fix: mode for gamma distribution is 0 for shape<=1

fix: return None for Gamma::mode when α < 1

src/distribution/gamma.rs

@@ -133,17 +133,13 @@ impl ContinuousCDF<f64, f64> for Gamma {
     fn sf(&self, x: f64) -> f64 {
         if x <= 0.0 {
             1.0
-        }
-        else if ulps_eq!(x, self.shape) && self.rate.is_infinite() {
+        } else if ulps_eq!(x, self.shape) && self.rate.is_infinite() {
             0.0
-        }
-        else if self.rate.is_infinite() {
+        } else if self.rate.is_infinite() {
             1.0
-        }
-        else if x.is_infinite() {
+        } else if x.is_infinite() {
             0.0
-        }
-        else {
+        } else {
             gamma::gamma_ur(self.shape, x * self.rate)
         }
     }
@@ -239,13 +235,17 @@ impl Mode<Option<f64>> for Gamma {
     ///
     /// # Formula
     ///
-    /// ```ignore
-    /// (α - 1) / β
+    /// ```text
+    /// (α - 1) / β, where α > 1
     /// ```
     ///
     /// where `α` is the shape and `β` is the rate
     fn mode(&self) -> Option<f64> {
-        Some((self.shape - 1.0) / self.rate)
+        if self.shape >= 1.0 {
+            Some((self.shape - 1.0) / self.rate)
+        } else {
+            None
+        }
     }
 }
 
@@ -353,6 +353,7 @@ pub fn sample_unchecked<R: Rng + ?Sized>(rng: &mut R, shape: f64, rate: f64) ->
 
 #[cfg(all(test, feature = "nightly"))]
 mod tests {
+
     use super::*;
     use crate::consts::ACC;
     use crate::distribution::internal::*;
@@ -452,10 +453,12 @@ mod tests {
 
     #[test]
     fn test_mode() {
+        use rand::distributions::uniform::UniformFloat;
+        use rand::rngs;
         let f = |x: Gamma| x.mode().unwrap();
-        let test = [((1.0, 0.1), 0.0), ((1.0, 1.0), 0.0)];
-        for &(arg, res) in test.iter() {
-            test_case_special(arg, res, 10e-6, f);
+        let test = [(1.0, 0.1), (1.0, 1.0)];
+        for &arg in test.iter() {
+            test_case_special(arg, 0.0, 10e-6, f);
         }
         let test = [((10.0, 10.0), 0.9), ((10.0, 1.0), 9.0), ((10.0, INF), 0.0)];
         for &(arg, res) in test.iter() {