I am trying to draw the Rogers Diffusion of Innovations Curve in Tikz figures Latex. I am a beginner in Tikz and not sure where to start. It is the curve on the right and shown here.enter image description here


3 Answers 3


Here's an alternative approach using luamplib to include some Metapost code. Compile with lualatex.

enter image description here

\usepackage{fontspec}\setmainfont{TeX Gyre Heros}

    vardef exp(expr x) = mexp(256x) enddef; % hide MP's version of exp

    vardef normal_cdf(expr x) = 
        numeric sum, value;
        sum = value = x;
        for i=1 upto infinity:
           value := value * x * x / (2i+1);
           exitif abs(value)<eps;
           sum := sum + value;

    vardef normal_pdf(expr x) = 
        exp(-1/2x*x)/2.50662827463  % \sqrt(2\pi) \simeq 2.50663 

    path cdf_curve, pdf_curve;

    % horizontal and vertical units
    numeric u,v;
    u = 16mm; v = 16mm;

    numeric s, r; r=3; s=1/64;
    cdf_curve = ((-r,normal_cdf(-r)) for t=s-r step s until r: -- (t,normal_cdf(t)) endfor) xscaled u yscaled 4v;
    pdf_curve = ((-r,normal_pdf(-r)) for t=s-r step s until r: -- (t,normal_pdf(t)) endfor) xscaled u yscaled 5v;

    path xx;
    xx = (left--right) scaled (r*u);

    z1 = cdf_curve intersectionpoint (xx shifted (0,4v * 0.025)); % 2.5%
    z2 = cdf_curve intersectionpoint (xx shifted (0,4v * 0.160)); % 16%

    drawoptions(withpen pencircle scaled 1/4 withcolor 1/2 white);

    draw ( x1,-2) -- ( x1,4v) cutafter pdf_curve;
    draw ( x2,-2) -- ( x2,4v) cutafter pdf_curve;
    draw (  0,-2) -- (  0,4v) cutafter pdf_curve; % cheating
    draw (-x2,-2) -- (-x2,4v) cutafter pdf_curve; % because centred on 0

    % x-axis
    draw xx shifted 2 down;

    % y-scale
    draw (origin -- up scaled 4v) shifted (3u+4,0);
    for y=0 step 25 until 100:
       draw (3u+4,y/100*4v) -- (3u+6,y/100*4v);
       label.rt(decimal y,     (3u+6,y/100*4v));


    draw cdf_curve withcolor red + 1/2green;
    draw pdf_curve withcolor 2/3 blue;



  • I've assumed the curves are supposed to be the normal PDF and CDF but the OP does not really make this explicit.

  • You have to cheat to get the curves to meet in the middle like that. Notice that I've exaggerated the vertical scale of the PDF by 25%.

  • I've used the double-precision number system to avoid some turbulence in calculating the PDF for values outside the band -3 < x < 3.

  • If you want flatter ends to the curves, set r to a larger value (but the PDF is essentially zero outside the range -4 < r < 4).

  • The constant 2.50662827463 is \sqrt{2\pi}.

  • The remaining labels are left as an exercise for the reader.


This should give you a starting point.

    axis x line=bottom,
    axis y line=right,
    axis line style={-},
      Innovators 2.5\%,
      Early Adopters 13.5\%,
      Early Najority 34\%,
      Late Najority 34\%,
      Laggards 16\%,
    x tick label style={rotate=45,anchor=east},
    ylabel={Market share \%},
    ymin=0, ymax=110,
    samples=51, smooth, no markers,

    \addplot+[blue,very thick] {50*exp(-.5*x^2)};

    \addplot+[orange,very thick] {100 / (1 + exp(-2*x))};

    \pgfplotsinvokeforeach{-3,...,1} {
      \draw[help lines] (axis cs:#1,{50*exp(-.5*(#1)^2)}) -- (axis cs:#1,0);


enter image description here


This will draw the Logistics function with the parameter k, as well as the first two labels. For a complete answer, the equation of the blue curve and the position of the vertical lines would be necessary.

        \draw[yellow] [domain=0:1, scale=10] plot (\x,{1/(1+exp(-\k*(2*\x-1))});
        \draw node[anchor=north west, text width=2cm] {Innovators \\ 2.5\%} (0,0) -- node[anchor=north west, text width=2cm] {Early Adopters \\ 13.5\%}(2.7,0) -- (10,0) node[anchor=west] {0} -- (10,2.5)  node[anchor=west] {25} -- (10,5)  node[anchor=west] {50} -- (10,7.5)  node[anchor=west] {75} -- (10,10) node[anchor=west] {100};
        \node[rotate=-90, anchor = south, yshift=.75cm] at (10,5) {Market Share \%};
  • It's not really clear from the OP but I think the curve that looks like the logit is really supposed to the the normal CDF...
    – Thruston
    Dec 22, 2016 at 14:16

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