File:Linea.jpg

Density \(F(t)\) of likelihood of the mean logarithm of Duration to have value \(:\) evaluates with 5 examples from article Duration5 for the Second model (moral distribution of logarithm of Duration).

The figure is prepared for 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]; float d[N]; float 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 %6.4f\n", Y1,M1,D1, Y2,M2,D2, s[n], D[n], d[n], L[n]);
} fclose(i);

p=0.; for(n=0;n<N;n++) p+=L[n];  p/=N; printf("p=%5.2f\n",p);
q=0.; for(n=0;n<N;n++) {r=L[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("Duration5Logari.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,"\\Large\n");
//fprintf(o,"\\begin{tikzpicture}[scale=2]\n");
fprintf(o,"\\begin{tikzpicture}[scale=5]\n");
fprintf(o,"\\draw [line width=0.981] (0,0) grid (6,2);\n");
fprintf(o,"\\draw [line width=2.3] (0,2.2) -- (0,0) -- (6.1,0) ;\n");
// fprintf(o,"\\draw(0,0) -- (0,3.2) ;\n");

fprintf(o,"\\definecolor{light}{rgb}{1,1,.6};\n");
fprintf(o,"\\definecolor{dark}{rgb}{0,1,1};\n");
fprintf(o,"\\draw[line width=12, light] (3,0.03) -- (3,1.4) ;\n");
//fprintf(o,"\\draw (8,0.6) node[rotate=90,right] {\\bf Russia 2028};\n");
fprintf(o,"\\draw (3,0.6) node[rotate=90,right] {\\bf Russia 2028};\n");
fprintf(o,"\\draw[line width=12, light] (%4.2f,0.03) -- (%4.2f,1.4) ;\n",log2(22.),log2(22.));
fprintf(o,"\\draw(%4.2f,0.6) node[rotate=90,right] {\\bf Moscow 2042};\n", log2(22.));

for(n=0;n<N;n++)
{
fprintf(o,"\\draw[line width=8, dark] (%5.3f,0.04) -- (%5.3f,0.4) ;\n",L[n], L[n]);
fprintf(o,"\\draw (%5.3f,0.3) node[rotate=90,left] {\\bf %s};\n",L[n],s[n]);
printf("%1d %s\n",n,s[n]);
}

fprintf(o,"\\Huge\n");
fprintf(o,"\\draw (.04,2.1) node[right] {\\(F(L)\\)};\n");
for(n=0;n<3;n+=1) fprintf(o,"\\draw (0,%d) node[left] {%d};\n",n,n);
for(n=0;n<6;n++) fprintf(o,"\\draw (%d,0) node[below] {%d};\n",n,n);
                 fprintf(o,"\\draw (%d,0) node[below] {$L$};\n",n);

int m=1;
//for(n=0;n<7;n++){ fprintf(o,"\\draw (%d,-.2 node[below] {%d};\n",n,m); m*=2;}
for(n=0;n<6;n++) {fprintf(o,"\\draw (%d,-0.2) node[below] {%d};\n",n,m); m*=2;}
                 fprintf(o,"\\draw (%d,-0.2) node[below] {$t$, y.};\n",n);

fprintf(o,"\\draw[line width=5, red] (0,0)");
for(n=1;n<601;n+=2){x=.01*n; y=Student(N-1,(x-p)/U)/U;	fprintf(o," -- (%6.4f,%6.4f)",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 Duration5Logari.tex");
system("open Duration5Logari.pdf");
//system("convert Linear.pdf png8:Linear8.png");
//system("convert Linear.pdf Linear.jpg");
printf("p=0.; for(n=0;n<N;n++) p+=L[n]; p/=N;      resulling p=%8.6f\n",p);
printf("q=0.; for(n=0;n<N;n++) {r=L[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-1,p,U,U);
printf("sqrt(T*T+W*W)=%8.6f \n",sqrt(T*T+W*W));
printf("p-sqrt(T*T+W*W))=%8.6f \n",p-sqrt(T*T+W*W) );
printf("p+sqrt(T*T+W*W))=%8.6f \n",p+sqrt(T*T+W*W) );
printf("p-2*sqrt(T*T+W*W))=%8.6f \n",p-2*sqrt(T*T+W*W) );
printf("p+2*sqrt(T*T+W*W))=%8.6f \n",p+2*sqrt(T*T+W*W) );
printf("2^p=%8.6f\n",pow(2.,p));
printf("2^(p-2*sqrt(T*T+W*W)))=%8.6f \n",pow(2.,p-2*sqrt(T*T+W*W)) );
printf("2^(p-sqrt(T*T+W*W)))=%8.6f \n",pow(2.,p-sqrt(T*T+W*W)) );
printf("2^(p+sqrt(T*T+W*W)))=%8.6f \n",pow(2.,p+sqrt(T*T+W*W)) );
printf("2^(p+2*sqrt(T*T+W*W)))=%8.6f \n",pow(2.,p+2*sqrt(T*T+W*W)) );

}

Output text

Output written on Duration5Logari.pdf (1 page, 33280 bytes).
Transcript written on Duration5Logari.log.

