ex-1: add Moyal functions

ex-1/moyal.c

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

ex-1/moyal.h

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+/* This file contains functions to
+ * compute the Moyal distribution
+ * PDF, CDF and QDF functions.
+ */
+
+#pragma once
+
+/* This is a wrapper needed by `moyal_cdf` and
+ * other optimisation functions because the GSL
+ * routines expect a function with parameters.
+ */
+double moyal_pdf(double x, void* params);
+
+
+/* The cumulative function of the Moyal distribution.
+ */
+double moyal_cdf(double x, void* params);
+
+
+/* The quantile function (inverse CDF) of the Moyal
+ * distribution.
+ */
+double moyal_qdf(double p0, void* params);