20 1 0.1550818229 0.0197732001 3.6533328240 80 60 18 0.5114474217 0.1550818229 9.6218711780 120 100 6 0.8582018359 0.5114474217 9.36236918

120 160 140 1 0.9828213245 0.8582018359 3.36472619160 200 180 0 0.9992096086 0.9828213245 0.44248367200 240 220 1 0.9999868304 0.9992096086 0.02098499

27 26.465768

alfa= 4.28Beta= 0.4031945917

F(Si) F(Ii) ei

0 40 20 1 0.0705056013 0 1.9036512440 80 60 18 0.5975854585 0.0705056013 14.231156180 120 100 6 0.8948486593 0.5975854585 8.02610642

120 160 140 0 0.9753645734 0.8948486593 2.17392968160 200 180 1 0.9941269084 0.9753645734 0.50658305200 240 220 1 0.9985200481 0.9941269084 0.11861477

27 26.9600413

alfa= 44.66Beta= 0.7365201386

d= 46.005160598grados de libertad 2

Limite inferior

Limite Superior

Marca de clase

Numero observado

Limite inferior

Limite Superior

Marca de clase

Numero observado

(𝜃_𝑖−𝜖_𝑖 )^2/𝜖_𝑖

(𝜃_𝑖−𝜖_𝑖 )^2/𝜖_𝑖

F(Si) F(Ii) ei

0 40 20 1 0 0 040 80 60 18 0.523967136 0 14.147112780 120 100 6 0.794307879 0.5235507246 7.31044317

120 160 140 0 0.9179246875 0.794307879 3.33765383160 200 180 1 0.9662937548 0.9179246875 1.30596482200 240 220 1 0.9857142964 0.9662937548 0.52435462

27 26.6255291

alfa= 0.03Beta= 60.32344204

F(Si) F(Ii) ei

0 40 20 1 0.1666829333 0.0035331634 4.4050437940 80 60 18 0.5663191416 0.1666829333 10.790177680 120 100 6 0.8348954785 0.5663191416 7.2515611

120 160 140 0 0.9443421065 0.8348954785 2.95505896160 200 180 1 0.9819901052 0.9443421065 1.01649596200 240 220 1 0.9942489293 0.9819901052 0.33098825

27 26.7493257

Distribución Gumbel 2 poblaciones P= 0.81481481481 alfa= 0.071 Beta= 56.8793819392 alfa= 0.018179992 Beta= 166.65064156

F(Si) F(Ii) ei

0 40 20 1 0.0398786883 9.288095E-19 1.0767245840 80 60 18 0.6548722614 0.0398786883 16.604826580 120 100 6 0.8194471711 0.6548722614 4.44352256

Limite inferior

Limite Superior

Marca de clase

Numero observado

Limite inferior

Limite Superior

Marca de clase

Numero observado

Limite inferior

Limite Superior

Marca de clase

Numero observado

(𝜃_𝑖−𝜖_𝑖 )^2/𝜖_𝑖

(𝜃_𝑖−𝜖_𝑖 )^2/𝜖_𝑖

(𝜃_𝑖−𝜖_𝑖 )^2/𝜖_𝑖

120 160 140 0 0.8736970958 0.8194471711 1.46474797160 200 180 1 0.922074089 0.8736970958 1.30617882200 240 220 1 0.9570893429 0.922074089 0.94541186

27 25.8414123

1.927055482457.295155117451.207549744421.66192719548 según tablas0.4424836725245.6741007367 χ2 7.8158.2082719491

No pasa

0.42895754290.998104713680.511469325372.17392968014 según tablas0.48059305016.5492678847 χ2 7.81

