%   [m,PDF_NPT,CDF_NPT]=dist_NPT(Md,Mu,dM,Mmin,eps,h,xx,ambd,Mmax)
%
% USING THE NONPARAMETRIC ADAPTATIVE KERNEL ESTIMATORS EVALUATES THE DENSITY 
%   AND CUMULATIVE DISTRIBUTION FUNCTIONS FOR THE UPPER-BOUNDED MAGNITUDE 
%   DISTRIBUTION.
%
% AUTHOR: Stanislaw. Lasocki, Institute of Geophysics Polish Academy of
% Sciences, Warsaw, Poland
%
% DESCRIPTION: The kernel estimator approach is a model-free alternative 
% to estimating the magnitude distribution functions. It is assumed that 
% the magnitude distribution has a hard end point Mmax from the right hand  
% side.The estimation makes use of the previously estimated parameters 
% namely the mean activity rate lamb, the length of magnitude round-off 
% interval, eps, the smoothing factor, h, the background sample, xx, the 
% scaling factors for the background sample, ambd, and the end-point of 
% magnitude distribution Mmax. The background sample,xx, comprises the 
% randomized values of observed magnitude doubled symmetrically with 
% respect to the value Mmin-eps/2.
%
% REFERENCES:
%  Silverman B.W. (1986) Density Estimation for Statistics and Data Analysis, 
%   Chapman and Hall, London 
%  Kijko A., Lasocki S., Graham G. (2001) Pure appl. geophys. 158, 1655-1665
%  Lasocki S., Orlecka-Sikora B. (2008) Tectonophysics 456, 28-37
%
%INPUT:
%   Md - starting magnitude for distribution functions calculations
%   Mu - ending magnitude for distribution functions calculations
%   dM - magnitude step for distribution functions calculations
%   Mmin - lower bound of the distribution - catalog completeness level
%   eps - length of round-off interval of magnitudes.  
%   h - kernel smoothing factor.
%   xx - the background sample
%   ambd - the weigthing factors for the adaptive kernel
%   Mmax - upper limit of magnitude distribution
%
% OUTPUT:
%   m - vector of the independent variable (magnitude)
%   PDF_NPT - PDF vector
%   CDF_NPT - CDF vector
%
% LICENSE
%     This file is a part of the IS-EPOS e-PLATFORM.
%
%     This is free software: you can redistribute it and/or modify it under 
%     the terms of the GNU General Public License as published by the Free 
%     Software Foundation, either version 3 of the License, or 
%     (at your option) any later version.
% 
%     This program is distributed in the hope that it will be useful,
%     but WITHOUT ANY WARRANTY; without even the implied warranty of
%     MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
%     GNU General Public License for more details , <http://www.gnu.org/licenses/>.
% 

function [m,PDF_NPT,CDF_NPT]=dist_NPT(Md,Mu,dM,Mmin,eps,h,xx,ambd,Mmax)

m=(Md:dM:Mu)';
nn=length(m);

mian=2*(Dystr_npr(Mmax,xx,ambd,h)-Dystr_npr(Mmin-eps/2,xx,ambd,h));
for i=1:nn
    if m(i)<Mmin-eps/2
        PDF_NPT(i)=0;CDF_NPT(i)=0;
    elseif m(i)>Mmax
        PDF_NPT(i)=0;CDF_NPT(i)=1;
    else
    PDF_NPT(i)=dens_npr1(m(i),xx,ambd,h,Mmin-eps/2)/mian;
    CDF_NPT(i)=2*(Dystr_npr(m(i),xx,ambd,h)-Dystr_npr(Mmin-eps/2,xx,ambd,h))/mian;
    end
end
PDF_NPT=PDF_NPT';CDF_NPT=CDF_NPT';
end

function [gau]=dens_npr1(y,x,ambd,h,x1)

%Nonparametric adaptive density for a variable from the interval [x1,inf)

% x - the sample data doubled and sorted in the ascending order.
% ambd - the local scaling factors for the adaptive estimation 
% h - the optimal smoothing factor 
% y - the value of random variable X for which the density is calculated
% gau - the density value f(y)

n=length(x);
c=sqrt(2*pi);
if y<x1
    gau=0;
else
    gau=2*sum(exp(-0.5*(((y-x)./ambd')./h).^2)./ambd')/c/n/h;
end
end


function [Fgau]=Dystr_npr(y,x,ambd,h)

%Nonparametric adaptive cumulative distribution for a variable from the
%interval (-inf,inf)

% x - the sample data 
% ambd - the local scaling factors for the adaptive estimation 
% h - the optimal smoothing factor 
% y - the value of random variable X for which the density is calculated
% gau - the density value f(y)

n=length(x);
Fgau=sum(normcdf(((y-x)./ambd')./h))/n;
end