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/*
Theseus - maximum likelihood superpositioning of macromolecular structures
Copyright (C) 2004-2015 Douglas L. Theobald
This program 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 2 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.
You should have received a copy of the GNU General Public License
along with this program; if not, write to the:
Free Software Foundation, Inc.,
59 Temple Place, Suite 330,
Boston, MA 02111-1307 USA
-/_|:|_|_\-
*/
#include <stdio.h>
#include <math.h>
#include <stdlib.h>
#include <float.h>
#include <gsl/gsl_rng.h>
#include <gsl/gsl_randist.h>
#include "DLTmath.h"
#include "statistics.h"
#include "pareto_dist.h"
double
pareto_dev(const double a, const double c, const gsl_rng *r2)
{
double logdum;
logdum = log(a) - (1.0 / c) * log(1.0 - gsl_rng_uniform(r2));
return (exp(logdum));
}
double
pareto_pdf(const double x, const double a, const double c)
{
if (x < c)
return (0.0);
else
return(exp(log(c) + c * log(a) - (c+1) * log(x)));
}
double
pareto_lnpdf(const double x, const double a, const double c)
{
if (x == 0.0)
return(log(c) + c * log(a));
else
return(log(c) + c * log(a) - (c+1) * log(x));
}
double
pareto_cdf(const double x, const double a, const double c)
{
if (x < a)
return(0.0);
else
return(1.0 - pareto_sdf(x, a, c));
}
double
pareto_sdf(const double x, const double a, const double c)
{
if (x <= a)
return(1.0);
else if (a == 0.0)
return(0.0);
else if (c == 0.0)
return(1.0);
else
return(exp(c * log(a / x)));
}
double
pareto_int(const double x, const double y, const double a, const double c)
{
return (pareto_sdf(x, a, c) - pareto_sdf(y, a, c));
}
double
pareto_logL(const double a, const double c)
{
return (-log(a / c) - 1.0 - 1.0 / c);
}
/* Maximum likelihood fit to a pareto distribution
Based on _Statistical Distributions_ 3rd ed. Evans, Hastings, and Peacock, p 154. */
double
pareto_fit(const double *data, const int num, double *a, double *c, double *prob)
{
double invc, min = DBL_MAX;
int i;
for (i = 0; i < num; ++i)
if(data[i] < min)
min = data[i];
if (min <= 0.0)
{
fprintf(stderr, "\n ERROR345: min data = %e; Pareto distributed data must be > 0.0 ", min);
return(-1.0);
}
*a = min;
invc = 0.0;
for (i = 0; i < num; ++i)
invc += log(data[i] / min);
invc /= (double) num;
*c = 1.0 / invc;
return(chi_sqr_adapt(data, num, 0, prob, *a, *c, pareto_pdf, pareto_lnpdf, pareto_int));
}
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