SU590790A1 - Random number generator - Google Patents

Description

one

The invention relates to the field of computer technology and can be used in modeling a Markov random number sequence with a gamma distribution.

Known random number generators.

One of the known random number generators contains a shift register, a random symbol generator, a clock pulse generator, a probability (1, t) field, an OR element, and element I. However, this generator does not allow one to obtain Markov sequences of random numbers with one-dimensional The distribution of the probability m is different from the Berioulli distribution.

Another known random number generator comprises a source of random impulses, a pulse shaping unit, a low frequency filter, an electronic key, an amplitude selector, a multiphase standby multivibrator, memory blocks, a control unit, and a matrix switch. However, this generator does not allow obtaining random numbers with a precisely specified one-dimensional probability distribution, but can only approximate a given exact probability distribution using a low-pass filter and a dummy switch 2.

And the closest technical solution to this invention is a generator

random numbers containing the first multiplier, the output of which is the generator output, the first input is connected to the output of the first number sensor, and the second input is connected to the output of a sequential sum block, the first input of which is connected to the output of the comparison unit, the inputs of which are connected respectively to the outputs A memory unit and a counter whose input is connected to the generator output and multiple pulses and to the sensor input of normal random numbers 3.

Although this generator of a sequence of random numbers is based on the exact dependencies between the distributions of the original and the vi: random numbers of random numbers, its disadvantage is that they only generate random numbers that are uncorrelated with each other. This circumstance limits the scope of the generator, since the complication of problems solved by digital modeling and statistical testing requires not only generating sequences of random numbers with random distributions that are more complicated than even or normal distributions, but also with certain adjustable correlations between sequence numbers.

The aim of the invention is to extend the functionality of the generator by obtaining a Markovian sequence of random numbers with gamma distribution.

To achieve the delivered product, the sensor further comprises a second multiplier, a first adder, a first quad, a delay element, a second memory block, a third multiplier, a square measles extraction unit, a second adder, a second number sensor, and a ivertor, a second quad, and a third number sensor, whose output connected to the first input of the second multiplier and through the second quad and inverter to the first input of the second adder, the second input of which is connected to the output of the second number sensor, and the output through the square block extraction block the first input of the third multiplier, the output of which is connected to the first input of the first court, and the second input through the second memory unit and the delay element to the output of the first adder and the input of the first quad, the output of which is connected to the second input of the sequential summation unit, and the second input of the first adder - with the output of the second multiplier, and the second input of the second multiplier is connected to the output of the sensor of normal random numbers.

The block diagram of the generator is shown in the drawing.

The generator contains a pulse generator 1, a sensor 2 and a normal random number, a counter 3, the first quad 4, a sequential summation block 5, a first multiplier 6, a second multiplier 7, a first adder 8, a second block 9 of memory, a delay element 10, a third multiplier 11, a third number sensor 12, a second quad 13, an inverter 14, a second adder 15, a square root extraction unit 16, a second number sensor 17, a first memory block 18, a comparison unit 19, a first number sensor 20 and an output terminal 21.

The output of the pulse generator 1 is connected to the inputs of the sensor 2 normal random numbers and Counter 3. The output of the sensor 2 normal random numbers connected to the second input of the second multiplier 7, the output of which is connected to the second input of the first adder 8. The output of the first adder 8 is connected to the input of the first quad by 4 , the output of which is to the second input of the block 5 of sequential summation. The output of the sequential summation unit 5 is connected to the second input of the first multiplier 6, the output of which is connected to the output terminal 21. The output of the first quadrant 8 is also connected via a serially connected second 9 memory and a delay element 10 to the second input of the third multiplier 11, the output of which is connected to the first the input of the first adder 8. The output of the third sensor 12 numbers attached to the first input of the second multiplier 7 and through series-connected second quadrant 3 n inverter

14 - to the first input of the second adder 15. To the second input of the second adder 15 is connected to the output of the second sensor 17 numbers. The output of the second adder 15 is connected via the extraction unit 16 to the first input of the third multiplier I. The output of the counter 3 is connected to one of the inputs of the comparison unit 19, to the other input of which is a switch the output of the first memory block 18, and to the output the first input of the block 5 consecutive sum. The output of the first sensor 20 numbers connected to the first input of the first multiplier 6.

The device works as follows.

