File:Linea.jpg

Density \(F(t)\) of likelihood of the mean duration \(\bar D\) to have value \(t\) evaluates with 5 examples from article Duration5.

Input file:

1653 12 16 1661 04 23 eng
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

Generator

#include <stdio.h> 
#include <math.h>
#include <stdlib.h>
#include "ju24da.cin"
#include "Student.cin"
int main(){ int n,N=5; FILE *i,*o; 
int Y1,M1,D1;
int Y2,M2,D2; char s[N][4]; int D[N],Ya[N],Yb[N]; float d[N];  //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);
Ya[n]=Y1;
Yb[n]=Y2;
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("Linea.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) -- (8,3.8) ;\n");
fprintf(o,"\\draw (8,0.8) node[rotate=90,right] {\\bf Russia 2028};\n");
fprintf(o,"\\draw[line width=32, light] (22,0.03) -- (22,3.8) ;\n");
fprintf(o,"\\draw(22,0.8) 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,3.3) ;\n",d[n], d[n]);
fprintf(o,"\\draw (%5.3f,3.2) node[rotate=90,left] {\\bf %s %4d-%4d};\n",d[n],s[n],Ya[n],Yb[n]);
printf("%1d %s\n",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+=2){x=.1*n; y=20*Student(N-1,(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 Linea.tex");
system("open Linea.pdf");
//system("convert Linear.pdf png8:Linear8.png");
//system("convert Linear.pdf Linear.jpg");
//system("open Linear.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)=student%d((d-%8.6f)/%8.6f)/%6.6f\n",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) );
}

Output text

Output written on Linea.pdf (1 page, 35730 bytes).
Transcript written on Linea.log.
1653 12 16 1661 04 23 eng 2685 7.3513
1802 08 04 1815 11 20 fra 4856 13.2953
1928 05 17 1947 12 27 ita 7163 19.6116
1933 03 24 1945 05 08 ger 4428 12.1235
1977 10 07 1991 08 20 sov 5065 13.8675
p=13.25
T= 4.39
U= 1.96
W= 2.77
0 eng
1 fra
2 ita
3 ger
4 sov
p=0.; for(n=0;n<N;n++) p+=d[n]; p/=N;      resulling p=13.249838
q=0.; for(n=0;n<N;n++) {r=d[n]-p; q+=r*r;} resulting q=76.917809
T=sqrt(q/(N-1.))     = 4.385140
U=sqrt(q/(N*(N-1.))) = 1.961094
W=sqrt(q/(N*(N-3.))) = 2.773406
g(d)=student4((d-13.249838)/1.961094)/1.961094
sqrt(T*T+W*W)=5.188568 years
p-sqrt(T*T+W*W))=8.061270 years
p+sqrt(T*T+W*W))=18.438406 years
p-2*sqrt(T*T+W*W))=2.872703 years
p+2*sqrt(T*T+W*W))=23.626972 years

