10.DISTRIBUCIONES TEORICAS

7/24/2019 10.DISTRIBUCIONES TEORICAS

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PRUEBA DE CHI CUADRADO

m P P(ORDENADO)

1 74.84 61.632 78.85 66.53

3 72.36 68.53

4 73.40 68.92

5 72.10 70.17

6 73.42 71.06

7 80.89 71.59

8 78.78 72.10

9 71.06 72.36

10 71.59 73.40

11 68.92 73.42

12 68.53 74.84

13 77.29 77.29

14 70.17 78.78

15 84.65 78.85

16 61.63 80.89

17 83.13 83.13

18 66.53 84.65

19 89.50 86.30

20 95.79 89.50

21 86.30 95.79

PROMEDIO 76.18

DESV.EST 8.2762188196

PRUEBA DE CHI CUADRADO

NC = 1 1.33!N (N)

NC = 5

"# = (#MA#$#MIN)%(NC$1)

"# = 9

CA!CU!O DE &RCUENCIA ACUMU!ADA'

INTERVALOS DE CLASE Xi.fi

1 2 3 4

MARCAS DECLASE

FRECUENCIAABSOLUTA


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61.63 0.00 0.00

61.63 70.63 66.13 5.00 330.63

70.63 79.63 75.13 10.00 751.25

79.63 88.63 84.13 4.00 336.50

88.63 97.63 93.13 2.00 186.25

97.63 106.63 102.13 0.00 0.00

21.00 1604.63

X 76.41

S 8.19

CA!CU!O DE !A &RECUENCIA ABSO!UTA

INTERVALOS DE CLASE LIMITE DE CLASE

1 2 3 4

61.63 $1.80 0.42507

61.63 70.63 66.13 $1.26 0.32894

70.63 79.63 75.13 $0.16 0.01197

79.63 88.63 84.13 0.94 0.34134

88.63 97.63 93.13 2.04 0.47558

97.63 106.63 102.13 3.14 0.49841

4.71

*+,- + / *+ = $1$ 2

N / + - * *

D /* * /* A.8 + / *: + - '

# ;2 = 5.99

# ;2 < # ;2

AREA BAJO LACURVA NORMAL

C*/


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(Xi-X !2.fi

" # $

FRECUENCIARELATIVA

FRECUENCIAACUMULADA


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0.00

528.98 0.238095 0.238095

16.53 0.476190 0.714286

238.04 0.190476 0.904762

558.73 0.095238 1.000000

0.00 0.000000 1.000000

1342.29 1.00

ei i

" # $

0.0961 8.00 5.00

0.3409 27.00 10.00

0.3294 26.00 4.00

0.1342 11.00 2.00

0.0228 2.00 0.00

# ;2 39.81

FRECUENCIARELATIVA

FRECUENCIAACUMULADA

FRECUENCIAACUMULADA


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PRUEBA DE SMIRNOV KOLMOGOR

m Q Q = X

1 61.476 5 .!1 . 4761" #1.1$ 7!.%5 5 5%.61 . "5$!%1 # .5%! %1.46"5 61.4% .14$%571 # .$54 5%.61 5 6".!1 .1" 476$ #1.$$5 6".! 5 7 .74 .$!% "5$ # .776 77.657 7!.64 .$%5714! # .417 7!.6!75 7!.%5 .!!!!!!! # .5%% 5 .!1 5 77.66 .!% "5$4 #1.5%" % . !75 7".5% .4$%5714 # .!1

1 7 .7!5 % . 4 .4761" 5 # .7111 7".5%$5 %1.47 .5$!% "5 # .!!1$ %".447 %4.%$ .5714$%6 . "1! %4.%1" %".45 .61" 476 # .1114 "7.$5$ "7.$5 .6666667 .4$15 1 ".%$7 "7.7 .714$%57 ."616 1!4.$ 5 1 !.!5 .761" 4% $.17 1!!.6!! 1 ".%! .% "5$!% 1."71% 1 !.!5!5 11".% .%5714$" .6%1" 11".% 5 1!!.6! ." 4761" 1.!%$ "7.6"" 1!4.$1 ."5$!%1 .44

PROMEDIO %7.!!5!75DESV.ES& $!.45147 7

'm()= ABS*+*,-#P*X-- .5$64%1"

= . 5 ' = 1.!6/*N-0 .5 .! 41 5$4

C 23 2 2 2 89 ' = .5$64%1" : ' = .! 41 5$4

P*X- m/*N;1-

C( ' = 'm()

