function [PDF, PDF_interp, CDF, CDF_interp] = economics_pdf(X,fx, rnd)

% function to analyse economic datasets with expenditures of Cereals, other
% Foods, Non-food given as input X with frequency bins fx and rounds rnd 
%(multiple per year)

% prepare variables and index the observations in each round.
%PDF = 0; PDF_interp = 0; CDF = 0; CDF_interp = 0;

N = length(X);
index = find((rnd(1:end-1)-rnd(2:end))<0);
index = [0,index']; index(end+1) = N;

rounds = length(index)-1;
interp_length = 100;

for i = 1:rounds %1:rounds
    % CDF for X data
    rnd_length = index(i+1)-(index(i));
CDF{i}(2,:) = cumsum(fx(index(i)+1:index(i+1)));
CDF{i}(1,:) = X(index(i)+1:index(i+1))./max(X(index(i)+1:index(i+1)));

    % PDF for X data
PDF{i}(2,:) = [0;diff(cumsum(fx(index(i)+1:index(i+1))))];
PDF{i}(1,:) = X(index(i)+1:index(i+1))./max(X(index(i)+1:index(i+1)));

% smoothing of CDF and PDF using piecewise cubic hermite interpolating polynomials
l1 = pchip(X(index(i)+1:index(i+1),1)./(max(X(index(i)+1:index(i+1),1))),[0;diff(cumsum(fx(index(i)+1:index(i+1))))],linspace(min(X(index(i)+1:index(i+1),1)./(ones(rnd_length,1)*max(X(index(i)+1:index(i+1),1)))),1,interp_length));
l2 = pchip(X(index(i)+1:index(i+1))./(max(X(index(i)+1:index(i+1)))), cumsum(fx(index(i)+1:index(i+1)))./100,linspace(min(X(index(i)+1:index(i+1))./(max(X(index(i)+1:index(i+1))))), 1, interp_length));

CDF_interp{i}(2,:) = l2;
CDF_interp{i}(1,:) = linspace(min(X(index(i)+1:index(i+1))./(max(X(index(i)+1:index(i+1))))), 1, interp_length);

PDF_interp{i}(2,:) = l1;
PDF_interp{i}(1,:) = linspace(min(X(index(i)+1:index(i+1),1)./(ones(rnd_length,1)*max(X(index(i)+1:index(i+1),1)))),1,interp_length);
end
end