1653 12 16 1661 04 23 eng 2685  7.3513 2.8780
1802 08 04 1815 11 20 fra 4856 13.2953 3.7328
1928 05 17 1947 12 27 ita 7163 19.6116 4.2936
1933 03 24 1945 05 08 ger 4428 12.1235 3.5997
1977 10 07 1991 08 20 sov 5065 13.8675 3.7936
p= 3.66
T= 0.51
U= 0.23
W= 0.32
0 eng
1 fra
2 ita
3 ger
4 sov
p=0.; for(n=0;n<N;n++) p+=L[n]; p/=N;      resulling p=3.659569
q=0.; for(n=0;n<N;n++) {r=L[n]-p; q+=r*r;} resulting q=1.039824
T=sqrt(q/(N-1.))     = 0.509859
U=sqrt(q/(N*(N-1.))) = 0.228016
W=sqrt(q/(N*(N-3.))) = 0.322463
g(d)=student4((d-3.659569)/0.228016)/0.228016
sqrt(T*T+W*W)=0.603273 
p-sqrt(T*T+W*W))=3.056296 
p+sqrt(T*T+W*W))=4.262842 
p-2*sqrt(T*T+W*W))=2.453023 
p+2*sqrt(T*T+W*W))=4.866115 
2^p=12.636883
2^(p-2*sqrt(T*T+W*W)))=5.475622 
2^(p-sqrt(T*T+W*W)))=8.318341 
2^(p+sqrt(T*T+W*W)))=19.197436 
2^(p+2*sqrt(T*T+W*W)))=29.163958 

Warning

Warning: the code numerates the cases beginning with zero.

