diff --git a/src/transforms/distribution_transform.jl b/src/transforms/distribution_transform.jl
index d1e60bb67..4a84a0f96 100644
--- a/src/transforms/distribution_transform.jl
+++ b/src/transforms/distribution_transform.jl
@@ -319,7 +319,12 @@ function apply_dist_trafo(trg_d::DT, src_d::DT, src_v) where {DT <: StdMvDist}
 end
 
 
-_dist_params_numtype(d::Distribution) = promote_type(map(typeof, Distributions.params(d))...)
+_dist_params_numtype(d::Distribution) = realnumtype(typeof(params(d)))
+
+function ChainRulesCore.rrule(::typeof(_dist_params_numtype), d::Distribution)
+    _dist_params_numtype_pullback(ΔΩ) = (NoTangent(), NoTangent())
+    _dist_params_numtype(d), _dist_params_numtype_pullback
+end
 
 
 @inline _trafo_cdf(d::Distribution{Univariate,Continuous}, x::Real) = _trafo_cdf_impl(_dist_params_numtype(d), d, x)
@@ -370,7 +375,7 @@ end
 
 
 @inline function _eval_dist_trafo_func(f::typeof(_trafo_cdf), d::Distribution{Univariate,Continuous}, src_v::Real)
-    R_V = float(promote_type(typeof(src_v), eltype(params(d))))
+    R_V = float(promote_type(typeof(src_v), _dist_params_numtype(d)))
     if insupport(d, src_v)
         trg_v = f(d, src_v)
         convert(R_V, trg_v)
@@ -380,7 +385,7 @@ end
 end
 
 @inline function _eval_dist_trafo_func(f::typeof(_trafo_quantile), d::Distribution{Univariate,Continuous}, src_v::Real)
-    R_V = float(promote_type(typeof(src_v), eltype(params(d))))
+    R_V = float(promote_type(typeof(src_v), _dist_params_numtype(d)))
     if 0 <= src_v <= 1
         trg_v = f(d, src_v)
         convert(R_V, trg_v)