[apps/proba] Student cumulativeDistributiveInverseForProbability

apps/probability/law/incomplete_beta_function.cpp

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+/*
+ * zlib License
+ *
+ * Regularized Incomplete Beta Function
+ *
+ * Copyright (c) 2016, 2017 Lewis Van Winkle
+ * http://CodePlea.com
+ *
+ * This software is provided 'as-is', without any express or implied
+ * warranty. In no event will the authors be held liable for any damages
+ * arising from the use of this software.
+ *
+ * Permission is granted to anyone to use this software for any purpose,
+ * including commercial applications, and to alter it and redistribute it
+ * freely, subject to the following restrictions:
+ *
+ * 1. The origin of this software must not be misrepresented; you must not
+ *    claim that you wrote the original software. If you use this software
+ *    in a product, an acknowledgement in the product documentation would be
+ *    appreciated but is not required.
+ * 2. Altered source versions must be plainly marked as such, and must not be
+ *    misrepresented as being the original software.
+ * 3. This notice may not be removed or altered from any source distribution.
+ */
+
+// WARNING: this code has been modified
+
+#include "incomplete_beta_function.h"
+#include <math.h>
+#include <cmath>
+
+#define STOP 1.0e-8
+#define TINY 1.0e-30
+
+double IncompleteBetaFunction(double a, double b, double x) {
+    if (x < 0.0 || x > 1.0) return NAN;
+
+    /*The continued fraction converges nicely for x < (a+1)/(a+b+2)*/
+    if (x > (a+1.0)/(a+b+2.0)) {
+        return (1.0-IncompleteBetaFunction(b,a,1.0-x)); /*Use the fact that beta is symmetrical.*/
+    }
+
+    /*Find the first part before the continued fraction.*/
+    const double lbeta_ab = std::lgamma(a)+std::lgamma(b)-std::lgamma(a+b);
+    const double front = std::exp(std::log(x)*a+std::log(1.0-x)*b-lbeta_ab) / a;
+
+    /*Use Lentz's algorithm to evaluate the continued fraction.*/
+    double f = 1.0, c = 1.0, d = 0.0;
+
+    //TODO LEA: Use Helper::ContinuedFractionEvaluation
+    int i, m;
+    for (i = 0; i <= 200; ++i) {
+        m = i/2;
+
+        double numerator;
+        if (i == 0) {
+            numerator = 1.0; /*First numerator is 1.0.*/
+        } else if (i % 2 == 0) {
+            numerator = (m*(b-m)*x)/((a+2.0*m-1.0)*(a+2.0*m)); /*Even term.*/
+        } else {
+            numerator = -((a+m)*(a+b+m)*x)/((a+2.0*m)*(a+2.0*m+1)); /*Odd term.*/
+        }
+
+        /*Do an iteration of Lentz's algorithm.*/
+        d = 1.0 + numerator * d;
+        if (std::fabs(d) < TINY) d = TINY;
+        d = 1.0 / d;
+
+        c = 1.0 + numerator / c;
+        if (std::fabs(c) < TINY) c = TINY;
+
+        const double cd = c*d;
+        f *= cd;
+
+        /*Check for stop.*/
+        if (std::fabs(1.0-cd) < STOP) {
+            return front * (f-1.0);
+        }
+    }
+
+    return NAN; /*Needed more loops, did not converge.*/
+}