<br><font size=2 face="sans-serif">Hi,</font>
<br>
<br><font size=2 face="sans-serif">I need to draw the density function
of the Vasicek distribution: This density function has the following structure:</font>
<br>
<br><font size=2 face="sans-serif">a * Exp[ (b * norminv(x) + c)^2 + d
* norminv(x)^2 ] where a,b,c and d are constants.</font>
<br>
<br><font size=2 face="sans-serif">Since there exist an Exp-operator in
pstricks, the only thing I need is a norminv operator (an approximation
of the inverse of the standard normal distribution). </font>
<br><font size=2 face="sans-serif">Is there someone who can help me to
build this in pstricks?</font>
<br>
<br><font size=2 face="sans-serif">On</font>
<br><font size=2 face="sans-serif">http://home.online.no/~pjacklam/notes/invnorm/index.html#The_algorithm</font>
<br><font size=2 face="sans-serif">you can find the algorithm in several
programming languages.</font>
<br>
<br><font size=2 face="sans-serif">Here a perl implementation:</font>
<br>
<br><font size=2 face="sans-serif">sub ltqnorm ($) {</font>
<br><font size=2 face="sans-serif"> #</font>
<br><font size=2 face="sans-serif"> # Lower tail quantile
for standard normal distribution function.</font>
<br><font size=2 face="sans-serif"> #</font>
<br><font size=2 face="sans-serif"> # This function returns
an approximation of the inverse cumulative</font>
<br><font size=2 face="sans-serif"> # standard normal distribution
function. I.e., given P, it returns</font>
<br><font size=2 face="sans-serif"> # an approximation to
the X satisfying P = Pr{Z <= X} where Z is a</font>
<br><font size=2 face="sans-serif"> # random variable from
the standard normal distribution.</font>
<br><font size=2 face="sans-serif"> #</font>
<br><font size=2 face="sans-serif"> # The algorithm uses a
minimax approximation by rational functions</font>
<br><font size=2 face="sans-serif"> # and the result has a
relative error whose absolute value is less</font>
<br><font size=2 face="sans-serif"> # than 1.15e-9.</font>
<br><font size=2 face="sans-serif"> #</font>
<br><font size=2 face="sans-serif"> # Author:
Peter John Acklam</font>
<br><font size=2 face="sans-serif"> # Time-stamp: 2000-07-19
18:26:14</font>
<br><font size=2 face="sans-serif"> # E-mail:
pjacklam@online.no</font>
<br><font size=2 face="sans-serif"> # WWW URL:
http://home.online.no/~pjacklam</font>
<br>
<br><font size=2 face="sans-serif"> my $p = shift;</font>
<br><font size=2 face="sans-serif"> die "input argument
must be in (0,1)\n" unless 0 < $p && $p < 1;</font>
<br>
<br><font size=2 face="sans-serif"> # Coefficients in rational
approximations.</font>
<br><font size=2 face="sans-serif"> my @a = (-3.969683028665376e+01,
2.209460984245205e+02,</font>
<br><font size=2 face="sans-serif">
-2.759285104469687e+02, 1.383577518672690e+02,</font>
<br><font size=2 face="sans-serif">
-3.066479806614716e+01, 2.506628277459239e+00);</font>
<br><font size=2 face="sans-serif"> my @b = (-5.447609879822406e+01,
1.615858368580409e+02,</font>
<br><font size=2 face="sans-serif">
-1.556989798598866e+02, 6.680131188771972e+01,</font>
<br><font size=2 face="sans-serif">
-1.328068155288572e+01 );</font>
<br><font size=2 face="sans-serif"> my @c = (-7.784894002430293e-03,
-3.223964580411365e-01,</font>
<br><font size=2 face="sans-serif">
-2.400758277161838e+00, -2.549732539343734e+00,</font>
<br><font size=2 face="sans-serif">
4.374664141464968e+00, 2.938163982698783e+00);</font>
<br><font size=2 face="sans-serif"> my @d = ( 7.784695709041462e-03,
3.224671290700398e-01,</font>
<br><font size=2 face="sans-serif">
2.445134137142996e+00, 3.754408661907416e+00);</font>
<br>
<br><font size=2 face="sans-serif"> # Define break-points.</font>
<br><font size=2 face="sans-serif"> my $plow = 0.02425;</font>
<br><font size=2 face="sans-serif"> my $phigh = 1 - $plow;</font>
<br>
<br><font size=2 face="sans-serif"> # Rational approximation
for lower region:</font>
<br><font size=2 face="sans-serif"> if ( $p < $plow ) {</font>
<br><font size=2 face="sans-serif"> my $q =
sqrt(-2*log($p));</font>
<br><font size=2 face="sans-serif"> return ((((($c[0]*$q+$c[1])*$q+$c[2])*$q+$c[3])*$q+$c[4])*$q+$c[5])
/</font>
<br><font size=2 face="sans-serif">
(((($d[0]*$q+$d[1])*$q+$d[2])*$q+$d[3])*$q+1);</font>
<br><font size=2 face="sans-serif"> }</font>
<br>
<br><font size=2 face="sans-serif"> # Rational approximation
for upper region:</font>
<br><font size=2 face="sans-serif"> if ( $phigh < $p )
{</font>
<br><font size=2 face="sans-serif"> my $q =
sqrt(-2*log(1-$p));</font>
<br><font size=2 face="sans-serif"> return -((((($c[0]*$q+$c[1])*$q+$c[2])*$q+$c[3])*$q+$c[4])*$q+$c[5])
/</font>
<br><font size=2 face="sans-serif">
(((($d[0]*$q+$d[1])*$q+$d[2])*$q+$d[3])*$q+1);</font>
<br><font size=2 face="sans-serif"> }</font>
<br>
<br><font size=2 face="sans-serif"> # Rational approximation
for central region:</font>
<br><font size=2 face="sans-serif"> my $q = $p - 0.5;</font>
<br><font size=2 face="sans-serif"> my $r = $q*$q;</font>
<br><font size=2 face="sans-serif"> return ((((($a[0]*$r+$a[1])*$r+$a[2])*$r+$a[3])*$r+$a[4])*$r+$a[5])*$q
/</font>
<br><font size=2 face="sans-serif"> ((((($b[0]*$r+$b[1])*$r+$b[2])*$r+$b[3])*$r+$b[4])*$r+1);</font>
<br><font size=2 face="sans-serif">}</font>
<br>
<br><font size=2 face="sans-serif">Kind regards,<br>
Matt</font>
<br>
<span style="font-family:'Microsoft Sans Serif',sans-serif; font-size:8pt; color:#000000">-- </span><br>
<br>
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