function eps = misfit(time_steps,par_tuts,par_tu,x)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%
%%% Misfit (root mean square) between cdf of tu+ts (weibull approximation of the data, with
%%% parameters par_tuts = (a_tuts, b_tuts)), and connvolved cdf of tu (weibull 
%%% approximation of the data, with parameters par_tu = (a_tu, b_tu)) and the unknown
%%% component, ts (weibul parameters x = (x(1), x(2)))
%%%
%%% time_steps: vector of steps covering the given time range
%%%
%%% Dmitry Yumashev, 20/11/2019
%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

total_time_steps = length(time_steps);

y = x(1:2);
% w = x(3);

% first vector: convolution (transformed to cdf) of the known tu and unknown tx (both pdfs)
[~, cdf_conv] = pdf_convolution(time_steps,par_tu,y);

a_tuts = par_tuts(1);
b_tuts = par_tuts(2);

% second vector: known tuts (cdf)

cdf_ref = wblcdf(time_steps,a_tuts,b_tuts); 

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

% make sure the dimensions are in agreement
if size(cdf_ref,1) == size(cdf_conv,2) && size(cdf_ref,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 = sqrt(sum((cdf_ref - cdf_conv).^2) / total_time_steps);

%%%

end