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Executive Editor:Publishing house "Academy of Natural History"
Editorial Board:
Asgarov S. (Azerbaijan), Alakbarov M. (Azerbaijan), Aliev Z. (Azerbaijan), Babayev N. (Uzbekistan), Chiladze G. (Georgia), Datskovsky I. (Israel), Garbuz I. (Moldova), Gleizer S. (Germany), Ershina A. (Kazakhstan), Kobzev D. (Switzerland), Kohl O. (Germany), Ktshanyan M. (Armenia), Lande D. (Ukraine), Ledvanov M. (Russia), Makats V. (Ukraine), Miletic L. (Serbia), Moskovkin V. (Ukraine), Murzagaliyeva A. (Kazakhstan), Novikov A. (Ukraine), Rahimov R. (Uzbekistan), Romanchuk A. (Ukraine), Shamshiev B. (Kyrgyzstan), Usheva M. (Bulgaria), Vasileva M. (Bulgar).
Engineering
I. Simulation of hereditary effects
The informational method of simulation of hereditary effects is grounded on introducing of a lineup of factors interacting sequentially against each other in the form of an information channel in which the information on the first factor arrives and sequentially will be transformed to the information on a total indication.
Let's consider a case when initially unique factor X sequentially will be transformed to Y (graf. 1).
Here H(X1),H(X2), … H(Xn) – an information quantity concluded in factor Х after first, second, … last operation; H (Y) – an information quantity concluded in indication Y; I(XkÞY/X1,X2,…,Xk1) – an information quantity, transmitted to Y after working off k factors.
Graf. 1. The Information channel
The consecutive increment of the information is equal:
(1)
Here H(Y)  an information quantity (entropy) about Y; H(Y/X1X2…)  the information quantity (entropy) received as a result of action on Y of various not considered factors. Since, then
(2)
The level of influence of factor X on an indication Y at informational simulation can be evaluated by means of coefficient of informational connection q:
(3)
The coefficient of informational correlation is equal to unit if the information on an indication is completely defined by the information on factors; it is equal to zero if the indication does not depend on factors; generally the coefficient of informational correlation is concluded between zero and unit.
II. Simulation of simultaneous processes
Let the correlation between three factorsindications X, Y, Z is defined. On the basis of the chart of John Venn (graf. 2) is received:
(4)
For the quantitative estimation of associations between parametres it is necessary to calculate coefficients of informational connection
(5)
Graf. 2. The chart of informational connection
Generalising the received outcomes on n parametres, association in between we will express the following formula:
. (6)
III. The Analysis of models
At creation of models all theoretical values of entropies in the formulas reduced above are substituted by their estimations:
(7)
where empirical probability of hit of an aleatory variable X in a state number i; fi  empirical frequency of hit of values X in this state; n  number of experiences.
It is displayed that the estimation of the information I (XY) ®to within a constant factor has c2 allocation (see [2]):
(8)
Here  number of degree of freedoms; an amount of intervals of a partition of input and output parametres accordingly.
The information transmitted from one parametre to another, is considered significant, if
(9)
Where  α  a quantile c2  allocations; α – a confidence level.
Allocation of the Pearson at m> 25 can be substituted Gaussian distribution with a variance s2=2m that gives the chance to define a confidence interval for the information:
(10)
Value tα  αkvantil of a normal distribution. A confidence interval for coefficient of informational connection q is:
(11)
The minimum sample size is determined by means of necessary precision of ΔI value:
(12)
In case of linear model the coefficient of correlation and coefficient of informational connection have a close connection among themselves, defined by statistical equality q=r2 [1].
IV. The Example of application of an informational model
It is necessary to research association of labour productivity (Y) from a salary (X) (in percentage of basic value) (tab. 1).
The first step – creation of the chart of dispersion (graf. 3.).
Than we build the twodimensional histogram. It is for this purpose defined the main statistical performances of researched aleatory variables (tab. 2) and we divide ranges of factors Х and Y into the intervals which breadth is close to an average quadratic deviation.
Table 1
Input datas for model creation
№ 
Х 
Y 
№ 
X 
Y 
№ 
X 
Y 
№ 
X 
Y 
№ 
X 
Y 
1 
134 
109 
21 
147 
112 
41 
102 
69 
61 
146 
113 
81 
127 
116 
2 
136 
116 
22 
180 
140 
42 
132 
108 
62 
154 
102 
82 
101 
75 
3 
148 
102 
23 
125 
108 
43 
131 
97 
63 
176 
138 
83 
153 
122 
4 
127 
98 
24 
113 
80 
44 
122 
98 
64 
128 
106 
84 
111 
89 
5 
133 
87 
25 
124 
84 
45 
139 
99 
65 
116 
81 
85 
152 
107 
6 
121 
95 
26 
116 
84 
46 
147 
117 
66 
110 
83 
86 
154 
107 
7 
155 
106 
27 
147 
113 
47 
121 
92 
67 
124 
96 
87 
129 
101 
8 
104 
69 
28 
159 
107 
48 
122 
97 
68 
103 
85 
88 
156 
115 
9 
146 
106 
29 
110 
83 
49 
136 
108 
69 
166 
119 
89 
143 
114 
10 
158 
115 
30 
101 
72 
50 
136 
100 
70 
173 
137 
90 
120 
88 
11 
154 
116 
31 
132 
109 
51 
133 
84 
71 
124 
86 
91 
117 
89 
12 
166 
131 
32 
107 
85 
52 
105 
76 
72 
122 
92 
92 
128 
98 
13 
101 
73 
33 
106 
92 
53 
135 
103 
73 
118 
99 
93 
139 
105 
14 
129 
94 
34 
152 
117 
54 
133 
104 
74 
159 
128 
94 
148 
110 
15 
102 
86 
35 
124 
100 
55 
111 
85 
75 
161 
119 
95 
146 
104 
16 
119 
94 
36 
120 
82 
56 
116 
90 
76 
172 
144 
96 
156 
113 
17 
156 
114 
37 
126 
90 
57 
140 
109 
77 
139 
105 
97 
101 
76 
18 
150 
121 
38 
127 
106 
58 
159 
139 
78 
125 
94 
98 
129 
95 
19 
177 
145 
39 
150 
130 
59 
162 
143 
79 
114 
101 
99 
102 
86 
20 
147 
111 
40 
114 
94 
60 
115 
90 
80 
120 
95 
100 
119 
94 
The third step is an evaluation of entropies H (X), H (Y), H (X, Y).
Graf. 3. A field of dispersion of the experimental observations of association of labour productivity (Y) from a salary (X) (in percentage of basic value).
Table 2
The main statistical performances

