44 lines
1023 B
C
44 lines
1023 B
C
/* This file contains functions to
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* compute the Moyal distribution
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* PDF, CDF and QDF functions.
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*/
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#include <gsl/gsl_cdf.h>
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#include <gsl/gsl_sf.h>
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#include <math.h>
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/* The Moyal PDF.
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*
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* This is a wrapper needed by `moyal_cdf` and
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* other optimisation functions because the GSL
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* routines expect a function with parameters.
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*/
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double moyal_pdf(double x, double* params) {
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double mu = params[0];
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double sigma = params[1];
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double z = (x - mu)/sigma;
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return exp(-(z + exp(-z))/2) /sqrt(2*M_PI) /sigma;
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}
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/* The cumulative function of the Moyal distribution.
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*/
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double moyal_cdf(double x, double* params) {
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double mu = params[0];
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double sigma = params[1];
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double z = (x - mu)/sigma;
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return 2 * (1 - gsl_cdf_gaussian_P(exp(-z/2), 1));
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}
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/* The quantile function (inverse CDF) of the Moyal
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* distribution.
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*/
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double moyal_qdf(double p0, double* params) {
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double mu = params[0];
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double sigma = params[1];
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double z = -2 * log(gsl_cdf_gaussian_Pinv(1 - p0/2, 1));
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return z*sigma + mu;
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}
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