%Simulate error in magnitude due to error in flux measurements % mag = -2.5*log10(f/F) where %f is the spectral flux density %F is the "zero point" flux density (a constant) %Due to noise in detectors,etc the quantity f has %errors. That is f=<f> +/- df (here <f> means mean value of f and df is the %noise) %We assume that noise is Gaussian with zero mean (mu=0) and sigma

However, the first term is nothing but the mean magnitue, say "<mag>" The second term is the error in magnitude. What is plotted below is the sum of the first and second term.

n=10000; %number of variates meanmag=18; %we set "mag" to 18 rms=[0.01 0.03 0.1 0.3]; %redo the simulations for several values of sigma m=numel(rms); for j=1:m figure(j) sigma=rms(j); OutFile=['MagError' num2str(sigma) '.pdf']; x=normrnd(0,sigma,1,n); mag=meanmag-2.5*log10(max((1+x),eps)); %looks complicated. %what is happening here? %eps is a small value in %MATLAB histogram(mag); xlim([meanmag-5*sigma meanmag+10*sigma]); str=sprintf('meanmag:%3.0f sigma:%4.2f',meanmag,sigma); legend(str); title('Histogram: mag$-2.5\log10(1+x)$','Interpreter','LaTeX') print(OutFile,'-dpdf'); end