function eps = misfit(time_steps,pdf_tuts,pdf_tu,pdf_ts,w)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%
%%% Misfit (mean of the differences) between cdf of tu+ts (known from the data), 
%%% and connvolved cdf of tu (known from the data) and the unknown
%%% component, ts; w is the weight of ts cdf relative to conv(tu,ts) cdf in
%%% the misfit calcualtion vs tuts cdf
%%%
%%% time_steps: vector of steps covering the given time range
%%%
%%% Dmitry Yumashev, 20/11/2019
%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

total_time_steps = length(time_steps);

% first vector: convolution (transformed to cdf) of the known tu and unknown ts (both pdfs)

[~, cdf_conv] = pdf_convolution(time_steps,pdf_tu,pdf_ts);


% second vector: reconstructed cdf of the known tuts distribution

cdf_tuts = zeros(total_time_steps,1);
cdf_ts = zeros(total_time_steps,1);

cdf_tuts(1) = 0; % initial value (just in case)
cdf_ts(1) = 0; % initial value (just in case)

for i=2:total_time_steps % NOTE the starting value
    
    delta = time_steps(i) - time_steps(i-1);
      
    cdf_tuts(i) = cdf_tuts(i-1) + pdf_tuts(i-1) * delta;
    cdf_ts(i) = cdf_ts(i-1) + pdf_ts(i-1) * delta;
   
end


% cdf_ts = wblcdf(time_steps,y(1),y(2)); 

% make sure the dimensions are in agreement
if size(cdf_tuts,1) == size(cdf_conv,2) && size(cdf_tuts,2) == size(cdf_conv,1)

    cdf_conv = transpose(cdf_conv);
    
end


% eps = sqrt(sum((cdf_ref - (w * cdf_ts + (1-w) * cdf_conv)).^2) / total_time_steps);

% eps = sum(abs(cdf_tuts - cdf_conv));

eps = sum(abs(cdf_tuts - (w*cdf_ts + (1-w)*cdf_conv))) / total_time_steps;

%%%

end