diff --git a/include/boost/accumulators/statistics/extended_p_square.hpp b/include/boost/accumulators/statistics/extended_p_square.hpp
index e6cc8dc..ab9959f 100644
--- a/include/boost/accumulators/statistics/extended_p_square.hpp
+++ b/include/boost/accumulators/statistics/extended_p_square.hpp
@@ -10,6 +10,9 @@
 
 #include <vector>
 #include <functional>
+#include <sstream>
+#include <boost/foreach.hpp>
+#include <boost/throw_exception.hpp>
 #include <boost/range/begin.hpp>
 #include <boost/range/end.hpp>
 #include <boost/range/iterator_range.hpp>
@@ -92,6 +95,16 @@ namespace impl
           , desired_positions(heights.size())
           , positions_increments(heights.size())
         {
+            BOOST_FOREACH(float_type p, this->probabilities)
+            {
+                if (p < 0 || p > 1)
+                {
+                    std::ostringstream msg;
+                    msg << "extended_p_square_probabilities = " << p << " is not valid range [0, 1]";
+                    boost::throw_exception(std::logic_error(msg.str()));
+                }
+            }
+
             std::size_t num_quantiles = this->probabilities.size();
             std::size_t num_markers = this->heights.size();
 
diff --git a/include/boost/accumulators/statistics/extended_p_square_quantile.hpp b/include/boost/accumulators/statistics/extended_p_square_quantile.hpp
index a17843d..fb97533 100644
--- a/include/boost/accumulators/statistics/extended_p_square_quantile.hpp
+++ b/include/boost/accumulators/statistics/extended_p_square_quantile.hpp
@@ -10,6 +10,8 @@
 
 #include <vector>
 #include <functional>
+#include <sstream>
+#include <boost/foreach.hpp>
 #include <boost/throw_exception.hpp>
 #include <boost/range/begin.hpp>
 #include <boost/range/end.hpp>
@@ -77,6 +79,15 @@ namespace impl
               , boost::end(args[extended_p_square_probabilities])
             )
         {
+            BOOST_FOREACH(float_type p, this->probabilities)
+            {
+                if (p < 0 || p > 1)
+                {
+                    std::ostringstream msg;
+                    msg << "extended_p_square_probabilities = " << p << " is not valid range [0, 1]";
+                    boost::throw_exception(std::logic_error(msg.str()));
+                }
+            }
         }
 
         template<typename Args>
diff --git a/include/boost/accumulators/statistics/p_square_quantile.hpp b/include/boost/accumulators/statistics/p_square_quantile.hpp
index 636fea7..c5efe3a 100644
--- a/include/boost/accumulators/statistics/p_square_quantile.hpp
+++ b/include/boost/accumulators/statistics/p_square_quantile.hpp
@@ -10,6 +10,8 @@
 
 #include <cmath>
 #include <functional>
+#include <sstream>
+#include <boost/throw_exception.hpp>
 #include <boost/array.hpp>
 #include <boost/mpl/placeholders.hpp>
 #include <boost/type_traits/is_same.hpp>
@@ -67,6 +69,13 @@ namespace impl
           , desired_positions()
           , positions_increments()
         {
+            if (this->p < 0 || this->p > 1)
+            {
+                std::ostringstream msg;
+                msg << "quantile_probability = " << this->p << " is not in valid range [0, 1]";
+                boost::throw_exception(std::logic_error(msg.str()));
+            }
+
             for(std::size_t i = 0; i < 5; ++i)
             {
                 this->actual_positions[i] = i + 1.;
diff --git a/include/boost/accumulators/statistics/peaks_over_threshold.hpp b/include/boost/accumulators/statistics/peaks_over_threshold.hpp
index f04f743..a510be6 100644
--- a/include/boost/accumulators/statistics/peaks_over_threshold.hpp
+++ b/include/boost/accumulators/statistics/peaks_over_threshold.hpp
@@ -219,6 +219,12 @@ namespace impl
           , fit_parameters_(boost::make_tuple(0., 0., 0.))
           , is_dirty_(true)
         {
+            if (this->threshold_probability_ < 0 || this->threshold_probability_ > 1)
+            {
+                std::ostringstream msg;
+                msg << "pot_threshold_probability = " << this->threshold_probability_ << " is not in valid range [0, 1]";
+                boost::throw_exception(std::logic_error(msg.str()));
+            }
         }
 
