Probability density function for the normal distribution

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gnuplot source under GPL; originally by MarkSweep:

_ln_dnorm(x, m, s) = -0.5 * log(2*pi) - log(s) - 0.5*((x-m)*1.0/s)**2
dnorm(x, mean, sd) = exp(_ln_dnorm(x, mean, sd))
pnorm(x, mean, sd) = norm((x-mean) * 1.0/sd)

set terminal svg
set output 'Normal distribution pdf.svg' 

set xrange [-5:5]
set xtics 1
set yrange [0:1]
set ytics 0.1

f(x,y,z) = dnorm(x, y, sqrt(z)) #use variance, not sd!
set key 3.8,0.94

#f(x,y,z) = pnorm(x, y, sqrt(z))
#set key 3.8,0.2

plot \
   
    f(x,  0, 1)   title "μ =  0, σ² = 1.0", \
    f(x,  0, 5)   title "μ =  0, σ² = 5.0", \
    f(x, -2, 0.5) title "μ = -2, σ² = 0.5"

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