diff --git a/dlib/statistics/statistics.h b/dlib/statistics/statistics.h
index c332dc510..8543b486b 100644
--- a/dlib/statistics/statistics.h
+++ b/dlib/statistics/statistics.h
@@ -40,18 +40,10 @@ namespace dlib
             sum_four = 0;
 
             n = 0;
-            maximum_n = std::numeric_limits<T>::max();
             min_value = std::numeric_limits<T>::infinity();
             max_value = -std::numeric_limits<T>::infinity();
         }
 
-        void set_max_n (
-            const T& val
-        )
-        {
-            maximum_n = val;
-        }
-
         void add (
             const T& val
         )
@@ -66,14 +58,7 @@ namespace dlib
             if (val > max_value)
                 max_value = val;
 
-            if (n < maximum_n)
-                ++n;
-        }
-
-        T max_n (
-        ) const
-        {
-            return maximum_n;
+            ++n;
         }
 
         T current_n (
@@ -204,15 +189,6 @@ namespace dlib
             const running_stats& rhs
         ) const
         {
-            // make sure requires clause is not broken
-            DLIB_ASSERT(max_n() == rhs.max_n(),
-                "\trunning_stats running_stats::operator+(rhs)"
-                << "\n\t invalid inputs were given to this function"
-                << "\n\t max_n():     " << max_n() 
-                << "\n\t rhs.max_n(): " << rhs.max_n() 
-                << "\n\t this:        " << this
-                );
-
             running_stats temp(*this);
 
             temp.sum += rhs.sum;
@@ -243,7 +219,6 @@ namespace dlib
         T sum_cub;
         T sum_four;
         T n;
-        T maximum_n;
         T min_value;
         T max_value;
     
@@ -265,7 +240,6 @@ namespace dlib
         serialize(item.sum_cub, out);
         serialize(item.sum_four, out);
         serialize(item.n, out);
-        serialize(item.maximum_n, out);
         serialize(item.min_value, out);
         serialize(item.max_value, out);
     }
@@ -286,7 +260,6 @@ namespace dlib
         deserialize(item.sum_cub, in);
         deserialize(item.sum_four, in);
         deserialize(item.n, in);
-        deserialize(item.maximum_n, in);
         deserialize(item.min_value, in);
         deserialize(item.max_value, in);
     }
diff --git a/dlib/statistics/statistics_abstract.h b/dlib/statistics/statistics_abstract.h
index 74f0b0209..baf44f0cf 100644
--- a/dlib/statistics/statistics_abstract.h
+++ b/dlib/statistics/statistics_abstract.h
@@ -116,28 +116,12 @@ namespace dlib
                 - T must be a float, double, or long double type
 
             INITIAL VALUE
-                - max_n() == std::numeric_limits<T>::max()
                 - mean() == 0
                 - current_n() == 0
 
             WHAT THIS OBJECT REPRESENTS
                 This object represents something that can compute the running mean, 
                 variance, skewness, and excess kurtosis of a stream of real numbers.  
-
-                As this object accumulates more and more numbers it will be the case
-                that each new number impacts the current mean and variance estimate
-                less and less.  This may be what you want.  But it might not be. 
-
-                For example, your stream of numbers might be non-stationary, that is,
-                the mean and variance might change over time.  To enable you to use
-                this object on such a stream of numbers this object provides the 
-                ability to set a "max_n."  The meaning of the max_n() parameter
-                is that after max_n() samples have been seen each new sample will
-                have the same impact on the mean and variance estimates from then on.
-
-                So if you have a highly non-stationary stream of data you might
-                set the max_n to a small value while if you have a very stationary
-                stream you might set it to a very large value.
         !*/
     public:
 
@@ -156,27 +140,11 @@ namespace dlib
                 - clears all memory of any previous data points
         !*/
 
-        void set_max_n (
-            const T& val
-        );
-        /*!
-            ensures
-                - #max_n() == val
-        !*/
-
-        T max_n (
-        ) const;
-        /*!
-            ensures
-                - returns the max value that current_n() is allowed to take on
-        !*/
-
         T current_n (
         ) const;
         /*!
             ensures
-                - returns the number of points given to this object so far or
-                  max_n(), whichever is smallest.
+                - returns the number of points given to this object so far. 
         !*/
 
         void add (
@@ -191,10 +159,7 @@ namespace dlib
                 - #variance() == the updated variance that takes this new value into account.
                 - #skewness() == the updated skewness that takes this new value into account.
                 - #ex_kurtosis() == the updated kurtosis that takes this new value into account.
-                - if (current_n() < max_n()) then
-                    - #current_n() == current_n() + 1
-                - else
-                    - #current_n() == current_n()
+                - #current_n() == current_n() + 1
         !*/
 
         T mean (
@@ -277,8 +242,6 @@ namespace dlib
             const running_stats& rhs
         ) const;
         /*!
-            requires
-                - max_n() == rhs.max_n()
             ensures
                 - returns a new running_stats object that represents the combination of all
                   the values given to *this and rhs.  That is, this function returns a
diff --git a/dlib/test/statistics.cpp b/dlib/test/statistics.cpp
index ca31651f9..ab2e4c3e7 100644
--- a/dlib/test/statistics.cpp
+++ b/dlib/test/statistics.cpp
@@ -422,8 +422,6 @@ namespace
             DLIB_TEST(std::abs((rc1+rc2).covariance() - rc3.covariance()) < 1e-13);
             DLIB_TEST((rc1+rc2).current_n() == rc3.current_n());
 
-            rs1.set_max_n(50);
-            DLIB_TEST(rs1.max_n() == 50);
         }
 
         void test_average_precision()