test: add check for derivative of CDF to ensure it matches PDF

src/distribution/internal.rs

@@ -418,9 +418,41 @@
         assert!(sum <= 1.0 + 1e-10);
     }
 
+    /// pdf should be derivative of cdf
+    fn check_derivative_of_cdf_is_pdf<D: ContinuousCDF<f64, f64> + Continuous<f64, f64>>(
+        dist: &D,
+        x_min: f64,
+        x_max: f64,
+        step: f64,
+    ) {
+        const DELTA: f64 = 1e-12;
+        const DX: f64 = 2.0 * DELTA;
+        let mut prev_x = x_min;
+
+        loop {
+            let x = prev_x + step;
+            let x_ahead = x + DELTA;
+            let x_behind = x - DELTA;
+            let density = dist.pdf(x);
+
+            let d_cdf = dist.cdf(x_ahead) - dist.cdf(x_behind);
+
+            assert_almost_eq!(d_cdf, DX * density, 1e-11);
+
+            if x >= x_max {
+                break;
+            } else {
+                prev_x = x;
+            }
+        }
+    }
+
     /// Does a series of checks that all continuous distributions must obey.
-    /// 99% of the probability mass should be between x_min and x_max.
-    pub fn check_continuous_distribution<D: ContinuousCDF<f64, f64> + Continuous<f64, f64>>(
+    /// 99% of the probability mass should be between x_min and x_max or the finite
+    /// difference of cdf should be near to the pdf for much of the support.
+    pub fn check_continuous_distribution<
+        D: ContinuousCDF<f64, f64> + Continuous<f64, f64> + std::panic::RefUnwindSafe,
+    >(
         dist: &D,
         x_min: f64,
         x_max: f64,
@@ -432,7 +464,16 @@
         assert_eq!(dist.cdf(f64::NEG_INFINITY), 0.0);
         assert_eq!(dist.cdf(f64::INFINITY), 1.0);
 
-        check_integrate_pdf_is_cdf(dist, x_min, x_max, (x_max - x_min) / 100000.0);
+        if std::panic::catch_unwind(|| {
+            check_integrate_pdf_is_cdf(dist, x_min, x_max, (x_max - x_min) / 100000.0);
+        })
+        .or(std::panic::catch_unwind(|| {
+            check_derivative_of_cdf_is_pdf(dist, x_min, x_max, (x_max - x_min) / 100000.0);
+        }))
+        .is_err()
+        {
+            panic!("Integration of pdf doesn't equal cdf and derivative of cdf doesn't equal pdf!");
+        }
     }
 
     /// Does a series of checks that all positive discrete distributions must