         void operator ()(dont_care)
diff --git a/include/boost/accumulators/statistics/pot_quantile.hpp b/include/boost/accumulators/statistics/pot_quantile.hpp
index 470bdba..d831dd5 100644
--- a/include/boost/accumulators/statistics/pot_quantile.hpp
+++ b/include/boost/accumulators/statistics/pot_quantile.hpp
@@ -12,6 +12,8 @@
 #include <limits>
 #include <numeric>
 #include <functional>
+#include <sstream>
+#include <boost/throw_exception.hpp>
 #include <boost/parameter/keyword.hpp>
 #include <boost/tuple/tuple.hpp>
 #include <boost/mpl/if.hpp>
@@ -61,6 +63,13 @@ namespace impl
         template<typename Args>
         result_type result(Args const &args) const
         {
+            if (args[quantile_probability] < 0 || args[quantile_probability] > 1)
+            {
+                std::ostringstream msg;
+                msg << "quantile_probability = " << args[quantile_probability] << " is not in valid range [0, 1]";
+                boost::throw_exception(std::logic_error(msg.str()));
+            }
+
             typedef
                 typename mpl::if_<
                     is_same<Impl, weighted>
diff --git a/include/boost/accumulators/statistics/pot_tail_mean.hpp b/include/boost/accumulators/statistics/pot_tail_mean.hpp
index a78043f..86732c9 100644
--- a/include/boost/accumulators/statistics/pot_tail_mean.hpp
+++ b/include/boost/accumulators/statistics/pot_tail_mean.hpp
@@ -12,6 +12,8 @@
 #include <limits>
 #include <numeric>
 #include <functional>
+#include <sstream>
+#include <boost/throw_exception.hpp>
 #include <boost/range.hpp>
 #include <boost/parameter/keyword.hpp>
 #include <boost/tuple/tuple.hpp>
@@ -64,6 +66,13 @@ namespace impl
         template<typename Args>
         result_type result(Args const &args) const
         {
+            if (args[quantile_probability] < 0 || args[quantile_probability] > 1)
+            {
+                std::ostringstream msg;
+                msg << "quantile_probability = " << args[quantile_probability] << " is not in valid range [0, 1]";
+                boost::throw_exception(std::logic_error(msg.str()));
+            }
+
             typedef
                 typename mpl::if_<
                     is_same<Impl, weighted>
diff --git a/include/boost/accumulators/statistics/tail_mean.hpp b/include/boost/accumulators/statistics/tail_mean.hpp
index 67dae37..eb1aab7 100644
--- a/include/boost/accumulators/statistics/tail_mean.hpp
+++ b/include/boost/accumulators/statistics/tail_mean.hpp
@@ -71,6 +71,13 @@ namespace impl
         template<typename Args>
         result_type result(Args const &args) const
         {
+            if (args[quantile_probability] < 0 || args[quantile_probability] > 1)
+            {
+                std::ostringstream msg;
+                msg << "quantile_probability = " << args[quantile_probability] << " is not in valid range [0, 1]";
+                boost::throw_exception(std::logic_error(msg.str()));
+            }
+
             std::size_t cnt = count(args);
 
             std::size_t n = static_cast<std::size_t>(
diff --git a/include/boost/accumulators/statistics/tail_quantile.hpp b/include/boost/accumulators/statistics/tail_quantile.hpp
index 9ff56b5..1f4a617 100644
--- a/include/boost/accumulators/statistics/tail_quantile.hpp
+++ b/include/boost/accumulators/statistics/tail_quantile.hpp
@@ -68,6 +68,13 @@ namespace impl
         template<typename Args>
         result_type result(Args const &args) const
         {
+            if (args[quantile_probability] < 0 || args[quantile_probability] > 1)
+            {
+                std::ostringstream msg;
+                msg << "quantile_probability = " << args[quantile_probability] << " is not in valid range [0, 1]";
+                boost::throw_exception(std::logic_error(msg.str()));
+            }
+
             std::size_t cnt = count(args);
 
             std::size_t n = static_cast<std::size_t>(
diff --git a/include/boost/accumulators/statistics/tail_variate_means.hpp b/include/boost/accumulators/statistics/tail_variate_means.hpp
index d34d4ab..4c9bbdf 100644
--- a/include/boost/accumulators/statistics/tail_variate_means.hpp
+++ b/include/boost/accumulators/statistics/tail_variate_means.hpp
@@ -89,6 +89,13 @@ namespace impl
         template<typename Args>
         result_type result(Args const &args) const
         {
+            if (args[quantile_probability] < 0 || args[quantile_probability] > 1)
+            {
+                std::ostringstream msg;
+                msg << "quantile_probability = " << args[quantile_probability] << " is not in valid range [0, 1]";
+                boost::throw_exception(std::logic_error(msg.str()));
+            }
+
             std::size_t cnt = count(args);
 
             std::size_t n = static_cast<std::size_t>(
diff --git a/include/boost/accumulators/statistics/weighted_extended_p_square.hpp b/include/boost/accumulators/statistics/weighted_extended_p_square.hpp
index ac857e0..6ba3484 100644
--- a/include/boost/accumulators/statistics/weighted_extended_p_square.hpp
+++ b/include/boost/accumulators/statistics/weighted_extended_p_square.hpp
@@ -10,6 +10,8 @@
 
