Pruebas de Uniformidad y Aletoriedad

ALGORITMO CONGRUENCIAL LINEAL ADITIVO

1) Secuencia previa de "n" numeros n= 8 X1 = 17 X2 = 72 X3 = 95 X4 = 3 X5 = 53 X6 = 61 X7 = 29 X8 = 88 2) Asignamos valor a "m" m= 3 3) %eneramos los "X i" ! Xi 1 X9 2 X1 X 1 3 X1 X11 4 X12 5 X13 6 X14 7 X15 8 X16 9 X17

= = = = = = = = = =

# # # # # # # # #

88 15 27 2 5 28 29 28 26

#Xi&1 $ Xi&n) mod #m) $ 17 ) mod $ 72 ) mod $ 95 ) mod $ 3 ) mod $ 53 ) mod $ 61 ) mod $ 29 ) mod $ 88 ) mod $ 15 ) mod

# # # # # # # # #

3 3 3 3 3 3 3 3 3

) ) ) ) ) ) ) ) )

= = = = = = = = =

15 27 2 5 28 29 28 26 11

'i '1 '2 '3 '4 '5 '6 '7 '8 '9

= = = = = = = = = =

15 27 2 5 28 29 28 26 11

( ( ( ( ( ( ( ( (

# # # # # # # # #

Xi(#m&1) 3 3 3 3 3 3 3 3 3

& & & & & & & & &

1 1 1 1 1 1 1 2 3

) ) ) ) ) ) ) ) )

= = = = = = = = =

517 931 69 172 966 1 966 897  379

!ivel de con*an+a

95,

.a/la de calculos de

!-meros alea.orios 517

i

931

i(n

69

ri

172

#i&1)(n

966

i(n & ri

1

ri & #i & 1)(n

966

n

897

^+

1

2

3

1

2

3

517

931

69



1

2

&417 &731

231

517

831 &131

1 7241

^−

831

379 276 

'0SA

_(∝,)= D #396)



5 1

#495)

n=1 no se desi.ri/uen uniormen.e

 

rue/a 4

5

6

7

8

9

1

4

5

6

7

8

9

1

966

897

379

276

5

6

7

8

9

228

&466 &4

&266

&97

521

724

&128

566 5

366

197 &421

&624

172 3



966 1 4

831

Prueba Chi-cuadrada '1

517

n

1

'2

931

m

3162

'3

69

Ei

3

'4

172

'5

966

'6

1

'7

966

'8

897

'9

379

'1

276

:!0';A

i

0i

##0i&i)<2)(0i

&1

1

3

15

1&2 2&3

1 1

3 3

15 15

3&4

1

3

15

4&5



3

32

5&6

1

3

15

6&7



3

32

7&8



3

32

8&9

1

3

15

9&1

4

3

2

TOTAL

1



5

%rad i/er.ad

v

9

18.6 CONCLUION

dad! "ue 18.6 e# $a

%!r "ue 16.&1 #e 'uede recha(ar "ue e) c!*+u*,! de *$er!# Ri #iue u*a di#,ribuci!* u*i/!r

e

PRUE0A DE ALETORIEDAD DE NMERO PEUDOALEATORIO PRUE0A DE ERIE 'eali+amos la prue/a de series a los siguien.es 1 n-meros 'i Cue resul.aron del G.N. '1 '2 '3 '4 '5 '6 '7 '8 '9 '1

= = = = = = = = = =

517 931 69 172 966 1 966 897 379 276

1) %eneramos la gr>*ca de dispersion con la secuencia de 9 pares ordenados #X?@) #'1?'2) #'2?'3) #'3?'4) #'4?'5) #'5?'6) #'6?'7) #'7?'8) #'8?'9) #'9?'1)

= = = = = = = = = =

#'i?'i$1) # 5172 ? # 931 ? # 69 ? # 172 ? # 966 ? # 1 ? # 966 ? # 897 ? # 379 ?

1)2

931 69 172 966 1 966 897 379 276

) ) ) ) ) ) ) ) )

1

)8

)6

)4

)2

 

os in.ervalos seran

2) B>lculo de la prue/a :n.ervalo i

3

4

1

2

0i=#n&1)(m

m

=

4

n&1

=

9

)2

2 3 4 o.al

2 2 3 9

225 225 225 9

28 28 25 333

X<2

=

333

3) !ivel de Bon E p v

= =

X<2 X5D3<2

= =

5 3

= =

95 1&95

=

5

p valo v=grad m=4

333 7815

ado Cue X<2 F X5D3<2 #333F7815) en.onces no se puede recGa+ar Cue e

A. C!*rue*cia) Adi2!D con un nivel de con*an+a de 95,

)4

)6

)8

1

1)2

de E s de li/er.ad #m&1)

l conHun.o de numeros 'i sigue una dis.ri/uciIn uniorme

PRUE0A DE ALETORIEDAD DE NMERO PEUDOALEATORIO PRUE0A DE LA DITANCIA 4PRUE0A DE 5UECO 'eali+amos la prue/a de Guecos a los siguien.es 1 n-meros 'i Cue resul.aron del G. '1 '2 '3 '4 '5 '6 '7 '8 '9 '1

= = = = = = = = = =

517 931 69 172 966 1 966 897 379 276

1) e*nimos el in.ervalo #EDN)

= s

G

=

=

# 2

D

8

)

J1D D D D D D D D 1D 1K

2

amaLo del Gueco i i  1 1  2  3  4  M=5 1 G= 2 T!,a)

0i=#G)#N&E)#1&#N&E))
0i 12 48 192 77 31 12

33333 48 192 768 372 793925 82535

ado Cue M #825M1175) en.onces se recGa+a la Gipo.esis de la independencia en.re los numeros

v= p=

N.A. C!*rue*cia) Adi2!D con un nivel de con*an+a de 95,

 

825

5 5