File:Lognot300.jpg

Explicit plot of Lognormal distribution $\displaystyle F(r)=\frac{1}{r\sqrt{\pi}} \exp\!\Big(\!-\ln(r)^2 \Big)$ versus $r$.

C++ generator of curve
//#include //#define DB double //typedef std::complex z_type; //#define Re(x) x.real //#define Im(x) x.imag //#define RI(x) x.real,x.imag //#define I z_type(0.,1.) //#include"fafo.cin"
 * 1) include
 * 2) include
 * 3) include 
 * 1) define DB float
 * 1) define DO(x,y) for(x=0;x<y;x++)
 * 2) include "ado.cin"

//DB F(DB x,DB t){ return exp(-x*x/(4.*t))/sqrt(t);} //DB F(DB x){ x-=.1; return exp(-x*x*4.);}

DB distribu(DB z) { DB L=log(z); return (1./sqrt(M_PI))*exp(-L*L)/z;}

int main{ int j,m,n, N=128; FILE *o; DB x,y; o=fopen("logno.eps","w"); ado(o,404,104); fprintf(o,"2 2 translate 100 100 scale\n"); for(m=0;m<5;m++) { M(m,1) if(m==0) L(m,-.1) else L(m,0) } for(n=0;n<2;n++) {M(0,n) L(4,n)} fprintf(o,".004 W S\n"); DO(m,501){x=.001+.01*m; y=distribu(x); if(m==0)M(x,y)else L(x,y); printf("%8.4f %8.4f\n",x,y); } fprintf(o,".02 W 0 0 1 RGB S\n"); // initial fprintf(o,"showpage\n%cTrailer",'%'); fclose(o); printf("close o\n"); system("epstopdf logno.eps"); system(  "open  logno.pdf"); }
 * 1) define M(x,y) fprintf(o,"%6.4f %6.4f M\n",0.+x,0.+y);
 * 2) define L(x,y) fprintf(o,"%6.4f %6.4f L\n",0.+x,0.+y);
 * 3) define o(x,y) fprintf(o,"%6.4f %6.4f o\n",0.+x,0.+y);

Latex generator of curve
\documentclass[12pt]{article} \usepackage{geometry} \usepackage{graphics} \paperwidth 410pt \paperheight 118pt \textwidth 420pt \textheight 300pt \topmargin -108pt \oddsidemargin -73pt \newcommand \ds {\displaystyle} \newcommand \sx {\scalebox} \newcommand \rme {\mathrm{e}} \newcommand \rot {\begin{rotate}} \newcommand \ero {\end{rotate}} \newcommand \ing {\includegraphics} \newcommand \rmi {\mathrm{i}} \newcommand \iL[1] {~ \label{#1} ~{~}~{\rm [#1]}\!{\!}\!} % make labels visible %\newcommand \iL[1] {~ \label{#1} } % hide the labels \newcommand \be {\begin{eqnarray}} \newcommand \ee {\end{eqnarray}} \newcommand \eL[1] {\iL{#1} \end{eqnarray}} \newcommand \rf[1] {(\ref{#1})} \newcommand \JP[1] {} % Japanese is not supported \pagestyle{empty} \parindent 0pt \begin{document} \begin{picture}(410,114) \put(6,8){\ing{logno}} \put(0,105){\sx{1.3}{$1$}} \put(0, 5){\sx{1.3}{$0$}} \put(105,-2){\sx{1.3}{$1$}} \put(205,-2){\sx{1.3}{$2$}} \put(305,-2){\sx{1.3}{$3$}} \put(403,-2){\sx{1.3}{$r$}} \put(43,89){\sx{1.2}{$\displaystyle F(r)\!=\!\frac{1}{r \sqrt{\pi}} \exp\!\Big(\!-\ln(r)^2 \Big)$}} \end{picture} \end{document}