A geerator of I pulses, controlling sensor 2 of normal random numbers and counter 3, as well as serially connected first quadrant 4, block 5 of sequential summation and first multiplier 6 are needed to generate a sequence of random quaps with a one-dimensional gamma-distributed semipopular parameter. Sensor 2 forms normally distributed independent random numbers with zero mean value and unit variance. The obtaining of the required one-dimensional probability distribution is settled on the fact that the sum of squares of independent normal random numbers that are equally distributed with the zero mean value has the gamma distribution of the semi-melted parameter. The sequence of random numbers acquires the Markov property due to the fact that a normal random number raised to a quarter by the first quadrant 4 is formed by adding a succession in the first sum.mator 8 generated in sensor 2 to each new tact of a new independent normal number multiplied in the second multiplier 7 by a positive number less than edippi, and formed on the previous .m cycle of a normal number from the output of the first adder 8, stored in the second block

9 and these are delayed by the element 10 of the delay by one clock and multiplied by a positive number less than one in the third multiplier 11. Positive numbers, smaller ones, are sent to the first inputs of the amplifiers 7 and II: to the input of the second multiplier 7 directly from the output of the third sensor 12, and to the input of the third multiplier 11 - after conversion.

A Markov sequence of random numbers with a gamma distribution is characterized by three parameters: a degree of correlation, a form parameter, and a scale of numbers. For ease of use generator

random numbers it is desirable that the change of these parameters occur independently of each other. In order to change the degree of correlation not depend on the scale of the generated numbers,

the following relationship should be observed

between the numbers at the first inputs of multiplicates of numbers 7 and 11

Cj - CSS - Ci,

where Ci is the level of the first input of the second multiplier 7; The Cz-level of the first input of the third multiplier And and C is a positive constant.

To ensure this condition, a positive number from the third sensor 12 numbers is supplied to the first input of the third multiplier 11 through the second quadrant 13 connected in series, the inverter 14, the second adder 15 and the square root extractor 16, and the second input of the second adder 15 is supplied from second gauge 17 numbers.

The shape of the curve of the one-dimensional probability density of random numbers with a gamma distribution is determined by the number of terms in the sum of the pre-squared normal random numbers formed in block 5 of sequential summation. The summation is terminated by a pulse at the initial input of block 5 of sequential summation after a certain number of clock pulses from pulse generator 3. To change the shape of the one-dimensional distribution of random numbers, the first memory block 18 is used to store various positive integers determined from the sequence of random numbers . When the number of clock pulses coincides with the contents of the first memory block 18 in the comparison block 19, a pulse is formed that stops summing and transfers the contents of the sequential summation block 5 to the second input of the first multiplier 6. The Markov sequence of random numbers with gamma distribution is removed from the output of the multiplier 6.

Thus, the present invention makes it possible to obtain a Markov sequence of random numbers with a gamma distribution, i.e., it ensures the achievement of its goal.

In the random number generator, you can change the scale of the generated numbers, for example, using the first sensor of 20 numbers.

The advantages of the generator include independent control of three parameters characterizing the Markov sequence of random numbers with gamma distribution.

An uncorrelated sequence of random numbers with a gamma distribution can be obtained by setting the maximum number at the output of the third gauge to 12 numbers. In this case, the first input of the third multiplier 11 will be the number O, and hence the second term at the input of the first adder 8 will be equal to zero.

With the help of this generator, it is possible to obtain a Markov approximately normal sequence of random numbers. For this, a sufficiently large number, presumably at least several tens, must be stored in the first block 18 of the memory. In the technique of digital modeling and in solving various problems by the method of statistical istapy pseudo-random numbers

have certain advantages over random ones. The advantages of the generator include the fact that it is possible to generate both random and pseudo-random sequences, depending on whether

sensor 2 is a sensor of random normal numbers or a pseudo-random normal number sensor.

The chi-squared distribution, the Erlang distribution, and the exponential distribution that are important in practice are special cases of the gamma distribution for certain values of its two parameters. Therefore, by introducing certain numbers into the first memory block 18 and establishing a definite number on the output of the first sensor 20 numbers, using the proposed generator, generate Markov random number sequences with "chi square distribution, Erlang distribution and exponential distribution, with adjustment of the degree of correlation between consecutive random numbers by means of a third sensor 12 numbers. Thus, the proposed random number generator has new and wider possibilities in comparison with existing generators and allows solving more complex problems from the field of digital modeling and statistical tests.

Claims (3)

1. USSR author's certificate No. 437061, cl. G 06F 1/02, 1973. 2. USSR author's certificate №466500, cl. G 06F 1/02, 1973. 3. US Patent No. 3.811.038, cl. G 06F 7/38, 1972.