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\newdimen\unit \unit=1.375in
\newdimen\shadeunit
\newif \ifFirstPass
\FirstPasstrue
%\FirstPassfalse % uncomment this after you have the size you want
%
\def\DF{{\cal A}}%
%
%The following figure appears in the preface to the \PiCTeX\ manual
%
$$
\beginpicture
\ifFirstPass
\savelinesandcurves on "pictex-Arcsine.tex"
\else
\replot "pictex-Arcsine.tex"
\fi
% \ninepoint % (See Appendix E of the TeXbook.)
\normalgraphs
% Density plot
\setcoordinatesystem units <\unit,.4\unit> point at 0 0
\setplotarea x from 0 to 1, y from 0 to 2.5
\axis bottom invisible label {\lines {$t$\cr
shaded area is $\DF(\beta) - \DF(\alpha)$\cr}} ticks
numbered from 0.0 to 1.0 by 0.5
unlabeled short quantity 11
length <0pt> withvalues $\alpha$ $\beta$ / at .65 .85 / /
\axis left invisible label {$a(t)$} ticks
numbered from 0.0 to 2.0 by 1.0
unlabeled short from 0.5 to 2.5 by 1.0 /
\plotheading{\lineskiplimit=1pt \lines{%
Density\cr
$a(t) = 1\big/\bigl(\pi \sqrt{t(1-t)}\,\bigr)$\cr
of the arc sine law\cr}}
\grid 1 1
\putrule from .65 0.0 to .65 .66736
\putrule from .85 0.0 to .85 .89145
\shadeunit=.2\unit \divide\shadeunit by 12
\setshadegrid span <\shadeunit> point at .75 0
\setquadratic
\vshade .65 0 .66736 <,,,1pt> .75 0 .73511 .85 0 .89145 /
% Move origin to (.5,0)
% Left half}
\ifFirstPass
\setcoordinatesystem point at -.5 0
\inboundscheckon
\plot -.48429 2.55990 -.47553 2.06015 -.46489 1.72936 /
\inboundscheckoff
\plot -.46489 1.72936 -.43815 1.32146 -.40451 1.08308
-.36448 .92999 -.31871 .82623 -.26791 .75400
-.21289 .70358 -.12434 .65727 .0 .63662 /
% Right half
\inboundscheckon
\plot .48429 2.55990 .47553 2.06015 .46489 1.72936 /
\inboundscheckoff
\plot .46489 1.72936 .43815 1.32146 .40451 1.08308
.36448 .92999 .31871 .82623 .26791 .75400
.21289 .70358 .12434 .65727 .0 .63662 /
\fi
% Distribution function
% Set origin of new coordinate system 1.7*1.375in=2.34in
% to the right of the original origin.
\setcoordinatesystem units <\unit,\unit> point at -1.7 0
\setplotarea x from 0 to 1, y from 0 to 1
\axis bottom label {$x\vphantom{t}$} ticks
numbered from 0.0 to 1.0 by 0.5 unlabeled short quantity 11 /
\axis left label {$\DF(x)$} ticks
numbered from 0.0 to 1.0 by 0.5 unlabeled short quantity 11 /
\plotheading{\lines{%
Distribution function\cr
$\DF(x) = {2\over \raise1pt\hbox{\seveni ^^Y}}
\arcsin(\sqrt{x}\,)$\cr
of the arc sine law\cr}}
\linethickness=.25pt \grid {20} {20}
\linethickness=.4pt \grid 2 2
% Left half
% Now move origin of coordinate system up to (.5,.5)
\ifFirstPass
\setcoordinatesystem point at -2.2 -.5
\plot -.50000 -.50 -.49901 -.48 -.49606 -.46
-.49104 -.44 -.48439 -.42 -.47553 -.40 -.46489 -.38
-.43815 -.34 -.40451 -.30 -.36448 -.26 -.31871 -.22
-.26791 -.18 -.21289 -.14 -.12434 -.08 .0 .0 /
% Right half
\plot .50000 .50 .49901 .48 .49606 .46
.49104 .44 .48439 .42 .47553 .40 .46489 .38
.43815 .34 .40451 .30 .36448 .26 .31871 .22
.26791 .18 .21289 .14 .12434 .08 .0 .0 /
\fi
\endpicture
$$
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