Output Latex

\usepackage{graphicx}
\usepackage{tikz}
\begin{document}
\Large
\begin{tikzpicture}[scale=5]
\draw [line width=0.981] (0,0) grid (6,2);
\draw [line width=2.3] (0,2.2) -- (0,0) -- (6.1,0) ;
\definecolor{light}{rgb}{1,1,.6};
\definecolor{dark}{rgb}{0,1,1};
\draw[line width=12, light] (3,0.03) -- (3,1.4) ;
\draw (3,0.6) node[rotate=90,right] {\bf Russia 2028};
\draw[line width=12, light] (4.46,0.03) -- (4.46,1.4) ;
\draw(4.46,0.6) node[rotate=90,right] {\bf Moscow 2042};
\draw[line width=8, dark] (2.878,0.04) -- (2.878,0.4) ;
\draw (2.878,0.3) node[rotate=90,left] {\bf eng};
\draw[line width=8, dark] (3.733,0.04) -- (3.733,0.4) ;
\draw (3.733,0.3) node[rotate=90,left] {\bf fra};
\draw[line width=8, dark] (4.294,0.04) -- (4.294,0.4) ;
\draw (4.294,0.3) node[rotate=90,left] {\bf ita};
\draw[line width=8, dark] (3.600,0.04) -- (3.600,0.4) ;
\draw (3.600,0.3) node[rotate=90,left] {\bf ger};
\draw[line width=8, dark] (3.794,0.04) -- (3.794,0.4) ;
\draw (3.794,0.3) node[rotate=90,left] {\bf sov};
\Huge
\draw (.04,2.1) node[right] {\(F(L)\)};
\draw (0,0) node[left] {0};
\draw (0,1) node[left] {1};
\draw (0,2) node[left] {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] {$L$};
\draw (0,-0.2) node[below] {1};
\draw (1,-0.2) node[below] {2};
\draw (2,-0.2) node[below] {4};
\draw (3,-0.2) node[below] {8};
\draw (4,-0.2) node[below] {16};
\draw (5,-0.2) node[below] {32};
\draw (6,-0.2) node[below] {$t$, y.};
\draw[line width=5, red] (0,0) -- (0.0100,0.0000) -- (0.0300,0.0000) -- (0.0500,0.0001) -- (0.0700,0.0001) -- (0.0900,0.0001) -- (0.1100,0.0001) -- (0.1300,0.0001) -- (0.1500,0.0001) -- (0.1700,0.0001) -- (0.1900,0.0001) -- (0.2100,0.0001) -- (0.2300,0.0001) -- (0.2500,0.0001) -- (0.2700,0.0001) -- (0.2900,0.0001) -- (0.3100,0.0001) -- (0.3300,0.0001) -- (0.3500,0.0001) -- (0.3700,0.0001) -- (0.3900,0.0001) -- (0.4100,0.0001) -- (0.4300,0.0001) -- (0.4500,0.0001) -- (0.4700,0.0001) -- (0.4900,0.0001) -- (0.5100,0.0001) -- (0.5300,0.0001) -- (0.5500,0.0001) -- (0.5700,0.0001) -- (0.5900,0.0001) -- (0.6100,0.0001) -- (0.6300,0.0001) -- (0.6500,0.0001) -- (0.6700,0.0001) -- (0.6900,0.0001) -- (0.7100,0.0001) -- (0.7300,0.0001) -- (0.7500,0.0001) -- (0.7700,0.0002) -- (0.7900,0.0002) -- (0.8100,0.0002) -- (0.8300,0.0002) -- (0.8500,0.0002) -- (0.8700,0.0002) -- (0.8900,0.0002) -- (0.9100,0.0002) -- (0.9300,0.0002) -- (0.9500,0.0002) -- (0.9700,0.0002) -- (0.9900,0.0002) -- (1.0100,0.0002) -- (1.0300,0.0002) -- (1.0500,0.0002) -- (1.0700,0.0003) -- (1.0900,0.0003) -- (1.1100,0.0003) -- (1.1300,0.0003) -- (1.1500,0.0003) -- (1.1700,0.0003) -- (1.1900,0.0003) -- (1.2100,0.0003) -- (1.2300,0.0004) -- (1.2500,0.0004) -- (1.2700,0.0004) -- (1.2900,0.0004) -- (1.3100,0.0004) -- (1.3300,0.0004) -- (1.3500,0.0004) -- (1.3700,0.0005) -- (1.3900,0.0005) -- (1.4100,0.0005) -- (1.4300,0.0005) -- (1.4500,0.0006) -- (1.4700,0.0006) -- (1.4900,0.0006) -- (1.5100,0.0006) -- (1.5300,0.0007) -- (1.5500,0.0007) -- (1.5700,0.0007) -- (1.5900,0.0008) -- (1.6100,0.0008) -- (1.6300,0.0008) -- (1.6500,0.0009) -- (1.6700,0.0009) -- (1.6900,0.0010) -- (1.7100,0.0010) -- (1.7300,0.0011) -- (1.7500,0.0011) -- (1.7700,0.0012) -- (1.7900,0.0012) -- (1.8100,0.0013) -- (1.8300,0.0014) -- (1.8500,0.0014) -- (1.8700,0.0015) -- (1.8900,0.0016) -- (1.9100,0.0017) -- (1.9300,0.0018) -- (1.9500,0.0019) -- (1.9700,0.0020) -- (1.9900,0.0021) -- (2.0100,0.0022) -- (2.0300,0.0023) -- (2.0500,0.0025) -- (2.0700,0.0026) -- (2.0900,0.0028) -- (2.1100,0.0029) -- (2.1300,0.0031) -- (2.1500,0.0033) -- (2.1700,0.0035) -- (2.1900,0.0038) -- (2.2100,0.0040) -- (2.2300,0.0043) -- (2.2500,0.0045) -- (2.2700,0.0048) -- (