added a test on the skewness of the Skewed and Cauchy

ctapipe/image/tests/test_toy.py

@@ -58,7 +58,7 @@ def test_intensity(seed, monkeypatch, prod5_lst):
 
 
 def test_skewed(prod5_lst):
-    from ctapipe.image.toymodel import SkewedGaussian
+    from ctapipe.image.toymodel import SkewedCauchy, SkewedGaussian
 
     # test if the parameters we calculated for the skew normal
     # distribution produce the correct moments
@@ -84,6 +84,18 @@ def test_skewed(prod5_lst):
     assert np.isclose(var, length.to_value(u.m) ** 2)
     assert np.isclose(skew, skewness)
 
+    model = SkewedCauchy(
+        x=x, y=y, width=width, length=length, psi=psi, skewness=skewness
+    )
+    model.generate_image(geom, intensity=intensity, nsb_level_pe=5, rng=rng)
+
+    a, loc, scale = model._moments_to_parameters()
+    mean, var, skew = skewnorm(a=a, loc=loc, scale=scale).stats(moments="mvs")
+
+    assert np.isclose(mean, 0)
+    assert np.isclose(var, length.to_value(u.m) ** 2)
+    assert np.isclose(skew, skewness)
+
 
 def test_compare(prod5_lst):
     from ctapipe.image.toymodel import Gaussian, SkewedGaussian