11.1423221969

Se acepta

(𝜃_𝑖−𝜖_𝑖 )^2/𝜖_𝑖

(𝜃_𝑖−𝜖_𝑖 )^2/𝜖_𝑖

01.049312401490.234905225213.3376538287 según tablas

0.071682229210.4314609145 χ2 5.995.1250145991

Se acepta

2.632056286754.81748684320.2160093748

2.95505895672 según tablas0.000267700871.35224353662 χ2 7.8111.973122699

No pasa

0.005467193590.117225504820.54520304076

(𝜃_𝑖−𝜖_𝑖 )^2/𝜖_𝑖

(𝜃_𝑖−𝜖_𝑖 )^2/𝜖_𝑖

(𝜃_𝑖−𝜖_𝑖 )^2/𝜖_𝑖

1.46474796621 según tablas0.071770776280.00315192312 χ2 3.842.20756640478

Se acepta

m P orde Fo(Xm)Normal LogNormal

F(Xm) D F(Xm)1 225.50 0.96429 0.99993454 0.03565 0.997578612 131.60 0.92857 0.91542076 0.01315 0.930775823 120.00 0.89286 0.85820184 0.03466 0.894848664 116.80 0.85714 0.83861688 0.01853 0.882129075 108.00 0.82143 0.77613423 0.04529 0.839259556 96.90 0.78571 0.68068305 0.10503 0.764987457 96.80 0.75000 0.67975033 0.07025 0.764199748 82.00 0.71429 0.5322302 0.18206 0.621089979 79.00 0.67857 0.50104082 0.17753 0.5854688910 76.00 0.64286 0.46984506 0.17301 0.5477128911 74.30 0.60714 0.45223707 0.15491 0.5254261712 72.50 0.57143 0.43369591 0.13773 0.5011776713 71.20 0.53571 0.42039285 0.11532 0.4832796514 69.50 0.50000 0.40313507 0.09686 0.4594337215 68.40 0.46429 0.39206576 0.07222 0.4437654216 67.50 0.42857 0.38307314 0.04550 0.4308227217 65.20 0.39286 0.36038678 0.03247 0.3973302318 62.10 0.35714 0.33058355 0.02656 0.3515710619 60.00 0.32143 0.31097444 0.01045 0.3204629920 60.00 0.28571 0.31097444 0.02526 0.3204629921 57.90 0.25000 0.29188785 0.04189 0.2895271122 56.50 0.21429 0.27947455 0.06519 0.2691209423 46.50 0.17857 0.1989724 0.02040 0.1359742924 45.20 0.14286 0.18964271 0.04679 0.1212194225 44.60 0.10714 0.185429 0.07829 0.1146709226 42.30 0.07143 0.16982095 0.09839 0.0912045227 34.00 0.03571 0.12071595 0.08500 0.03038852

0.18206Se acepta

media 78.9 alfa 44.6625118desvi. Est 38.3297033 beta 0.73652014 1.47304028

d 46.0051606

LogNormal Pearson III Gumbel Gumbel 2D F(Xm) D F(Xm) D F(Xm) D

0.03329 0.98202755 0.01774 0.99129454 0.02701 0.94620749 0.018080.00220 0.85287617 0.07570 0.8786568 0.04991 0.8364325 0.092140.00199 0.80924302 0.08361 0.83489548 0.05796 0.81944717 0.073410.02499 0.79507404 0.06207 0.82053258 0.03661 0.81408857 0.043050.01783 0.75044434 0.07098 0.77521254 0.04622 0.79636245 0.025070.02073 0.68003469 0.10568 0.70460783 0.08111 0.76243274 0.023280.01420 0.67931748 0.07068 0.70389933 0.04610 0.76203612 0.012040.09320 0.55332748 0.16096 0.58456553 0.12972 0.6730392 0.041250.09310 0.52229369 0.15628 0.55702304 0.12155 0.64509016 0.033480.09514 0.48910374 0.15375 0.52848048 0.11438 0.61276463 0.030090.08172 0.46928254 0.13786 0.51189847 0.09524 0.59236248 0.014780.07025 0.44745656 0.12397 0.49404808 0.07738 0.5690471 0.002380.05243 0.43113722 0.10458 0.48098414 0.05473 0.55109332 0.015380.04057 0.4090671 0.09093 0.46370442 0.03630 0.52619949 0.026200.02052 0.39433221 0.06995 0.45241707 0.01187 0.50924504 0.044960.00225 0.38200352 0.04657 0.44312661 0.01456 0.49488849 0.066320.00447 0.34934465 0.04351 0.41919274 0.02634 0.45630286 0.063450.00557 0.3025788 0.05456 0.3866241 0.02948 0.40044462 0.043300.00097 0.26900338 0.05243 0.36446536 0.04304 0.36062824 0.039200.03475 0.26900338 0.01671 0.36446536 0.07875 0.36062824 0.074910.03953 0.23381157 0.01619 0.34231947 0.09232 0.31980732 0.069810.05484 0.20941409 0.00487 0.32760371 0.11332 0.29235466 0.078070.04260 0.01101837 0.16755 0.22609098 0.04752 0.11340677 0.065160.02164 0 0.14286 0.21366945 0.07081 0.0951939 0.047660.00753 0 0.10714 0.20801922 0.10088 0.0873529 0.019790.01978 0 0.07143 0.18688915 0.11546 0.06078476 0.010640.00533 0 0.03571 0.11904481 0.08333 0.00935011 0.026360.09514 0.16755 0.12972 0.09214

Se acepta Se acepta Se acepta Se acepta

alfa 0.02869315 alfa1 0.06542335beta 60.323442 beta1 56.8793819

alfa2 0.01817999beta2 166.650642

p 0.81481481

según tabala A5 aparicio

para n=27 d= 0.252

Pru. K-S Chi-cua ECMNoramal 5 Rechazado 4

Lognormal 2 Rechazado 3Pearson 4 2 2Gumbel 3 Rechazado 1

Gumbel 2 1 1 5