Implementation & Tests

src/distribution/exponential.rs

@@ -109,6 +109,19 @@ impl ContinuousCDF<f64, f64> for Exp {
             (-self.rate * x).exp()
         }
     }
+
+    /// Calculates the inverse cumulative distribution function.
+    ///
+    /// # Formula
+    ///
+    /// ```ignore
+    /// -ln(1 - p) / λ
+    /// ```
+    ///
+    /// where `p` is the probability and `λ` is the rate
+    fn inverse_cdf(&self, p: f64) -> f64 {
+        -(1.0 - p).ln() / self.rate
+    }
 }
 
 impl Min<f64> for Exp {
@@ -457,6 +470,27 @@ mod tests {
         test_case(f64::INFINITY, 1.0, cdf(f64::INFINITY));
     }
 
+    #[test]
+    fn test_inverse_cdf() {
+        let distribution = Exp::new(0.42).unwrap();
+        assert_eq!(distribution.median(), distribution.inverse_cdf(0.5));
+
+        let distribution = Exp::new(0.042).unwrap();
+        assert_eq!(distribution.median(), distribution.inverse_cdf(0.5));
+
+        let distribution = Exp::new(0.0042).unwrap();
+        assert_eq!(distribution.median(), distribution.inverse_cdf(0.5));
+
+        let distribution = Exp::new(0.33).unwrap();
+        assert_eq!(distribution.median(), distribution.inverse_cdf(0.5));
+
+        let distribution = Exp::new(0.033).unwrap();
+        assert_eq!(distribution.median(), distribution.inverse_cdf(0.5));
+
+        let distribution = Exp::new(0.0033).unwrap();
+        assert_eq!(distribution.median(), distribution.inverse_cdf(0.5));
+    }
+
     #[test]
     fn test_sf() {
         let sf = |arg: f64| move |x: Exp| x.sf(arg);