diff --git a/dlib/serialize.h b/dlib/serialize.h
index ae071b319..67db72400 100644
--- a/dlib/serialize.h
+++ b/dlib/serialize.h
@@ -62,6 +62,7 @@
         - std::string
         - std::wstring
         - std::vector
+        - std::deque
         - std::map
         - std::set
         - std::pair
@@ -79,6 +80,7 @@
         - std::string
         - std::wstring
         - std::vector
+        - std::deque
         - std::map
         - std::set
         - std::pair
@@ -143,6 +145,7 @@
 #include <fstream>
 #include <string>
 #include <vector>
+#include <deque>
 #include <complex>
 #include <map>
 #include <set>
@@ -652,6 +655,18 @@ namespace dlib
         std::istream& in
     );
 
+    template <typename T, typename alloc>
+    void serialize (
+        const std::deque<T,alloc>& item,
+        std::ostream& out
+    );
+
+    template <typename T, typename alloc>
+    void deserialize (
+        std::deque<T,alloc>& item,
+        std::istream& in
+    );
+
     inline void serialize (
         const std::string& item,
         std::ostream& out
@@ -1035,6 +1050,44 @@ namespace dlib
         { throw serialization_error(e.info + "\n   while deserializing object of type std::vector"); }
     }
 
+// ----------------------------------------------------------------------------------------
+
+    template <typename T, typename alloc>
+    void serialize (
+        const std::deque<T,alloc>& item,
+        std::ostream& out
+    )
+    {
+        try
+        { 
+            const unsigned long size = static_cast<unsigned long>(item.size());
+
+            serialize(size,out); 
+            for (unsigned long i = 0; i < item.size(); ++i)
+                serialize(item[i],out);
+        }
+        catch (serialization_error& e)
+        { throw serialization_error(e.info + "\n   while serializing object of type std::deque"); }
+    }
+
+    template <typename T, typename alloc>
+    void deserialize (
+        std::deque<T, alloc>& item,
+        std::istream& in
+    )
+    {
+        try 
+        { 
+            unsigned long size;
+            deserialize(size,in); 
+            item.resize(size);
+            for (unsigned long i = 0; i < size; ++i)
+                deserialize(item[i],in);
+        }
+        catch (serialization_error& e)
+        { throw serialization_error(e.info + "\n   while deserializing object of type std::deque"); }
+    }
+
 // ----------------------------------------------------------------------------------------
 
     inline void serialize (
diff --git a/dlib/statistics/running_gradient.h b/dlib/statistics/running_gradient.h
index c8fb3468b..a0d0c22d7 100644
--- a/dlib/statistics/running_gradient.h
+++ b/dlib/statistics/running_gradient.h
@@ -151,6 +151,51 @@ namespace dlib
         matrix<double,2,1> w;
         double residual_squared;
     };
+
+// ----------------------------------------------------------------------------------------
+
+    template <
+        typename T
+        >
+    double probability_gradient_less_than (
+        const T& container,
+        double thresh
+    )
+    {
+        running_gradient g;
+        for(auto&& v : container)
+            g.add(v);
+
+        // make sure requires clause is not broken
+        DLIB_ASSERT(g.current_n() > 2,
+            "\t double probability_gradient_less_than()"
+            << "\n\t You need more than 2 elements in the given container to call this function."
+        );
+        return g.probability_gradient_less_than(thresh);
+    }
+
+    template <
+        typename T
+        >
+    double probability_gradient_greater_than (
+        const T& container,
+        double thresh
+    )
+    {
+        running_gradient g;
+        for(auto&& v : container)
+            g.add(v);
+
+        // make sure requires clause is not broken
+        DLIB_ASSERT(g.current_n() > 2,
+            "\t double probability_gradient_greater_than()"
+            << "\n\t You need more than 2 elements in the given container to call this function."
+        );
+        return g.probability_gradient_greater_than(thresh);
+    }
+
+// ----------------------------------------------------------------------------------------
+
 }
 
 #endif // DLIB_RuNNING_GRADIENT_Hh_
diff --git a/dlib/statistics/running_gradient_abstract.h b/dlib/statistics/running_gradient_abstract.h
index 4af416fa3..4389721e3 100644
--- a/dlib/statistics/running_gradient_abstract.h
+++ b/dlib/statistics/running_gradient_abstract.h
@@ -116,6 +116,45 @@ namespace dlib
     /*!
         provides serialization support 
     !*/
+
+// ----------------------------------------------------------------------------------------
+
+    template <
+        typename T
+        >
+    double probability_gradient_less_than (
+        const T& container,
+        double thresh
+    );
+    /*!
+        requires
+            - container muse be a container of double values that can be enumerated with a
+              range based for loop.
+            - The container must contain more than 2 elements.
+        ensures
+            - Puts all the elements of container into a running_gradient object, R, and
+              then returns R.probability_gradient_less_than(thresh). 
+    !*/
+
+    template <
+        typename T
+        >
+    double probability_gradient_greater_than (
+        const T& container,
+        double thresh
+    );
+    /*!
+        requires
+            - container muse be a container of double values that can be enumerated with a
+              range based for loop.
+            - The container must contain more than 2 elements.
+        ensures
+            - Puts all the elements of container into a running_gradient object, R, and
+              then returns R.probability_gradient_greater_than(thresh).
+    !*/
+
+// ----------------------------------------------------------------------------------------
+
 }
 
 #endif // DLIB_RuNNING_GRADIENT_ABSTRACT_Hh_
diff --git a/docs/docs/term_index.xml b/docs/docs/term_index.xml
index 5149dc5fc..7bce81606 100644
--- a/docs/docs/term_index.xml
+++ b/docs/docs/term_index.xml
@@ -258,6 +258,8 @@
          <term file="linear_algebra.html" name="rotation_matrix"           include="dlib/geometry.h"/>
          <term file="algorithms.html" name="running_stats"                 include="dlib/statistics.h"/>
          <term file="algorithms.html" name="running_gradient"              include="dlib/statistics/running_gradient.h"/>
+         <term file="dlib/statistics/running_gradient_abstract.h.html" name="probability_gradient_greater_than"  include="dlib/statistics/running_gradient.h"/>
+         <term file="dlib/statistics/running_gradient_abstract.h.html" name="probability_gradient_less_than"  include="dlib/statistics/running_gradient.h"/>
          <term file="algorithms.html" name="running_scalar_covariance"     include="dlib/statistics.h"/>
          <term file="algorithms.html" name="mean_sign_agreement"           include="dlib/statistics.h"/>
          <term file="algorithms.html" name="correlation"                   include="dlib/statistics.h"/>