SU378879A1 - ALL-UNION - Google Patents

Description

The invention relates to the field of computer technology and is intended to obtain random numbers with given distribution laws by means of a stochastic implementation of a piecewise linear approximation of the distribution density.

Devices are known that contain a generator of uniformly distributed random numbers, an interval selection unit, a memory device, and an arithmetic unit for performing operations of addition, multiplication, division, and extraction of the root. The complexity of random number conversion algorithms makes it difficult to use them to build random value generators.

The purpose of the invention is to simplify the converter.

The proposed device is characterized in that it contains a distribution unit for the distribution laws of the composition operation, the inputs of which are connected to the generator outputs of uniformly distributed random numbers, and the output is connected to the input of the interval conversion unit.

The basis of the stochastic realization of a piecewise linear approximation of the density of distribution is a superposition operation.

). i T over random variables with triangular distributions

Oh, if xj x - 00;

Xi

 -

-Xi if xj

X

W- I

 - -

1-2

0

 + i

if l; + 22gl: lg / + 1

1 if 00; l; 5 l: / and-2

FIG. 1 is a block diagram of the proposed converter; in fig. 2 is a plot of the density distribution curve.

The proposed converter has a generator 1 of uniformly distributed random numbers, an interval selection block 2, a storage device 3, a distribution unit 4 for transforming the distribution laws for a composition operation, an interval conversion unit 5 and an output 6.

A generator of random numbers uniformly distributed in the interval of 0.1 is connected to the interval selection block 2 connected to the input and output with the storage device 3 and to the distribution law-to-4 unit of the operation

compositions whose outputs are connected to interval conversion block 5.

The preliminary preparation and operation of the stochastic functional converter is as follows:

1. The density of the distribution W (x) is replaced (see FIG. 2) with a piecewise linear approximation function Wa (x) with a uniform partition of the argument, when

For; : Xj + i - Xj const.

2. At each interval KJ, through points 5j + i we draw straight lines CjBj + i parallel to the x-axis, and areas of rectangles XjCjBj + -i} Ci + i are represented by areas of isosceles triangles XjBj-iXj + 2B in each interval xj, Xj + i the equation of the approximating direct BjlBj + i can be represented through the sum of the equations of the approximating direct BjXj + i, XjBj + i and, accordingly, the area bounded by the piecewise-linear approximating function Wa (x), can be replaced by the sum of the areas of equilateral triangles XjBj + iXj + 2- This makes it possible to reduce the process of obtaining random numbers to the operation of superposition, where the probability PJ is equal to the area of the rectangles XjCjBj + iXj + i or isosceles triangles XjBj + iXj + 2.

3. By probability PJ, the distribution function is calculated, the values of which F (xj) with the corresponding reference points .Xj are stored in memory 3.

4. From generator 1, three numbers are taken, uniformly distributed in the interval of 0.1 random sequence. One of them (Fi) is fed to the interval selection block 2, and the other two (U2 and UZ) to block 4 transform the distribution laws of the composition operation.

5. In interval selection block 2, the number} i is compared with the values of the distribution functions f (xj) and the interval Xj, Xj + i is determined, i.e., the value Xj is determined. 6. In block 4, the transformation of the distribution laws for the composition operation is performed the algorithm

1 Y, -} - y ,.

7. Certain values of Xj, Zk and constant difference

YES: const

served in interval conversion block 5 where the algorithm is implemented

Xk Xj-i-x-Z.

As a result, we obtain a sequence of numbers Xk, the distribution density of which with an accuracy of approximation corresponds to the given one.

Subject invention

A stochastic functional converter containing a generator of uniformly distributed random numbers connected through an interval selector to an input

memory device, one output of which is connected to the interval selection unit and the other through the interval conversion unit to the output terminal of the device, characterized in that, in order to simplify the converter, it contains the distribution unit of the distribution laws for the composition operation, the inputs of which are connected to the generator outputs uniformly distributed random numbers, and the output is connected to the input

interval conversion block.