File:Duration67.jpg

Density of likelihood \(f(t)\) for mean Duration \(\bar D\) to have value \(t\) measured in years (one year = 365.2422 days), calculated with sample of \(N\!=\!4\) cases:

\( f(t) = \) Student\(_{3}\big((t\!-\!s)/U\big)/U \)

Parameters \(s\) and \(U\) are estimated through the four observed values \(h\) in the following way:

\(\displaystyle ~ s=\frac{1}{N} \sum_{i=1}^N h_i \)

\(\displaystyle ~ U= \sqrt{\frac{1}{(N\!-\! 1)N} \sum_{i=1}^N (h_i-s)^2 } \)

Values \(h\) appear from the observed dates of nulling of the separation of powers
and following collaps of the empire.
These dates are picked up from historic documents ^{[1][2][3][4][5][6][7][8]}.

The input table is loaded below.

Input file i.txt

1802 08 04 1815 11 20 Fra
1928 05 17 1947 12 27 Ita
1933 03 24 1945 05 08 Ger
1977 10 07 1991 08 20 Sov

C++ code

// The table above is used as input file i.txt for generation of the picture. // Files ju24da.cin and Student.cin should be loaded in order to compile the code below:

#include <stdio.h> 
#include <math.h>
#include <stdlib.h>
#include "ju24da.cin"
#include "Student.cin"
int main(){ int n,N=4; FILE *i,*o; 
int Y1,M1,D1;
int Y2,M2,D2; char s[4][4]; int D[4]; float d[4];  //L[N]
float t, p,q,r,x,y,T,U,W;

i=fopen("i.txt","r"); 
for(n=0;n<N;n++)
{
fscanf(i,"%4d %2d %2d %4d %2d %2d %3s", &Y1,&M1,&D1, &Y2,&M2,&D2, s[n]);        
D[n]=daju24(Y2,M2,D2) - daju24(Y1,M1,D1) ; t=D[n]/365.2422; d[n]=t; // L[n]=log2(t);
printf("%4d %02d %02d %04d %02d %02d %3s %04d %6.4f\n", Y1,M1,D1, Y2,M2,D2, s[n], D[n], d[n]);
} fclose(i);

p=0.; for(n=0;n<N;n++) p+=d[n];  p/=N; printf("p=%5.2f\n",p);
q=0.; for(n=0;n<N;n++) {r=d[n]-p; q+=r*r;} 
T=sqrt(q/(N-1.));  printf("T=%5.2f\n",T);
U=sqrt(q/(N*(N-1.))); printf("U=%5.2f\n",U);
W=sqrt(q/(N*(N-3.))); printf("W=%5.2f\n",W);

o=fopen("o.tex","w");
fprintf(o,"\\documentclass{standalone}\n");
fprintf(o,"\\usepackage{graphicx}\n");
fprintf(o,"\\usepackage{tikz}\n");
//fprintf(o,"\\newcommand \\sx {\\scalebox}\n");
fprintf(o,"\\begin{document}\n");
fprintf(o,"\\Huge\n");
fprintf(o,"\\begin{tikzpicture}[scale=2]\n");
fprintf(o,"\\draw [line width=0.981] (0,0) grid (24,4);\n");
fprintf(o,"\\draw [line width=2.3] (0,4.4) -- (0,0) -- (24.1,0) ;\n");
// fprintf(o,"\\draw(0,0) -- (0,3.2) ;\n");
fprintf(o,"\\draw (-.08,4.3) node[right] {\\(f(t)\\)};\n");

fprintf(o,"\\definecolor{light}{rgb}{1,1,.6};\n");
fprintf(o,"\\definecolor{dark}{rgb}{0,1,1};\n");
fprintf(o,"\\draw[line width=32, light] (8,0.03) -- (8,3.7) ;\n");
fprintf(o,"\\draw (8,0.2) node[rotate=90,right] {\\bf Russia 2028};\n");
fprintf(o,"\\draw[line width=32, light] (22,0.03) -- (22,3.7) ;\n");
fprintf(o,"\\draw(22,0.2) node[rotate=90,right] {\\bf Moscow 2042};\n");

for(n=0;n<N;n++)
{
fprintf(o,"\\draw[line width=24, dark] (%5.3f,0.03) -- (%5.3f,1.4) ;\n",d[n], d[n]);
fprintf(o,"\\draw (%5.3f,1.2) node[rotate=90,left] {\\bf %s};\n",d[n],s[n]);
}

for(n=0;n<5;n+=2) fprintf(o,"\\draw (0,%d) node[left] {%3.1f};\n",n,0.05*n);
for(n=0;n<24;n++) fprintf(o,"\\draw (%d,0) node[below] {%d};\n",n,n);
                 fprintf(o,"\\draw (%d,0) node[below] {$t$};\n",n);

fprintf(o,"\\draw[line width=5, red] (0,0)");
for(n=1;n<241;n++){x=.1*n; y=20*Student(3,(x-p)/U)/U;	fprintf(o," -- (%6.3f,%6.3f)",x,y);}
fprintf(o,";\n");
//fprintf(o,"\\input \"Labels.tex\"\n");
fprintf(o,"\\end{tikzpicture}\n");
fprintf(o,"\\end{document}\n");
fclose(o);
system("pdflatex o.tex");
//system("open o.pdf");
//system("convert o.pdf png8:o.png");
system("convert o.pdf o.jpg");
system("open o.jpg");
printf("p=0.; for(n=0;n<N;n++) p+=d[n]; p/=N;      resulling p=%8.6f\n",p);
printf("q=0.; for(n=0;n<N;n++) {r=d[n]-p; q+=r*r;} resulting q=%8.6f\n",q);
printf("T=sqrt(q/(N-1.))     = %8.6f\n",T);
printf("U=sqrt(q/(N*(N-1.))) = %8.6f\n",U);
printf("W=sqrt(q/(N*(N-3.))) = %8.6f\n",W);
printf("g(d)=student3((d-%8.6f)/%8.6f)/%6.6f\n",p,U,U);
printf("sqrt(T*T+W*W)=%8.6f years\n",sqrt(T*T+W*W));
printf("p-sqrt(T*T+W*W))=%8.6f years\n",p-sqrt(T*T+W*W) );
printf("p+sqrt(T*T+W*W))=%8.6f years\n",p+sqrt(T*T+W*W) );
printf("p-2*sqrt(T*T+W*W))=%8.6f years\n",p-2*sqrt(T*T+W*W) );
printf("p+2*sqrt(T*T+W*W))=%8.6f years\n",p+2*sqrt(T*T+W*W) );
}

References

Keywords

«C++», «Collapse of RF», «Duration», «Student Distribution», «[[]]»,

«Предсказания революций», «Распад РФ»,