SU410380A1 - - Google Patents

Description

STOCHASTIC FUNCTIONAL CONVERTER

one

The invention relates to the field of digital computing and is intended to obtain random variables with given distribution laws based on the stochastic implementation of a piecewise linear approximation of the probability density distribution.

A stochastic functional converter is known for obtaining random numbers with a piecewise linear approximated probability distribution density, comprising a random number generator, the first output of which is connected to a sampling unit, and an AND circuit whose outputs are connected to an interval conversion unit through the OR circuit.

However, the presence of a probabilistic binary block in such a converter requires additional storage in the storage device / V of numbers that set the angle of inclination on the approximating direct, and an additional output from the generator evenly distributed in the interval of 0.1 random numbers.

The purpose of the invention is to simplify and extend the functionality of the stochastic functional converter.

In the proposed stochastic functional converter, this goal is achieved by introducing into the decoder circuit an additional AND circuit and a multiplication unit — adding the composition of the laws of distribution, connected to a generator of uniformly distributed random greatness and with the input of an additional I. In this case, the control inputs of all circuits "And" are connected to the output of the descrambler, whose input is connected to the sampling unit and to the conversion unit.

FIG. 1 is a block diagram of a converter; in fig. 2 is a plot of density distribution. The converter contains a generator I uniformly distributed in the random number interval, a block II of sampling (generation) of discrete random variables and signs of converting random variables according to multiplication operations — adding the composition of the distribution laws, multiplication block III — adding the commosycin distribution laws; delimiter IV, schemes "AND V, scheme" OR VI, and block VII of linear conversion of random variables.

The basis of the work of the proposed stochastic functional converter is laid:

1. Representation of the area bounded by the piecewise linear approximating distribution density, the sum of the squares of rectangles 1, the isosceles triangles 2, and the square triangles 3, 4. 2. Implementation of piecewise varying density by random sampling with Pji probabilities the above nr of the polygons and triangles 1, 2, 3, 4) of the boundary points Aj of the intervals xj, and of the random variables Y; (the index i thus takes the values 1, 2, 3, 4), which are linearly transformed on the interval xj, Xj + i by running the algorithm

Xt Xj + (x-j, i-Xj), (1)

Moreover, 2 1,, 2;

Y, max {Y,.,; Y ,, (3)

Y min {Y,; Y,} (4)

where uy; Yi, 2 — values of a random variable uniformly distributed over the interval, a, b.

The implementations of algorithm (1) NR, 2, 3, 4, respectively, give rectangular and triangular distributions 1, 2, 3, 4 at intervals xj, Xj + i. Algorithm (1) is executed in a block of linear conversion of random variables VII, algorithms ( 2), (3), (4) - in block III of multiplication - the composition of the laws of distribution. Generator I outputs random numbers uniformly distributed in the interval (a, c). In block II, discrete random variables Xj are generated and a sign of the conversion of random variables according to multiplication operations (3), addition (4), and composition (2) of the distribution laws. This feature is decrypted in decoder IV and feeds one of the values of U into block VII.

Stochastic functional Converter works as follows.

The generator I outputs three values uniformly distributed in the interval a, in a random variable. Two of them are fed into the multiplication block of the composition of the /// distribution laws, where the algorithms (2), (3) and (4) are executed. The third value of a random variable from generator 1 enters block II of generating discrete random variables Xj and the sign of converting random variables by multiplication operations — the addition of a composition of the distribution laws. The value Xj goes to the linear conversion block of random variables VII, and the sign of the conversion to the decoder IV.

The decoder opens one of the & V schemes through which the values of U are passed to block VII, where algorithm (1) is implemented. If algorithms (2), (3) and (4) are implemented over numerical values, then from generator I to

block II you can shoot a single number Y, and

as the second () use fractional

part of the execution of the algorithm (2), (Fig. 1

shown by the dotted line).

The stochastic functional converter can be used to obtain random variables in various forms of their task (numerical, pulsed, amplitude, etc.), since the algorithms (1), (2), (3) and (4) allow simple technical

implementation.

Subject invention

A stochastic function converter, comprising a random number generator, the first output of which is connected to a sampling unit, the AND circuit, whose outputs through the OR circuit are connected to a conversion unit, characterized in that

In order to expand the functionality of the converter, it contains a decoder, a multiplication unit — the addition of the composition of the distribution laws, and an additional AND circuit whose input is connected to a random number generator and with a multiplication unit — the composition of the distribution laws, the control inputs of all the And the output of the decoder, the input of which is connected to the output of the sampling unit

and with the input of the conversion unit.