V( 232 ' 3( 2 32 Sm2 8 >#K m ? > '@ ( (

S

X x Z

=


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V

+*,-

. 6! 1 . 15!"1 0.1147 0.2172

. %$$6 . 1$"7%1 0.1884 0.3382

. "51 . 477571 0.2172 0.3867

.111$! . 7"$46$ 0.2969 0.1884

.15!%6 . %4$!5$ 0.3105 0.2969

.15!%6 .1!1%54! 0.3364 0.3664

.17!61 .15"7$!! 0.3382 0.3364

.1761" .$ 476$4 0.3664 0.1147

.$ 611 .$$$4614 0.3777 0.3801

.$177 .$5%4" 5 0.3801 0.3105

.$$!6! .! 17"5 0.3867 0.3777.$4%$5 .!$!17%6 0.3967 0.3973

.$546! .!644176 0.3973 0.3967

.$% "6 .!%57 67 0.3648 0.3648

.! 15! .41$7557 0.3618 0.2519

.!$$76 .4!"144% 0.3159 0.0541

.!556" .45!%!!% 0.2519 0.0568

.!5"4$ .4"77$$" 0.1530 0.3159

.!7%$% .5$64%1" 0.0568 0.1530

.46 17 .4"$$11 0.0541 0.3618

'= ABS +*,-#P*X-

( 2 >( N 82> 2?82 2 ( 2 8


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DIS&RIBUCI N NORMAL

DA&OSA OS P*mm-

1 1""! 74.842$ 1""4 78.850! 1""5 72.3584 1""6 73.4005 1""7 72.1006 1""% 73.4177 1""" 80.892

% $ 78.783

" $ 1 71.0581 $ $ 71.59211 $ ! 68.9171$ $ 4 68.5331! $ 5 77.29214 $ 6 70.16715 $ 7 84.65016 $ % 61.62517 $ " 83.125

1% $ 1 66.5251" $ 11 89.500$ $ 1$ 95.792$1 $ 1! 86.300

% P (mm P!2(mm f(& '

1 61.6$5 !7"7.64 6! . $"557!% #1.75%$ 66.5$5 44$5.5756! . 7 $5111 #1.166! 6%.5!! 46"6.%177% . " 5$57" # ."$44 6%."17 474".5 6"4 . "4!% "6 # .%775 7 .167 4"$!.!6111 .1 65! $% # .7$66 71. 5% 5 4".$%674 .1145!!4! # .61%7 71.5"$ 51$5.!6674 .11%"4!$ # .554% 7$.1 51"%.41 .1$$%$%5$ # .4"!" 7$.!5% 5$!5.7$%4 .1$4671 ! # .461

1 7!.4 5!%7.56 .1!1 %! $ # .!!611 7!.417 5!" . 6"4 .1!1171!6 # .!!41$ 74.%4$ 56 1.$75 7 .1!6%% 4$ # .161

ES&ACI N HUANCAPI


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1! 77.$"$ 5"74. 174 .1!74$161 .1!514 7%.7%! 6$ 6.%1!61 .1!1"64"4 .!1515 7%.%5 6$17.!$$5 .1!16$6!! .!$!16 % .%"$ 654!.46174 .117" !1" .5717 %!.1$5 6" ".7656! . "74%%1 .%41% %4.65 7165.6$$5 . %$11 $1 1. $41" %6.! 7447.6" . 656!!$1 1.$$!$ %".5 % 1 .$5 . !7"55 " 1.61$1 "5.7"$ "176. 4!4 . %!616" $.!7

&O&AL 15"".717 1$!$!1.5 7

MEDIA ARI&ME&ICA DESVIACIONX= 76.177 S=


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f(' F(' ' )

. %5 !1"$ .6! "4$7 ."%6!$1 " 5. 4447"$7 . 1!77!!!

.$ $1 1!! .7$ 47661 ."5767"15 5. 4!47 6 . 4!$4$47

.$6 4$%!6 .764"6%5 ."!%17% $ 4."764$4!! . 6!%1556.$7151"1 .774 "$7 ."!!%"4"! 4."7 $$441 . 6%!"1!4.! 647 76 .% 541%%1 ."1%7 "6" 4."4% 4!$1 . %47%51.!$"4"457 .%$"!6 1" ." 67"!4 4."! 41!%1 . "7%4 64.!4$1% 7% .%44!7$%6 .%""$6%45 4."1"1776 .1 617!6%.!5!!5%$1 .%5"1"657 .%"1%41%5 4." % %$! .11446646.!5%65%%$ .%66"!1$ .%%7"7" " 4." $166"$ .11%% 7 %.!771 511 .%""5%5$7 .%71%6%4 4.%775646$ .1!71167%.!77!5"$4 ." 1$775 .%716 4!" 4.%7715%1" .1!741"64.!"!7%!!$ ."4" 5"" .%4%47%%! 4.%411!761 .164!1 15


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.!"5!4 $$ ."57115% .%44%$$74 4.%!5!65! .16%6$%45

.!7"64$$5 ." 517 $6 .%6"15715 4.%7!!%57! .14 $!1!!

