function px = LogNormal( x,  mu, sigma )
% calculates a scaled lognormal probability density
% we fix the mean and standard deviation so that the distributions have the same shape on a logarithmic axis
% we then scale x by a parameter s to shift this shape along the axis
% returns P_s(x)

muprime = log(mu^2 / sqrt(sigma^2 + mu^2));
sigmaprime = sqrt(log(1 + sigma^2 / mu^2));
px = 1/sqrt(2*pi)/sigmaprime/x * exp(-0.5*((log(x)-muprime)/sigmaprime)^2);

end

