diff --git a/src/distribution/mod.rs b/src/distribution/mod.rs
index 56deb09a..b3189276 100644
--- a/src/distribution/mod.rs
+++ b/src/distribution/mod.rs
@@ -2,6 +2,7 @@
 //! and provides
 //! concrete implementations for a variety of distributions.
 use super::statistics::{Max, Min};
+use crate::StatsError;
 use ::num_traits::{Bounded, Float, Num};
 use num_traits::{NumAssign, NumAssignOps, NumAssignRef};
 
@@ -71,7 +72,40 @@ mod weibull;
 mod ziggurat;
 mod ziggurat_tables;
 
-use crate::Result;
+type Result<T> = std::result::Result<T, DistributionError>;
+
+#[derive(Copy, Clone, PartialEq, Debug)]
+pub enum DistributionError {
+    InvalidConstruction(StatsError),
+    DegenerateConstruction(f64),
+    ExpectedProbability(f64),
+}
+
+impl std::fmt::Display for DistributionError {
+    fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result {
+        match self {
+            Self::InvalidConstruction(_) => {
+                write!(f, "provided value does not specify valid distribution")
+            }
+            Self::DegenerateConstruction(_) => write!(
+                f,
+                "provided value represents degenerate distribution, see statrs-dev/statrs#102"
+            ),
+            Self::ExpectedProbability(p) => write!(f, "expected probability, got {p:.3e}"),
+        }
+    }
+}
+
+impl std::error::Error for DistributionError {
+    fn source(&self) -> Option<&(dyn std::error::Error + 'static)> {
+        use core::ops::Bound::Included;
+        match self {
+            Self::InvalidConstruction(e) => Some(e),
+            Self::DegenerateConstruction(_) => None,
+            Self::ExpectedProbability(_) => None,
+        }
+    }
+}
 
 /// The `ContinuousCDF` trait is used to specify an interface for univariate
 /// distributions for which cdf float arguments are sensible.
diff --git a/src/distribution/normal.rs b/src/distribution/normal.rs
index 94e8c6b6..44e3338f 100644
--- a/src/distribution/normal.rs
+++ b/src/distribution/normal.rs
@@ -1,9 +1,11 @@
+use super::DistributionError as DistrError;
 use crate::distribution::{ziggurat, Continuous, ContinuousCDF};
 use crate::function::erf;
 use crate::statistics::*;
-use crate::{consts, Result, StatsError};
+use crate::{consts, StatsError};
 use rand::Rng;
 use std::f64;
+use std::ops::Bound;
 
 /// Implements the [Normal](https://en.wikipedia.org/wiki/Normal_distribution)
 /// distribution
@@ -24,6 +26,36 @@ pub struct Normal {
     std_dev: f64,
 }
 
+#[derive(Copy, Clone, PartialEq, Debug)]
+pub enum Error {
+    InvalidMean(DistrError),
+    InvalidStdDev(DistrError),
+}
+
+impl std::fmt::Display for Error {
+    fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result {
+        match self {
+            Self::InvalidMean(_) => write!(f, "expected finite and not nan mean"),
+            Self::InvalidStdDev(_) => write!(
+                f,
+                "expected finite, positive, and not nan standard deviation"
+            ),
+        }
+    }
+}
+
+impl std::error::Error for Error {
+    fn source(&self) -> Option<&(dyn std::error::Error + 'static)> {
+        Some(match self {
+            Self::InvalidMean(e) => e,
+            Self::InvalidStdDev(e) => e,
+        })
+    }
+}
+
+type Result<T> = std::result::Result<T, Error>;
+const POSITIVE_RANGE: (Bound<f64>, Bound<f64>) = (Bound::Excluded(0.0), Bound::Unbounded);
+
 impl Normal {
     ///  Constructs a new normal distribution with a mean of `mean`
     /// and a standard deviation of `std_dev`
@@ -45,8 +77,22 @@ impl Normal {
     /// assert!(result.is_err());
     /// ```
     pub fn new(mean: f64, std_dev: f64) -> Result<Normal> {
-        if mean.is_nan() || std_dev.is_nan() || std_dev <= 0.0 {
-            Err(StatsError::BadParams)
+        if mean.is_nan() {
+            Err(Error::InvalidMean(DistrError::InvalidConstruction(
+                StatsError::Finite(mean),
+            )))
+        } else if std_dev.is_nan() {
+            Err(Error::InvalidStdDev(DistrError::InvalidConstruction(
+                StatsError::NotNan,
+            )))
+        } else if std_dev == 0.0 {
+            Err(Error::InvalidStdDev(DistrError::DegenerateConstruction(
+                0.0,
+            )))
+        } else if std_dev < 0.0 {
+            Err(Error::InvalidStdDev(DistrError::InvalidConstruction(
+                StatsError::Bounded(POSITIVE_RANGE, std_dev),
+            )))
         } else {
             Ok(Normal { mean, std_dev })
         }
@@ -334,6 +380,7 @@ impl std::default::Default for Normal {
 #[rustfmt::skip]
 #[cfg(test)]
 mod tests {
+    use super::*;
     use crate::statistics::*;
     use crate::distribution::{ContinuousCDF, Continuous, Normal};
     use crate::distribution::internal::*;
@@ -563,4 +610,25 @@ mod tests {
         // Check that the standard deviation of the distribution is close to 1
         assert_almost_eq!(n_std, 1.0, 1e-15);
     }
+
+    #[test]
+    fn test_errors() {
+        let n = Normal::new(f64::NAN, f64::INFINITY);
+        assert!(matches!(n.err().unwrap(),
+            Error::InvalidMean(
+                DistrError::InvalidConstruction(
+                    StatsError::NotNan | StatsError::Finite(_)
+                )
+            )
+        ));
+
+        let n = Normal::new(0.0, 0.0);
+        assert!(matches!(n.err().unwrap(),
+            Error::InvalidStdDev(
+                DistrError::InvalidConstruction(
+                    StatsError::FiniteNonNegative(_)
+                )
+            )
+        ));
+    }
 }
diff --git a/src/error.rs b/src/error.rs
index a18aebbd..08fda6c8 100644
--- a/src/error.rs
+++ b/src/error.rs
@@ -3,7 +3,7 @@ use std::fmt;
 use std::ops::Bound;
 
 /// Enumeration of possible errors thrown within the `statrs` library
-#[derive(Clone, PartialEq, Debug)]
+#[derive(Copy, Clone, PartialEq, Debug)]
 pub enum StatsError {
     /// Generic bad input parameter error
     BadParams,