.!7%66%1$ ." $"7""" .%7 $1%5% 4.%75 $! 7 .1!" 1 %5

.!!"1%%%1 .%4 6%16% ." 111"61 4."$1"4"$6 .1 4117$%

.$% 457%4 .7%16%%66 ."! $741 4."64"6!"$ . 7$$76

.$!6$1% 7 .745"4554 ."46%$"6" 4."%%%7!6$ . 546!6 4

.1%%%16!5 .71 7% 7$ ."615456$ 5. "%$477 . !"$1!$7

.1 "1" 7" .651$4 7$ ."%1!$6"!

. $4 55$7 .55"14"75 .""6" 46" 5. 5" 5!" . !1 11

S&ANDAR%.$76$1%%$


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. $

. 4

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.14

.16

+ 8 2 8 8 2 ( ( 2 3 2F 2 8 8 m(

.$

.$5

.!

.!5

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.45

C ( 3 &23


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. 5

.1

.15


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DISTRIBUCIN LOG

A O P (>>) P (ORDENADO)

1 1994 74.842 95.8

2 1995 78.850 89.5

3 1996 72.358 86.3

4 1997 73.400 84.7

5 1998 72.100 83.1

6 1999 73.417 80.9

7 2000 80.892 78.9

8 2001 78.783 78.8

9 2002 71.058 77.3

10 2003 71.592 74.8

11 2004 68.917 73.4

12 2005 68.533 73.4

13 2006 77.292 72.4

14 2007 70.167 72.1

15 2008 84.650 71.6

16 2009 61.625 71.117 2010 83.125 70.2

18 2011 66.525 68.9

19 2012 89.500 68.5

20 2013 95.792 66.5

21 2014 86.300 61.6

MEDIA 76.177

DESV.ESTANDAR 8.276

ES&ACI N HUANCAPI

_

_


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ORMAL

?=/ # @ ( )

4.5622 2.2021 . !54.4942 1.5643 . 1$!4.4578 1.2226 . $ 64.4385 1.0413 . $574.4203 0.8707 . ! %4.3931 0.6150 . !%!4.3675 0.3751 . 44!4.3667 0.3671 . 4444.3476 0.1877 . 4764.3154 $0.1147 . 4"74.2962 $0.2951 . 4%%4.2959 $0.2973 . 4%%4.2816 $0.4314 . 47$4.2781 $0.4650 . 4664.2710 $0.5314 . 454

4.2635 $0.6016 . 444.2509 $0.7202 . 41$4.2329 $0.8889 . !664.2273 $0.9412 . !514.1976 $1.2204 . $674.1211 $1.9386 . "!

4.328

0.107

.

. 1

. $

. !

. 4

. 5

. 6

dx x

e x

x f x F y

y x

y

x

==

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00

.ln

21

21

)()(


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M &ODO D

(>3%-) ORDENADO PROBABI!IDAD

1 61.476 50.31 0.048

2 73.8505 58.61 0.095

3 81.4695 61.48 0.143

4 58.6105 69.31 0.190

5 69.305 70.74 0.238

6 77.657 73.64 0.286

7 73.6375 73.85 0.333

8 50.3105 77.66 0.381

9 80.0375 79.58 0.429

10 70.735 80.04 0.476

11 79.5825 81.47 0.524

12 89.447 84.82 0.571

13 84.819 89.45 0.619

14 97.252 97.25 0.667

15 109.827 97.70 0.714

16 134.205 103.35 0.762

17 133.633 109.83 0.810

18 103.3535 119.80 0.857

19 119.8005 133.63 0.905

20 97.699 134.21 0.952

1 CA!CU!O DE !OS PARAMETROS ESTADISTICOS

MEDIA 4.44

DESVIACION 0.264

2 ESTIMACION DE PARAMETROS METODO DE MOMENTOS

0.2060747466

F 4.317499946

3INCO NITAS

CAUDA! 70 >3%-

PERIODO 50 *G,-

PROBABI!IDAD 5

T

CAUDA! 168.29

PERIODO 0.2471562355 0.3

ES&ACI N HUANCAPI


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PROBABI!IDAD DE NO E#EDENCIA 24.72 98.04