Output Latex

\documentclass{standalone}
\usepackage{graphicx}
\usepackage{tikz}
\begin{document}
\Huge
\begin{tikzpicture}[scale=2]
\draw [line width=0.981] (0,0) grid (24,4);
\draw [line width=2.3] (0,4.4) -- (0,0) -- (24.1,0) ;
\draw (-.08,4.3) node[right] {\(f(t)\)};
\definecolor{light}{rgb}{1,1,.6};
\definecolor{dark}{rgb}{0,1,1};
\draw[line width=32, light] (8,0.03) -- (8,3.8) ;
\draw (8,0.8) node[rotate=90,right] {\bf Russia 2028};
\draw[line width=32, light] (22,0.03) -- (22,3.8) ;
\draw(22,0.8) node[rotate=90,right] {\bf Moscow 2042};
\draw[line width=24, dark] (7.351,0.03) -- (7.351,3.3) ;
\draw (7.351,3.2) node[rotate=90,left] {\bf eng 1653-1661};
\draw[line width=24, dark] (13.295,0.03) -- (13.295,3.3) ;
\draw (13.295,3.2) node[rotate=90,left] {\bf fra 1802-1815};
\draw[line width=24, dark] (19.612,0.03) -- (19.612,3.3) ;
\draw (19.612,3.2) node[rotate=90,left] {\bf ita 1928-1947};
\draw[line width=24, dark] (12.123,0.03) -- (12.123,3.3) ;
\draw (12.123,3.2) node[rotate=90,left] {\bf ger 1933-1945};
\draw[line width=24, dark] (13.868,0.03) -- (13.868,3.3) ;
\draw (13.868,3.2) node[rotate=90,left] {\bf sov 1977-1991};
\draw (0,0) node[left] {0.0};
\draw (0,2) node[left] {0.1};
\draw (0,4) node[left] {0.2};
\draw (0,0) node[below] {0};
\draw (1,0) node[below] {1};
\draw (2,0) node[below] {2};
\draw (3,0) node[below] {3};
\draw (4,0) node[below] {4};
\draw (5,0) node[below] {5};
\draw (6,0) node[below] {6};
\draw (7,0) node[below] {7};
\draw (8,0) node[below] {8};
\draw (9,0) node[below] {9};
\draw (10,0) node[below] {10};
\draw (11,0) node[below] {11};
\draw (12,0) node[below] {12};
\draw (13,0) node[below] {13};
\draw (14,0) node[below] {14};
\draw (15,0) node[below] {15};
\draw (16,0) node[below] {16};
\draw (17,0) node[below] {17};
\draw (18,0) node[below] {18};
\draw (19,0) node[below] {19};
\draw (20,0) node[below] {20};
\draw (21,0) node[below] {21};
\draw (22,0) node[below] {22};
\draw (23,0) node[below] {23};
\draw (24,0) node[below] {$t$};
\draw[line width=5, red] (0,0) -- ( 0.100, 0.007) -- ( 0.300, 0.008) -- ( 0.500, 0.008) -- ( 0.700, 0.009) -- ( 0.900, 0.010) -- ( 1.100, 0.010) -- ( 1.300, 0.011) -- ( 1.500, 0.012) -- ( 1.700, 0.013) -- ( 1.900, 0.014) -- ( 2.100, 0.015) -- ( 2.300, 0.017) -- ( 2.500, 0.018) -- ( 2.700, 0.020) -- ( 2.900, 0.021) -- ( 3.100, 0.023) -- ( 3.300, 0.025) -- ( 3.500, 0.028) -- ( 3.700, 0.030) -- ( 3.900, 0.033) -- ( 4.100, 0.036) -- ( 4.300, 0.040) -- ( 4.500, 0.044) -- ( 4.700, 0.048) -- ( 4.900, 0.053) -- ( 5.100, 0.059) -- ( 5.300, 0.065) -- ( 5.500, 0.072) -- ( 5.700, 0.080) -- ( 5.900, 0.088) -- ( 6.100, 0.098) -- ( 6.300, 0.110) -- ( 6.500, 0.122) -- ( 6.700, 0.137) -- ( 6.900, 0.153) -- ( 7.100, 0.172) -- ( 7.300, 0.193) -- ( 7.500, 0.217) -- ( 7.700, 0.245) -- ( 7.900, 0.276) -- ( 8.100, 0.312) -- ( 8.300, 0.353) -- ( 8.500, 0.400) -- ( 8.700, 0.454) -- ( 8.900, 0.515) -- ( 9.100, 0.585) -- ( 9.300, 0.664) -- ( 9.500, 0.755) -- ( 9.700, 0.857) -- ( 9.900, 0.972) -- (10.100, 1.102) -- (10.300, 1.247) -- (10.500, 1.408) -- (10.700, 1.584) -- (10.900, 1.776) -- (11.100, 1.983) -- (11.300, 2.202) -- (11.500, 2.429) -- (11.700, 2.661) -- (11.900, 2.891) -- (12.100, 3.112) -- (12.300, 3.317) -- (12.500, 3.496) -- (12.700, 3.643) -- (12.900, 3.749) -- (13.100, 3.810) -- (13.300, 3.823) -- (13.500, 3.786) -- (13.700, 3.701) -- (13.900, 3.574) -- (14.100, 3.410) -- (14.300, 3.217) -- (14.500, 3.003) -- (14.700, 2.776) -- (14.900, 2.545) -- (15.100, 2.314) -- (15.300, 2.091) -- (15.500, 1.878) -- (15.700, 1.678) -- (15.900, 1.494) -- (16.100, 1.325) -- (16.300, 1.172) -- (16.500, 1.035) -- (16.700, 0.913) -- (16.900, 0.804) -- (17.100, 0.708) -- (17.300, 0.623) -- (17.500, 0.549) -- (17.700, 0.483) -- (17.900, 0.426) -- (18.100, 0.376) -- (18.300, 0.332) -- (18.500, 0.294) -- (18.700, 0.260) -- (18.900, 0.231) -- (19.100, 0.205) -- (19.300, 0.182) -- (19.500, 0.162) -- (19.700, 0.145) -- (19.900, 0.129) -- (20.100, 0.116) -- (20.300, 0.104) -- (20.500, 0.093) -- (20.700, 0.084) -- (20.900, 0.076) -- (21.100, 0.068) -- (21.300, 0.062) -- (21.500, 0.056) -- (21.700, 0.051) -- (21.900, 0.046) -- (22.100, 0.042) -- (22.300, 0.038) -- (22.500, 0.035) -- (22.700, 0.032) -- (22.900, 0.029) -- (23.100, 0.026) -- (23.300, 0.024) -- (23.500, 0.022) -- (23.700, 0.020) -- (23.900, 0.019);
\end{tikzpicture}
\end{document}

Wartning

The C++ code numerates the cases beginning with zero.

References

Kywords

«Duration5», «ju24da.cin», «Student Distribution», «Student.cin»,