set term svg size 800,600 enhanced font 'Liberation Sans, 24'
set output 'f_pdf.svg'

set samples 500
set xrange [0:5]
set yrange [0:2.5]
set xtics 1
set ytics 0.5
set xzeroaxis lt -1 lc rgb "black" lw 1
set yzeroaxis lt -1 lc rgb "black" lw 1

# Draw the F distribution's pdf
set key default

f(x,d1,d2) = gamma(d1/2+d2/2)/gamma(d1/2)/gamma(d2/2)*((d1/d2)**(d1/2))*(x**(d1/2-1))*((1+d1*x/d2)**(-0.5*d1-0.5*d2))

plot f(x, 1.0, 1.0) t "d1=1, d2=1" lc rgb "red" lw 5,\
   f(x, 2.0, 1.0) t "d1=2, d2=1" lc rgb "black" lw 5,\
   f(x, 5.0, 2.0) t "d1=5, d2=2" lc rgb "blue" lw 5,\
   f(x,10.0, 1.0) t "d1=10, d2=1" lc rgb "green" lw 5,\
   f(x,100.0, 100.0) t "d1=100, d2=100" lc rgb "grey" lw 5

set output