Random number generation apparatus, method and program

Patent metadata

Field	Value
Publication number	US-2021286593-A1
Application number	US-201816476728-A
Country	US
Kind code	A1
Filing date	Jan 12, 2018
Priority date	Jan 19, 2017
Publication date	Sep 16, 2021
Grant date	—

Abstract

A random number generation apparatus comprises: a first random number generating part 2 generating a random number u=(u1, . . . ,uD)T∈[−∞,∞]D; a second random number generating part 3 generating a random number v∈[0,f′max]; and a determining part 4 determining whether f′(x1=u1, . . . ,xD=uD)≥v or not, and, if f′(x1=u1, . . . ,xD=uD)≥v, adopting u as a random number according to f′(x1, . . . ,xD), wherein D is a predetermined positive integer, for i=1, . . . ,D, [hi] is a predetermined possible range for a random variable xi, a hole [h] is [h]=([h1], . . . ,[hD])T, H is a probability of a predetermined basic distribution function f(x1, . . . ,xD) in the hole [h], α=1/(1−H), a corrected distribution function f′(x1, . . . ,xD) is defined by Expressions (1) and (2), and f′max is a maximum value of f′(x1, . . . ,xD).

First claim

1 . A random number generation apparatus, comprising:
a first random number generating part generating a random number u=(u 1 , . . . ,u D ) T ∈[−∞,∞] D ; a second random number generating part generating a random number v∈[0,f′ max ]; and a determining part determining whether f′(x 1 =u 1 , . . . ,x D =u D )≥v or not, and, if f′(x 1 =u 1 , . . . ,x D =u D )≥v, adopting u as a random number according to f′(x 1 , . . . ,x D ), wherein D is a predetermined positive integer, for i=1, . . . ,D, [h i ] is a predetermined possible range for a random variable x i , a hole [h] is [h]=([h 1 ], . . . ,[h D ]) T , H is a probability of a predetermined basic distribution function f(x 1 , . . . ,x D ) in the hole [h], α=1/(1−H), a corrected distribution function f′(x 1 , . . . ,x D ) is defined by Expressions (1) and (2):
[Formula 29]
H=∫ x 1 ∈[h 1 ] . . . ∫ x D ∈[h D ] f ( x 1 , . . . ,x D ) dx 1 . . . dx D

f ′( x 1 , . . . ,x D )=0 if x 1 ∈[ h 1 ] ∧ . . . ∧x D ∈[ h D ]  (1)

f ′( x 1 , . . . ,x D )=α· f ( x 1 , . . . ,x D ) otherwise  (2)

and f′ fax is a maximum value of f′(x 1 , . . . ,x D ).

2 . A random number generation apparatus comprising:
an arithmetic operation part obtaining r=(r 1 , . . . ,r D ) T in the end, by performing, for each of i=1, . . . ,D, a process for generating a random number u i ∈[0,1], obtaining a random number r i =F −1 (u i ) according to f′(x i ) using the generated and x i =r i , wherein D is a predetermined positive integer, for i=1, . . . ,D, [h i ] is a predetermined possible range for a random variable x i , a hole [h] is [h]=([h 1 ], . . . ,[h D ]) T , H is a probability of a predetermined basic distribution function f(x 1 , . . . ,x D ) in the hole [h], α=1/(1−H), a corrected distribution function f′(x 1 , . . . ,x D ) is defined by Expressions (1) and (2):
[Formula 30]
H=∫ x 1 ∈[h 1 ] . . . ∫ x D ∈[h D ] f ( x 1 , . . . ,x D ) dx 1 . . . dx D

f ′( x 1 , . . . ,x D )=0 if x 1 ∈[ h 1 ] ∧ . . . ∧x D ∈[ h D ]  (1)

f ′( x 1 , . . . ,x D )=α· f ( x 1 , . . . ,x D ) otherwise  (2)

f′(x i ) is a peripheral distribution of f′(x 1 , . . . ,x D ) of x i , F(t i ) is a function defined by Expression (2′):
[Formula 31]
f ′( x i )=∫ −∞ ∞ . . . ∫ −∞ ∞ f ′( x 1 , . . . ,x D ) dx 1 . . . dx i−1 dx i+1 . . . dx D

F ( t i )=∫ −∞ t i f ′( x i ) dx i   (2′)

and F −1 (t i ) is an inverse function of F(t i ).

3 . The random number generation apparatus according to claim 1 or 2 , wherein
when D=2, N is a predetermined positive integer, there are N predetermined possible ranges [h i ] for the random variable x i , the N predetermined possible ranges are {[h i ]} i=1 N {([h 1 ] i ,[h 2 ] i ) T } i=1 N ={([(s 1 ) i ,(e 1 ) i ],[(s 2 ) i ,(e 2 ) i ]) T } i=1 N , (μ x1 ,2σ x1 2 ),(μ x2 ,2σ x2 2 ) are predetermined parameters, the basic distribution function f(x 1 , . . . ,x D ) is Lap(x 1 ,x 2 ) defined by Expression (3), sign(a) is a function that outputs a sign {+,−} of an input a, a function g(s,e) is defined by Expressions (5) and (6) when s≤e, H described above is defined by Expression (4), and the corrected distribution function f′ is Lap′(x 1 ,x 2 ) defined by Expressions (7) and (8):

⁢

[

Formula
⁢

⁢
32

]

⁢

Lap
⁡

(

x
1

,

x
2

)

=

1

2
⁢

σ

x
1

⁢

exp
⁡

(

-



x
1

-

μ

x
1



σ

x
1

)

⁢

1

2
⁢

σ

x
2

⁢

exp
⁡

(

-



x
2

-

μ

Assignees

• Nippon Telegraph & Telephone

Inventors

• Okada Rina
• Hasegawa Satoshi
• Masaki Shogo

Classifications

• G06F7/58 Primary

  Random or pseudo-random number generators · CPC title

• G06F7/586 Primary

  using an integer algorithm, e.g. using linear congruential method · CPC title

• G06F17/18

  for evaluating statistical data {, e.g. average values, frequency distributions, probability functions, regression analysis (forecasting specially adapted for a specific administrative, business or logistic context G06Q10/04)} · CPC title