diff --git a/src/censored.jl b/src/censored.jl
index 98efa6e0f..fef3c9509 100644
--- a/src/censored.jl
+++ b/src/censored.jl
@@ -312,47 +312,54 @@ function entropy(d::Censored)
     
     # truncation contains ~ no probability
     if log_prob_trunc < log(eps(one(log_prob_trunc)))
-        return entropy_bound
+        entropy_trunc = zero(entropy_bound)
+    else
+        entropy_trunc = oftype(entropy_bound, entropy(_to_truncated(d)))
     end
-
-    dtrunc = _to_truncated(d)
-    entropy_interval = 
-        exp(log_prob_trunc) * entropy(dtrunc) - xexpx(log_prob_trunc) + xlogx_pl + xlogx_pu
+    entropy_interval = exp(log_prob_trunc) * entropy_trunc - xexpx(log_prob_trunc) + xlogx_pl + xlogx_pu
     return entropy_bound + entropy_interval
 end
 
 
 #### Evaluation
 
-function pdf(d::Censored{<:Any,<:Any,T}, x::Real) where {T}
+function pdf(d::Censored{<:Any,<:Any,T}, x0::Real) where {T}
     d0 = d.uncensored
     lower = d.lower
     upper = d.upper
-    S = Base.promote_eltype(T, x)
+    S = Base.promote_eltype(T, x0)
+    x = S(x0)
+    px = float(pdf(d0, x))
     return if lower !== missing && x == lower
-        result = cdf(d0, S(x))
-        _eqnotmissing(x, upper) ? one(result) : result
+        _eqnotmissing(x, upper) ? one(px) : oftype(px, cdf(d0, x))
     elseif _eqnotmissing(x, upper)
-        _ccdf_inclusive(d0, S(x))
+        if value_support(typeof(d0)) === Discrete
+            oftype(px, ccdf(d0, x) + px)
+        else
+            oftype(px, ccdf(d0, x))
+        end
     else
-        result = pdf(d0, S(x))
-        _in_open_interval(x, lower, upper) ? result : zero(result)
+        _in_open_interval(x, lower, upper) ? px : zero(px)
     end
 end
 
-function logpdf(d::Censored{<:Any,<:Any,T}, x::Real) where {T}
+function logpdf(d::Censored{<:Any,<:Any,T}, x0::Real) where {T}
     d0 = d.uncensored
     lower = d.lower
     upper = d.upper
-    S = Base.promote_eltype(T, x)
+    S = Base.promote_eltype(T, x0)
+    x = S(x0)
+    logpx = float(logpdf(d0, x))
     return if lower !== missing && x == lower
-        result = logcdf(d0, S(x))
-        _eqnotmissing(x, upper) ? zero(result) : result
+        _eqnotmissing(x, upper) ? zero(logpx) : oftype(logpx, logcdf(d0, x))
     elseif _eqnotmissing(x, upper)
-        _logccdf_inclusive(d0, S(x))
+        if value_support(typeof(d0)) === Discrete
+            oftype(logpx, logaddexp(logccdf(d0, x), logpx))
+        else
+            oftype(logpx, logccdf(d0, x))
+        end
     else
-        result = logpdf(d0, S(x))
-        _in_open_interval(x, lower, upper) ? result : oftype(result, -Inf)
+        _in_open_interval(x, lower, upper) ? logpx : oftype(logpx, -Inf)
     end
 end
 
@@ -360,14 +367,14 @@ function loglikelihood(d::Censored{<:Any,<:Any,T}, x::AbstractArray{<:Real}) whe
     d0 = d.uncensored
     lower = d.lower
     upper = d.upper
-    S = float(Base.promote_eltype(T, first(x)))
-    log_prob_lower = lower === missing ? 0 : logcdf(d0, S(lower))
-    log_prob_upper = upper === missing ? 0 : _logccdf_inclusive(d0, S(upper))
-    logzero = S(-Inf)
-
+    S = Base.promote_eltype(T, x)
+    x1 = S(first(x))
+    logpx1 = float(logpdf(d0, x1))
+    log_prob_lower = lower === missing ? zero(logpx1) : oftype(logpx1, logcdf(d0, S(lower)))
+    log_prob_upper = upper === missing ? zero(logpx1) : oftype(logpx1, _logccdf_inclusive(d0, S(upper)))
+    logzero = oftype(logpx1, -Inf)
     return sum(x) do xi
-        R = float(Base.promote_eltype(T, xi))
-        _in_open_interval(xi, lower, upper) && return logpdf(d0, R(xi))
+        _in_open_interval(xi, lower, upper) && return oftype(logpx1, logpdf(d0, oftype(x1, xi)))
         _eqnotmissing(xi, lower) && return log_prob_lower
         _eqnotmissing(xi, upper) && return log_prob_upper
         return logzero