2.2900,0.0052) -- (2.3100,0.0055) -- (2.3300,0.0059) -- (2.3500,0.0063) -- (2.3700,0.0068) -- (2.3900,0.0073) -- (2.4100,0.0078) -- (2.4300,0.0084) -- (2.4500,0.0090) -- (2.4700,0.0097) -- (2.4900,0.0104) -- (2.5100,0.0112) -- (2.5300,0.0121) -- (2.5500,0.0131) -- (2.5700,0.0141) -- (2.5900,0.0153) -- (2.6100,0.0165) -- (2.6300,0.0179) -- (2.6500,0.0194) -- (2.6700,0.0211) -- (2.6900,0.0230) -- (2.7100,0.0250) -- (2.7300,0.0273) -- (2.7500,0.0297) -- (2.7700,0.0325) -- (2.7900,0.0355) -- (2.8100,0.0389) -- (2.8300,0.0427) -- (2.8500,0.0468) -- (2.8700,0.0515) -- (2.8900,0.0566) -- (2.9100,0.0624) -- (2.9300,0.0688) -- (2.9500,0.0760) -- (2.9700,0.0840) -- (2.9900,0.0930) -- (3.0100,0.1030) -- (3.0300,0.1143) -- (3.0500,0.1269) -- (3.0700,0.1410) -- (3.0900,0.1569) -- (3.1100,0.1746) -- (3.1300,0.1946) -- (3.1500,0.2169) -- (3.1700,0.2419) -- (3.1900,0.2699) -- (3.2100,0.3012) -- (3.2300,0.3361) -- (3.2500,0.3749) -- (3.2700,0.4179) -- (3.2900,0.4655) -- (3.3100,0.5179) -- (3.3300,0.5752) -- (3.3500,0.6376) -- (3.3700,0.7051) -- (3.3900,0.7775) -- (3.4100,0.8543) -- (3.4300,0.9350) -- (3.4500,1.0187) -- (3.4700,1.1041) -- (3.4900,1.1898) -- (3.5100,1.2739) -- (3.5300,1.3545) -- (3.5500,1.4293) -- (3.5700,1.4961) -- (3.5900,1.5527) -- (3.6100,1.5970) -- (3.6300,1.6275) -- (3.6500,1.6428) -- (3.6700,1.6425) -- (3.6900,1.6265) -- (3.7100,1.5954) -- (3.7300,1.5505) -- (3.7500,1.4934) -- (3.7700,1.4263) -- (3.7900,1.3511) -- (3.8100,1.2703) -- (3.8300,1.1861) -- (3.8500,1.1004) -- (3.8700,1.0150) -- (3.8900,0.9315) -- (3.9100,0.8509) -- (3.9300,0.7743) -- (3.9500,0.7021) -- (3.9700,0.6348) -- (3.9900,0.5726) -- (4.0100,0.5155) -- (4.0300,0.4634) -- (4.0500,0.4160) -- (4.0700,0.3731) -- (4.0900,0.3345) -- (4.1100,0.2998) -- (4.1300,0.2687) -- (4.1500,0.2408) -- (4.1700,0.2159) -- (4.1900,0.1937) -- (4.2100,0.1738) -- (4.2300,0.1561) -- (4.2500,0.1404) -- (4.2700,0.1263) -- (4.2900,0.1137) -- (4.3100,0.1025) -- (4.3300,0.0926) -- (4.3500,0.0836) -- (4.3700,0.0756) -- (4.3900,0.0685) -- (4.4100,0.0621) -- (4.4300,0.0564) -- (4.4500,0.0513) -- (4.4700,0.0466) -- (4.4900,0.0425) -- (4.5100,0.0388) -- (4.5300,0.0354) -- (4.5500,0.0324) -- (4.5700,0.0296) -- (4.5900,0.0272) -- (4.6100,0.0249) -- (4.6300,0.0229) -- (4.6500,0.0210) -- (4.6700,0.0194) -- (4.6900,0.0179) -- (4.7100,0.0165) -- (4.7300,0.0152) -- (4.7500,0.0141) -- (4.7700,0.0130) -- (4.7900,0.0121) -- (4.8100,0.0112) -- (4.8300,0.0104) -- (4.8500,0.0096) -- (4.8700,0.0090) -- (4.8900,0.0083) -- (4.9100,0.0078) -- (4.9300,0.0072) -- (4.9500,0.0068) -- (4.9700,0.0063) -- (4.9900,0.0059) -- (5.0100,0.0055) -- (5.0300,0.0052) -- (5.0500,0.0048) -- (5.0700,0.0045) -- (5.0900,0.0043) -- (5.1100,0.0040) -- (5.1300,0.0038) -- (5.1500,0.0035) -- (5.1700,0.0033) -- (5.1900,0.0031) -- (5.2100,0.0029) -- (5.2300,0.0028) -- (5.2500,0.0026) -- (5.2700,0.0025) -- (5.2900,0.0023) -- (5.3100,0.0022) -- (5.3300,0.0021) -- (5.3500,0.0020) -- (5.3700,0.0019) -- (5.3900,0.0018) -- (5.4100,0.0017) -- (5.4300,0.0016) -- (5.4500,0.0015) -- (5.4700,0.0014) -- (5.4900,0.0014) -- (5.5100,0.0013) -- (5.5300,0.0012) -- (5.5500,0.0012) -- (5.5700,0.0011) -- (5.5900,0.0011) -- (5.6100,0.0010) -- (5.6300,0.0010) -- (5.6500,0.0009) -- (5.6700,0.0009) -- (5.6900,0.0008) -- (5.7100,0.0008) -- (5.7300,0.0008) -- (5.7500,0.0007) -- (5.7700,0.0007) -- (5.7900,0.0007) -- (5.8100,0.0006) -- (5.8300,0.0006) -- (5.8500,0.0006) -- (5.8700,0.0006) -- (5.8900,0.0005) -- (5.9100,0.0005) -- (5.9300,0.0005) -- (5.9500,0.0005) -- (5.9700,0.0004) -- (5.9900,0.0004);
\end{tikzpicture}
\end{document}

References

Kywords

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