 #include <vector>
 #include <functional>
+#include <sstream>
+#include <boost/throw_exception.hpp>
 #include <boost/range/begin.hpp>
 #include <boost/range/end.hpp>
 #include <boost/range/iterator_range.hpp>
@@ -89,6 +91,15 @@ namespace impl
           , actual_positions(heights.size())
           , desired_positions(heights.size())
         {
+            BOOST_FOREACH(float_type p, this->probabilities)
+            {
+                if (p < 0 || p > 1)
+                {
+                    std::ostringstream msg;
+                    msg << "extended_p_square_probabilities = " << p << " is not valid range [0, 1]";
+                    boost::throw_exception(std::logic_error(msg.str()));
+                }
+            }
         }
 
         template<typename Args>
diff --git a/include/boost/accumulators/statistics/weighted_p_square_quantile.hpp b/include/boost/accumulators/statistics/weighted_p_square_quantile.hpp
index 2ebc7b1..f43ac4e 100644
--- a/include/boost/accumulators/statistics/weighted_p_square_quantile.hpp
+++ b/include/boost/accumulators/statistics/weighted_p_square_quantile.hpp
@@ -11,6 +11,8 @@
 #include <cmath>
 #include <functional>
 #include <boost/array.hpp>
+#include <sstream>
+#include <boost/throw_exception.hpp>
 #include <boost/parameter/keyword.hpp>
 #include <boost/mpl/placeholders.hpp>
 #include <boost/type_traits/is_same.hpp>
@@ -67,6 +69,12 @@ namespace impl {
           , actual_positions()
           , desired_positions()
         {
+            if (this->p < 0 || this->p > 1)
+            {
+                std::ostringstream msg;
+                msg << "quantile_probability = " << this->p << " is not in valid range [0, 1]";
+                boost::throw_exception(std::logic_error(msg.str()));
+            }
         }
 
         template<typename Args>
diff --git a/include/boost/accumulators/statistics/weighted_peaks_over_threshold.hpp b/include/boost/accumulators/statistics/weighted_peaks_over_threshold.hpp
index 418b38c..79df0df 100644
--- a/include/boost/accumulators/statistics/weighted_peaks_over_threshold.hpp
+++ b/include/boost/accumulators/statistics/weighted_peaks_over_threshold.hpp
@@ -148,6 +148,12 @@ namespace impl
           , fit_parameters_(boost::make_tuple(0., 0., 0.))
           , is_dirty_(true)
         {
+            if (this->threshold_probability_ < 0 || this->threshold_probability_ > 1)
+            {
+                std::ostringstream msg;
+                msg << "pot_threshold_probability = " << this->threshold_probability_ << " is not in valid range [0, 1]";
+                boost::throw_exception(std::logic_error(msg.str()));
+            }
         }
 
         void operator ()(dont_care)
diff --git a/include/boost/accumulators/statistics/weighted_tail_mean.hpp b/include/boost/accumulators/statistics/weighted_tail_mean.hpp
index bae8530..e2a3fc6 100644
--- a/include/boost/accumulators/statistics/weighted_tail_mean.hpp
+++ b/include/boost/accumulators/statistics/weighted_tail_mean.hpp
@@ -91,6 +91,13 @@ namespace impl
         template<typename Args>
         result_type result(Args const &args) const
         {
+            if (args[quantile_probability] < 0 || args[quantile_probability] > 1)
+            {
+                std::ostringstream msg;
+                msg << "quantile_probability = " << args[quantile_probability] << " is not in valid range [0, 1]";
+                boost::throw_exception(std::logic_error(msg.str()));
+            }
+
             float_type threshold = sum_of_weights(args)
                              * ( ( is_same<LeftRight, left>::value ) ? args[quantile_probability] : 1. - args[quantile_probability] );
 
diff --git a/include/boost/accumulators/statistics/weighted_tail_quantile.hpp b/include/boost/accumulators/statistics/weighted_tail_quantile.hpp
index b143457..407ce38 100644
--- a/include/boost/accumulators/statistics/weighted_tail_quantile.hpp
+++ b/include/boost/accumulators/statistics/weighted_tail_quantile.hpp
@@ -75,6 +75,13 @@ namespace impl
         template<typename Args>
         result_type result(Args const &args) const
         {
+            if (args[quantile_probability] < 0 || args[quantile_probability] > 1)
+            {
+                std::ostringstream msg;
+                msg << "quantile_probability = " << args[quantile_probability] << " is not in valid range [0, 1]";
+                boost::throw_exception(std::logic_error(msg.str()));
+            }
+
             float_type threshold = sum_of_weights(args)
                              * ( ( is_same<LeftRight, left>::value ) ? args[quantile_probability] : 1. - args[quantile_probability] );
 
diff --git a/include/boost/accumulators/statistics/weighted_tail_variate_means.hpp b/include/boost/accumulators/statistics/weighted_tail_variate_means.hpp
index 2c90783..879ea7f 100644
--- a/include/boost/accumulators/statistics/weighted_tail_variate_means.hpp
+++ b/include/boost/accumulators/statistics/weighted_tail_variate_means.hpp
@@ -117,6 +117,13 @@ namespace impl
         template<typename Args>
         result_type result(Args const &args) const
         {
+            if (args[quantile_probability] < 0 || args[quantile_probability] > 1)
+            {
+                std::ostringstream msg;
+                msg << "quantile_probability = " << args[quantile_probability] << " is not in valid range [0, 1]";
+                boost::throw_exception(std::logic_error(msg.str()));
+            }
+
             float_type threshold = sum_of_weights(args)
                              * ( ( is_same<LeftRight, left>::value ) ? args[quantile_probability] : 1. - args[quantile_probability] );