reset
#
# This example taken from 
# http://amca01.wordpress.com/2012/05/29/a-piecewise-polynomial-approximation-to-the-normal-cdf/
# Original approximation from John Hoyt (1962), The American Statistician 22:25-26.
#
set termopt enhanced
set termopt dash
save_encoding = GPVAL_ENCODING; set encoding utf8

set title "Piecewise approximation to the\nNormal Cumulative Distribution Function"

set format "%.1f"
set key left Left reverse invert
set style data lines
set xtics nomirror
set xrange [ 0   : 4 ]
set yrange [ 0.5 : 1.1 ]
set style line 1 lt 0 lw 3
set style line 2 lt 0 lw 3 lc rgb "red"

part1(x) = 0.5 + (9.*x-x**3)/ 24.
part2(x) = 1.0 + (x-3.0)**3 / 48.

part1 = "part1: for x < 1  norm(x) ≈  ½ + (9x-x^3) / 24"
part2 = "part2: for x > 1  norm(x) ≈   1 +  (x-3)^3 / 48"

set label 1 at 1.0, 0.62
set label 1 "plot norm(x),  [0:1] part1(x),  [1:4] part2(x)"
set arrow 1 from 1.,.7 to 1.,.9 nohead

plot norm(x) lt -1, \
     [1:4] part2(x) ls 2 title part2, \
     [0:1] part1(x) ls 1 title part1


Click here for minimal script to generate this plot

set termopt solid
reset

set border 16
unset xtics
unset ytics
set style data lines
set key center at screen 0.5, screen 0.15
set title font ",15"
set title "Piecewise function of one parameter in 3D"

splot [-2:2][-2:2] sample \
   [h=1:5]   '+' using (cos(h)):(sin(h)):(h), \
   [h=5:10]  '+' using (cos(h)):(sin(h)):(h), \
   [h=10:15] '+' using (cos(h)):(sin(h)):(h)


Click here for minimal script to generate this plot

set encoding save_encoding
reset