Х 
Y 
Average 
133,21 
102,1 
Standard deviation 
20,27154 
17,34062 
Sampling variance 
410,9353 
300,697 
Minimum 
101 
69 
Maxima 
180 
145 
In tab. 3 frequencies of hit of values of a twodimensional aleatory variable in appropriate intervals are reduced.
Table 3
Twodimensional bar graph
Y 
X 
f (y) 

100120 
120140 
140160 
160180 

6986 
17 
4 


21 
86103 
13 
17 
3 

33 
103120 

12 
20 
2 
34 
120137 


5 
2 
7 
137145 



5 
5 
f (x) 
30 
33 
28 
9 

The mutual information is equal I(X®Y)=H(X)+H(Y)H(X,Y)=0,562502 , and coefficient of informational connection q(X®Y)= I(X®Y)/H(Y)=0,402844.
The fourth step. An estimation of significance of the discovered connection by criterion of the Pearson (8). In our case k1=4, k2=5. Calculated value of Pearson criterion of the Pearson is equal to . Table value at number of degree of freedoms m = (41 (51) =12 ×and a fiducial probability a=0,95 is equal to. Since a calculated value of Pearson criterion more than table connection between Y and Х it is significant.
Thus, in paper the technique of simulation which is based on methods of the information theory is offered and justified. The example of creation of an informational model is reduced.
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URL: www.sciencesd.com/46525012 (02.06.2023).