SU1478209A1 - Numeric comparator - Google Patents

Abstract

The invention relates to computing and can be used to compare the distribution functions of random variables. The purpose of the invention is to expand the scope by providing a comparison of the distribution functions of two random variables. The device contains registers 1-4, subtractors 5, 6, multipliers 7, 8, accumulating adders (NS) 9, 10, comparison element (ES) 11, information inputs 12, 13, clock input 14, initial installation input 15, outputs 16 17. At the input 12 and 13, the values of the distribution function F ₁ , F ₂ ... F _N and G ₁ , G ₂ ... G _{N of} two random variables ζ and * 98N are received in succession. In HC 9 and 10, the values S _F = Σ (F _I -F _I-1 ) are formed. C and S _G = Σ (G _I -G _I-1 ) .F _I , which are compared to ES 11

the latter chooses one of the functions F and G according to the principle "the function F is chosen if it is more likely that ζ * 98N and less likely that * 98N * 98z". 1 il.

Description

ten

The invention relates to computing and can be used to compare the distribution functions of random variables.

The purpose of the invention is to expand the scope by providing a comparison of the distribution functions of two random variables.

The drawing shows a diagram of the device.

The device contains registers 1-4, subtractors 5 and 6, multipliers 7 and 8, accumulating adders 9 and 10, reference element 11, informational J5 inputs 12 and 13, clock input 14, initial setting input 15 and outputs 16 and 17.

The device works as follows.

At the inputs 12 and 13 of the device, the values of the distribution functions F (x.,), F (x 7), ..., BCHx) (hereinafter, F ,, F7, ..., D) and G (y, ), G (ya), ..., G (yn) (hereinafter G ,, G4, ..., GJ 25 two random variables § and h. After the initial setup, input 15 inputs 12 and 13 receive the values F and G, respectively, which are recorded in registers 1 and 2. At the output of register 1 (2), the number recorded in it goes to the input of the decremented subtractor 5 (6). Since in register 3 (4) the zero number is written, the output of the subtractor 5 (6) the same number appears 35, and it arrives at the input of multiplier 8 (7). However, since its second input is zero from register 4 (3), the output of multiplier 8 (7) also has 40 zero places.

Next, input 14 receives a clock pulse, which rewrites numbers from register 1 (2) to register 3 (4), and the registers 1 and 2 record the values of the functions F / J and G. At the outputs of the subtractors 5 and 6, the numbers, and, appear. The outputs of the multipliers 8 and 7 are the numbers f, G1 and g, F. Each of these with “numbers” enters its accumulating adder 9 (Yu).

The next clock pulse rewrites the numbers Fc and C g from the registers

14782092

form numbers and pzF2. These numbers are fed to the adders 9 and 10 and summed with the numbers recorded in them at previous cycles. Therefore, after the second clock cycle, the number ffG, + faGi9 is fixed in the adder 9 and the number in the adder 10.

The operation of the device then proceeds in a similar way, so that after the n-th cycle in the accumulating adders 9 and 10, the numbers, 0, +

+ f2G2 + ... fnGn I f.G, -SFH in F, +

+ 8,1V

, gnFn X g, F (SG. Depending on which is greater than Sc or SG, comparison element 11 selects either function F or function G. You remove the physical meaning of such a preference.

Since F (x) and G (y) are distribution functions, F (x) p ($ x), G (y) p (h), where Ј and h are random variables with the F (x) and G distribution functions (y) respectively. Further, the quantities, -F, and p.Gf4.-G, are the probabilities f, p (x, -; «) g. T (Y;,) Since $ and h are independent, the product f; Gj

p (,;. ,,), Ie f1G, - 7S

-p (,) with u.x ,. Then SF Ј, G, “Z,,. ; J

p (. Similarly, ()). Consequently, if RF Rq, this means that p () p (l), i.e. the choice is made according to the principle, function F is selected, if it is more likely that c, and vice versa.

Claims (1)

Invention Formula A device for comparing numbers, containing the first and second accumulating adders and the first register, whose information input is the first information input of the device, characterized in that, in order to expand the field of application by providing a comparison of the distribution functions of two random variables, three registers are entered , two subtractors, two multipliers and a comparison element, with the second information input of the device connected to the information 1 and 2 in registers 3 and 4, and in registers 1 and 2, the numbers F 3 and G3 are recorded. Now, at the outputs of subtractors 5 and 6, the numbers f1 F3-F1 and gi Gj-G2 appear, Multipliers 8 and 7 at their outputs + 8,1V , gnFn X g, F (SG. Depending Most importantly, if comparison is greater than Sc or SG, comparison element 11 selects either function F or function G. You can see the physical meaning of this preference. Since F (x) and G (y) are distribution functions, F (x) p ($ x), G (y) p (h), where Ј and h are random variables with the F (x) and G distribution functions (y) respectively. Further, the quantities, -F, and p.Gf4.-G, are the probabilities f, p (x, -; «) g. T (Y;,) Since $ and h are independent, the product f; Gj p (,;. ,,), Ie f1G, - 7S -p (,) with u.x ,. Then SF Ј, G, “Z,,. ; J p (. Similarly, ()). Consequently, if RF Rq, this means that p () p (l), i.e. the choice is made according to the principle, function F is selected, if it is more likely that c, and vice versa. Invention Formula A device for comparing numbers, containing the first and second accumulating adders and the first register, whose information input is the first information input of the device, characterized in that, in order to expand the field of application by providing a comparison of the distribution functions of two random variables, three registers are entered , two subtractors, two multipliers and a comparison element, with the second information input of the device connected to the information 3 1478209 -4 the input of the second register, the outputs of the first and second multipliers, first and second registers are connected to the outputs which are connected to the inputs with the inputs of the first and second nano of the first and second subtractors and dropping adders, respectively, respectively, respectively, the outputs of the information inputs of the corresponding respectively are connected to the first and third register and second inputs of the element of the match, the outputs of which are connected; are first with the first inputs of the device, the initial input go and second multipliers and with input-jq setting and clock input device of the first and second subtractable respectively with the inputs subtractors whose outputs are connected to the zero state and are connected to the second inputs by the corresponding inputs of all the registers.