stationary seismic hazard analysis scripts added

src/StationarySeismicHazardAnalysis/dist_NPT.m

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+%   [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
+