PROBABI!IDAD DE E#EDENCIA 75.28 1.96


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LOG GUMBEL

!O ARITMOS ( ) ORDINARIO DE!TA

3.92 $1.938 0.001 0.047

4.07 $1.197 0.037 0.059

4.12 $0.965 0.072 0.070

4.24 $0.383 0.231 0.040

4.26 $0.284 0.265 0.027

4.30 $0.089 0.335 0.049

4.30 $0.075 0.340 0.007

4.35 0.169 0.430 0.049

4.38 0.288 0.472 0.044

4.38 0.315 0.482 0.006

4.40 0.401 0.512 0.012

4.44 0.597 0.577 0.005

4.49 0.855 0.654 0.034

4.58 1.261 0.753 0.087

4.58 1.283 0.758 0.044

4.64 1.556 0.810 0.048

4.70 1.851 0.855 0.045

4.79 2.273 0.902 0.045

4.90 2.803 0.941 0.036

4.90 2.824 0.942 0.010

P

59.82

0.053


21/34


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ME&ODO GUMBE

% A*O P

1 1994 213.20

2 1995 201.20

3 1996 218.60

4 1997 195.60

5 1998 206.50

6 1999 195.50

7 2000 204.70

8 2001 204.50

9 2002 186.5010 2003 171.00

11 2004 158.10

12 2005 181.10

13 2006 198.30

14 2007 194.50

15 2008 214.50

16 2009 201.60

17 2010 208.50

18 2011 233.30

19 2012 343.10

20 2013 271.40

21 2014 201.60

: ,> + , 209.68 =+ - . E- * +* 37.96 u=

ESTIMACION DE PARAMETROS METODO DE MOMENTOS

MEDIA(#) 209.68

37.9598

VARIAN@A(S2) 1440.9496

S 37.9598

29.5972

F 209.6810

DESVIACIONTIPICA

ES&ACI N HUANCAPI


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C ( 3 &23


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ME&ODO DE LOG PEARSON III

NUMERO DE DATOS 20

A*O 0 (m3 L%(0 ( %& - X %& !3

1994 61.476 4.119 $0.032

1995 73.8505 4.302 $0.002

1996 81.4695 4.400 0.000

1997 58.6105 4.071 $0.049

1998 69.305 4.239 $0.008

1999 77.657 4.352 $0.001

2000 73.6375 4.299 $0.003

2001 50.3105 3.918 $0.139

2002 80.0375 4.382 0.000

2003 70.735 4.259 $0.006

2004 79.5825 4.377 0.000

2005 89.447 4.494 0.000

2006 84.819 4.441 0.000

2007 97.252 4.577 0.003

2008 109.827 4.699 0.018

2009 134.205 4.899 0.0992010 133.633 4.895 0.096

2011 103.3535 4.638 0.008

2012 119.8005 4.786 0.043

2013 97.699 4.582 0.003

SUMA 88.729 0.031

#!N 4.436S/ 0.2642

CS/ 0.0989

2 ESTIMACION DE PARAMETROS METODO DE MOMENTOS

J= 409.1756K= 0.0131

#0= $0.9078

ES&ACI N HUANCAPI


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P ARSON III

% A*O 0(M3 S (XI-X !31 1994 61.476 $17292.352199555

2 1995 73.8505 $2452.1146677977

3 1996 81.4695 $201.8358984375

4 1997 58.6105 $23701.424157362

5 1998 69.305 $5861.574350619

6 1999 77.657 $906.5825094795

7 2000 73.6375 $2570.1566618326

8 2001 50.3105 $50755.230323376

9 2002 80.0375 $388.6773751326

10 2003 70.735 $4574.6060120032

11 2004 79.5825 $466.002606262

12 2005 89.447 9.415651706913 2006 84.819 $15.9340466955

14 2007 97.252 975.1954621466

15 2008 109.827 11377.9102026548

16 2009 134.205 102961.399326261

17 2010 133.633 99237.5739922195

18 2011 103.3535 4109.9357747044

19 2012 119.8005 34217.7333872312

20 2013 97.699 1113.1022738583

SUMA 144815.77526223

DATOS (N) 18MEDIA 87.335

DES.STDR 23.451SES O 0.7430

J= 7.2450525407K= 8.713

#0= 24.212

DATO

CAUDA! 70 >3%S

PERIODO 60

PROBABI!IDAD 5

&(J) 1144.5138344691

RESU!TADOS

T


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CAUDA! 44.94

PERIODO 0.08681 1.1

PROBABI!IDAD DE NO E#EDENCIA 8.68 98.36

PROBABI!IDAD DE E#EDENCIA 91.32 1.64


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P


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44.94

0.053

Documents

10.DISTRIBUCIONES TEORICAS