empirical p-value function

examples/exRand.cpp

@@ -32,9 +32,10 @@ int main(void)
     for (double s = 1.; s < 5.; ++s)
     {
         auto ci = h.confidenceInterval(s);
-        
+
         cout << static_cast<int>(s) << " sigma(s) interval= [";
         cout << ci.first << ", " << ci.second << "]" << endl;
+        cout << "P(X > " << s << ") = " << h.pValue(s) + 1. - h.pValue(-s) << endl;
     }
     p << PlotHistogram(h);
     p << PlotFunction(compile("return exp(-x_0^2/2)/sqrt(2*pi);", 1), -5., 5.);

lib/LatAnalyze/Statistics/Histogram.cpp

@@ -162,6 +162,20 @@ double Histogram::operator()(const double x) const
     return (*this)[static_cast<Index>(i)];
 }
 
+// p-value P(x > x0) ///////////////////////////////////////////////////////////
+double Histogram::pValue(const double x0) const
+{
+    Index n = data_.size();
+    double count = 0.;
+
+    FOR_STAT_ARRAY(data_, s)
+    {
+        count += (data_[s] > x0) ? 1. : 0.;
+    }
+    
+    return count/n;
+} 
+
 // percentiles & confidence interval ///////////////////////////////////////////
 double Histogram::percentile(const double p) const
 {

lib/LatAnalyze/Statistics/Histogram.hpp

@@ -54,6 +54,8 @@ public:
     double                    getX(const Index i) const;
     double                    operator[](const Index i) const;
     double                    operator()(const double x) const;
+    // p-value P(x > x0)
+    double                    pValue(const double x0) const;
     // percentiles & confidence interval
     double                    percentile(const double p) const;
     double                    median(void) const;