From a9c47a946837bf8d76fa0e625480cee13ca0c76b Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?L=C3=A9a=20Saviot?= <lea.saviot@numworks.com>
Date: Mon, 11 May 2020 16:27:37 +0200
Subject: [PATCH] [apps/probability] Change geometric distribution definition

THe distribution now represents the number of trials neded before a
success, so is defined for k in {1, 2, 3, ...}
---
 .../distribution/geometric_distribution.cpp     | 17 +++++++++--------
 .../distribution/geometric_distribution.h       |  4 +---
 2 files changed, 10 insertions(+), 11 deletions(-)

diff --git a/apps/probability/distribution/geometric_distribution.cpp b/apps/probability/distribution/geometric_distribution.cpp
index 6c76fd365..ed64b23ab 100644
--- a/apps/probability/distribution/geometric_distribution.cpp
+++ b/apps/probability/distribution/geometric_distribution.cpp
@@ -15,8 +15,7 @@ float GeometricDistribution::xMax() const {
 }
 
 float GeometricDistribution::yMax() const {
-  int maxAbscissa = 0;
-  float result = evaluateAtAbscissa(maxAbscissa);
+  float result = evaluateAtAbscissa(1.0); // Tha probability is max for x == 1
   return result * (1.0f + k_displayTopMarginRatio);
 }
 
@@ -29,16 +28,18 @@ bool GeometricDistribution::authorizedValueAtIndex(float x, int index) const {
 }
 
 template<typename T>
-T GeometricDistribution::templatedApproximateAtAbscissa(T x) const {
-  if (x < 0) {
+T GeometricDistribution::templatedApproximateAtAbscissa(T k) const {
+  constexpr T castedOne = static_cast<T>(1.0);
+  if (k < castedOne) {
     return static_cast<T>(0.0);
   }
   T p = static_cast<T>(m_parameter1);
-  if (p == static_cast<T>(1.0)) {
-    return static_cast<T>(x == 0 ? 1.0 : 0.0);
+  if (p == castedOne) {
+    return k == castedOne ? castedOne : static_cast<T>(0.0);
   }
-  T lResult = x * std::log(static_cast<T>(1.0) - p);
-  return p*std::exp(lResult);
+  // The result is p * (1-p)^{k-1}
+  T lResult = (k - castedOne) * std::log(castedOne - p);
+  return p * std::exp(lResult);
 }
 
 }
diff --git a/apps/probability/distribution/geometric_distribution.h b/apps/probability/distribution/geometric_distribution.h
index 035d2945e..e6903555a 100644
--- a/apps/probability/distribution/geometric_distribution.h
+++ b/apps/probability/distribution/geometric_distribution.h
@@ -7,9 +7,7 @@ namespace Probability {
 
 /* We chose the definition:
  * 0 < p <= 1 for success probability
- * k failures where k ∈ {0, 1, 2, ... }
- * The distribution follows the probability distribution of the number of failures before
- * the first success. */
+ * k number of trials needed to get one success, where k ∈ {1, 2, 3, ...}. */
 
 class GeometricDistribution final : public OneParameterDistribution {
 public: