diff --git a/stan/math/prim/prob/scaled_inv_chi_square_cdf.hpp b/stan/math/prim/prob/scaled_inv_chi_square_cdf.hpp
index 4eb742443fc..f4a65ab2b3c 100644
--- a/stan/math/prim/prob/scaled_inv_chi_square_cdf.hpp
+++ b/stan/math/prim/prob/scaled_inv_chi_square_cdf.hpp
@@ -12,6 +12,7 @@
 #include <stan/math/prim/fun/size.hpp>
 #include <stan/math/prim/fun/size_zero.hpp>
 #include <stan/math/prim/fun/tgamma.hpp>
+#include <stan/math/prim/fun/to_ref.hpp>
 #include <stan/math/prim/fun/value_of.hpp>
 #include <stan/math/prim/functor/operands_and_partials.hpp>
 #include <cmath>
@@ -39,25 +40,32 @@ return_type_t<T_y, T_dof, T_scale> scaled_inv_chi_square_cdf(const T_y& y,
   using T_partials_return = partials_return_t<T_y, T_dof, T_scale>;
   using std::exp;
   using std::pow;
+  using T_y_ref = ref_type_t<T_y>;
+  using T_nu_ref = ref_type_t<T_dof>;
+  using T_s_ref = ref_type_t<T_scale>;
   static const char* function = "scaled_inv_chi_square_cdf";
-  check_not_nan(function, "Random variable", y);
-  check_nonnegative(function, "Random variable", y);
-  check_positive_finite(function, "Degrees of freedom parameter", nu);
-  check_positive_finite(function, "Scale parameter", s);
   check_consistent_sizes(function, "Random variable", y,
                          "Degrees of freedom parameter", nu, "Scale parameter",
                          s);
+  T_y_ref y_ref = y;
+  T_nu_ref nu_ref = nu;
+  T_s_ref s_ref = s;
+
+  check_nonnegative(function, "Random variable", y_ref);
+  check_positive_finite(function, "Degrees of freedom parameter", nu_ref);
+  check_positive_finite(function, "Scale parameter", s_ref);
 
   if (size_zero(y, nu, s)) {
     return 1.0;
   }
 
   T_partials_return P(1.0);
-  operands_and_partials<T_y, T_dof, T_scale> ops_partials(y, nu, s);
+  operands_and_partials<T_y_ref, T_nu_ref, T_s_ref> ops_partials(y_ref, nu_ref,
+                                                                 s_ref);
 
-  scalar_seq_view<T_y> y_vec(y);
-  scalar_seq_view<T_dof> nu_vec(nu);
-  scalar_seq_view<T_scale> s_vec(s);
+  scalar_seq_view<T_y_ref> y_vec(y_ref);
+  scalar_seq_view<T_nu_ref> nu_vec(nu_ref);
+  scalar_seq_view<T_s_ref> s_vec(s_ref);
   size_t N = max_size(y, nu, s);
 
   // Explicit return for extreme values
diff --git a/stan/math/prim/prob/scaled_inv_chi_square_lccdf.hpp b/stan/math/prim/prob/scaled_inv_chi_square_lccdf.hpp
index e96fb4963ae..79e2a78dbb6 100644
--- a/stan/math/prim/prob/scaled_inv_chi_square_lccdf.hpp
+++ b/stan/math/prim/prob/scaled_inv_chi_square_lccdf.hpp
@@ -27,25 +27,31 @@ return_type_t<T_y, T_dof, T_scale> scaled_inv_chi_square_lccdf(
   using std::exp;
   using std::log;
   using std::pow;
+  using T_y_ref = ref_type_t<T_y>;
+  using T_nu_ref = ref_type_t<T_dof>;
+  using T_s_ref = ref_type_t<T_scale>;
   static const char* function = "scaled_inv_chi_square_lccdf";
-  check_not_nan(function, "Random variable", y);
-  check_nonnegative(function, "Random variable", y);
-  check_positive_finite(function, "Degrees of freedom parameter", nu);
-  check_positive_finite(function, "Scale parameter", s);
   check_consistent_sizes(function, "Random variable", y,
                          "Degrees of freedom parameter", nu, "Scale parameter",
                          s);
+  T_y_ref y_ref = y;
+  T_nu_ref nu_ref = nu;
+  T_s_ref s_ref = s;
+  check_nonnegative(function, "Random variable", y_ref);
+  check_positive_finite(function, "Degrees of freedom parameter", nu_ref);
+  check_positive_finite(function, "Scale parameter", s_ref);
 
   if (size_zero(y, nu, s)) {
     return 0;
   }
 
   T_partials_return P(0.0);
-  operands_and_partials<T_y, T_dof, T_scale> ops_partials(y, nu, s);
+  operands_and_partials<T_y_ref, T_nu_ref, T_s_ref> ops_partials(y_ref, nu_ref,
+                                                                 s_ref);
 
-  scalar_seq_view<T_y> y_vec(y);
-  scalar_seq_view<T_dof> nu_vec(nu);
-  scalar_seq_view<T_scale> s_vec(s);
+  scalar_seq_view<T_y_ref> y_vec(y_ref);
+  scalar_seq_view<T_nu_ref> nu_vec(nu_ref);
+  scalar_seq_view<T_s_ref> s_vec(s_ref);
   size_t N = max_size(y, nu, s);
 
   // Explicit return for extreme values
diff --git a/stan/math/prim/prob/scaled_inv_chi_square_lcdf.hpp b/stan/math/prim/prob/scaled_inv_chi_square_lcdf.hpp
index 1143cacdf29..3e81a71b730 100644
--- a/stan/math/prim/prob/scaled_inv_chi_square_lcdf.hpp
+++ b/stan/math/prim/prob/scaled_inv_chi_square_lcdf.hpp
@@ -27,25 +27,31 @@ return_type_t<T_y, T_dof, T_scale> scaled_inv_chi_square_lcdf(
   using std::exp;
   using std::log;
   using std::pow;
+  using T_y_ref = ref_type_t<T_y>;
+  using T_nu_ref = ref_type_t<T_dof>;
+  using T_s_ref = ref_type_t<T_scale>;
   static const char* function = "scaled_inv_chi_square_lcdf";
-  check_not_nan(function, "Random variable", y);
-  check_nonnegative(function, "Random variable", y);
-  check_positive_finite(function, "Degrees of freedom parameter", nu);
-  check_positive_finite(function, "Scale parameter", s);
   check_consistent_sizes(function, "Random variable", y,
                          "Degrees of freedom parameter", nu, "Scale parameter",
                          s);
+  T_y_ref y_ref = y;
+  T_nu_ref nu_ref = nu;
+  T_s_ref s_ref = s;
+  check_nonnegative(function, "Random variable", y_ref);
+  check_positive_finite(function, "Degrees of freedom parameter", nu_ref);
+  check_positive_finite(function, "Scale parameter", s_ref);
 
   if (size_zero(y, nu, s)) {
     return 0;
   }
 
   T_partials_return P(0.0);
-  operands_and_partials<T_y, T_dof, T_scale> ops_partials(y, nu, s);
+  operands_and_partials<T_y_ref, T_nu_ref, T_s_ref> ops_partials(y_ref, nu_ref,
+                                                                 s_ref);
 
-  scalar_seq_view<T_y> y_vec(y);
-  scalar_seq_view<T_dof> nu_vec(nu);
-  scalar_seq_view<T_scale> s_vec(s);
+  scalar_seq_view<T_y_ref> y_vec(y_ref);
+  scalar_seq_view<T_nu_ref> nu_vec(nu_ref);
+  scalar_seq_view<T_s_ref> s_vec(s_ref);
   size_t N = max_size(y, nu, s);
 
   // Explicit return for extreme values
diff --git a/stan/math/prim/prob/scaled_inv_chi_square_lpdf.hpp b/stan/math/prim/prob/scaled_inv_chi_square_lpdf.hpp
index 430da2df82e..3018710527e 100644
--- a/stan/math/prim/prob/scaled_inv_chi_square_lpdf.hpp
+++ b/stan/math/prim/prob/scaled_inv_chi_square_lpdf.hpp
@@ -44,13 +44,19 @@ return_type_t<T_y, T_dof, T_scale> scaled_inv_chi_square_lpdf(
     const T_y& y, const T_dof& nu, const T_scale& s) {
   using T_partials_return = partials_return_t<T_y, T_dof, T_scale>;
   using std::log;
+  using T_y_ref = ref_type_t<T_y>;
+  using T_nu_ref = ref_type_t<T_dof>;
+  using T_s_ref = ref_type_t<T_scale>;
   static const char* function = "scaled_inv_chi_square_lpdf";
-  check_not_nan(function, "Random variable", y);
-  check_positive_finite(function, "Degrees of freedom parameter", nu);
-  check_positive_finite(function, "Scale parameter", s);
   check_consistent_sizes(function, "Random variable", y,
                          "Degrees of freedom parameter", nu, "Scale parameter",
                          s);
+  T_y_ref y_ref = y;
+  T_nu_ref nu_ref = nu;
+  T_s_ref s_ref = s;
+  check_not_nan(function, "Random variable", y_ref);
+  check_positive_finite(function, "Degrees of freedom parameter", nu_ref);
+  check_positive_finite(function, "Scale parameter", s_ref);
 
   if (size_zero(y, nu, s)) {
     return 0;
@@ -60,11 +66,12 @@ return_type_t<T_y, T_dof, T_scale> scaled_inv_chi_square_lpdf(
   }
 
   T_partials_return logp(0);
-  operands_and_partials<T_y, T_dof, T_scale> ops_partials(y, nu, s);
+  operands_and_partials<T_y_ref, T_nu_ref, T_s_ref> ops_partials(y_ref, nu_ref,
+                                                                 s_ref);
 
-  scalar_seq_view<T_y> y_vec(y);
-  scalar_seq_view<T_dof> nu_vec(nu);
-  scalar_seq_view<T_scale> s_vec(s);
+  scalar_seq_view<T_y_ref> y_vec(y_ref);
+  scalar_seq_view<T_nu_ref> nu_vec(nu_ref);
+  scalar_seq_view<T_s_ref> s_vec(s_ref);
   size_t N = max_size(y, nu, s);
 
   for (size_t n = 0; n < N; n++) {
diff --git a/stan/math/prim/prob/scaled_inv_chi_square_rng.hpp b/stan/math/prim/prob/scaled_inv_chi_square_rng.hpp
index 444e26e24a7..2eaa46a4c41 100644
--- a/stan/math/prim/prob/scaled_inv_chi_square_rng.hpp
+++ b/stan/math/prim/prob/scaled_inv_chi_square_rng.hpp
@@ -4,6 +4,7 @@
 #include <stan/math/prim/meta.hpp>
 #include <stan/math/prim/err.hpp>
 #include <stan/math/prim/fun/max_size.hpp>
+#include <stan/math/prim/fun/to_ref.hpp>
 #include <boost/random/chi_squared_distribution.hpp>
 #include <boost/random/variate_generator.hpp>
 
@@ -35,13 +36,15 @@ scaled_inv_chi_square_rng(const T_deg& nu, const T_scale& s, RNG& rng) {
   using boost::variate_generator;
   using boost::random::chi_squared_distribution;
   static const char* function = "scaled_inv_chi_square_rng";
-  check_positive_finite(function, "Degrees of freedom parameter", nu);
-  check_positive_finite(function, "Scale parameter", s);
   check_consistent_sizes(function, "Location parameter", nu, "Scale Parameter",
                          s);
+  const auto& nu_ref = to_ref(nu);
+  const auto& s_ref = to_ref(s);
+  check_positive_finite(function, "Degrees of freedom parameter", nu_ref);
+  check_positive_finite(function, "Scale parameter", s_ref);
 
-  scalar_seq_view<T_deg> nu_vec(nu);
-  scalar_seq_view<T_scale> s_vec(s);
+  scalar_seq_view<T_deg> nu_vec(nu_ref);
+  scalar_seq_view<T_scale> s_vec(s_ref);
   size_t N = max_size(nu, s);
   VectorBuilder<true, double, T_deg, T_scale> output(N);
 
diff --git a/test/expressions/stan_math_sigs_exceptions.expected b/test/expressions/stan_math_sigs_exceptions.expected
index bf1a45d581d..71058c11441 100644
--- a/test/expressions/stan_math_sigs_exceptions.expected
+++ b/test/expressions/stan_math_sigs_exceptions.expected
@@ -2680,418 +2680,6 @@ vector rows_dot_product(vector, vector)
 vector rows_dot_product(row_vector, row_vector)
 vector rows_dot_product(matrix, matrix)
 matrix scale_matrix_exp_multiply(real, matrix, matrix)
-real scaled_inv_chi_square_ccdf_log(real, real, vector)
-real scaled_inv_chi_square_ccdf_log(real, real, row_vector)
-real scaled_inv_chi_square_ccdf_log(real, vector, real)
-real scaled_inv_chi_square_ccdf_log(real, vector, vector)
-real scaled_inv_chi_square_ccdf_log(real, vector, row_vector)
-real scaled_inv_chi_square_ccdf_log(real, vector, real[])
-real scaled_inv_chi_square_ccdf_log(real, row_vector, real)
-real scaled_inv_chi_square_ccdf_log(real, row_vector, vector)
-real scaled_inv_chi_square_ccdf_log(real, row_vector, row_vector)
-real scaled_inv_chi_square_ccdf_log(real, row_vector, real[])
-real scaled_inv_chi_square_ccdf_log(real, real[], vector)
-real scaled_inv_chi_square_ccdf_log(real, real[], row_vector)
-real scaled_inv_chi_square_ccdf_log(vector, real, real)
-real scaled_inv_chi_square_ccdf_log(vector, real, vector)
-real scaled_inv_chi_square_ccdf_log(vector, real, row_vector)
-real scaled_inv_chi_square_ccdf_log(vector, real, real[])
-real scaled_inv_chi_square_ccdf_log(vector, vector, real)
-real scaled_inv_chi_square_ccdf_log(vector, vector, vector)
-real scaled_inv_chi_square_ccdf_log(vector, vector, row_vector)
-real scaled_inv_chi_square_ccdf_log(vector, vector, real[])
-real scaled_inv_chi_square_ccdf_log(vector, row_vector, real)
-real scaled_inv_chi_square_ccdf_log(vector, row_vector, vector)
-real scaled_inv_chi_square_ccdf_log(vector, row_vector, row_vector)
-real scaled_inv_chi_square_ccdf_log(vector, row_vector, real[])
-real scaled_inv_chi_square_ccdf_log(vector, real[], real)
-real scaled_inv_chi_square_ccdf_log(vector, real[], vector)
-real scaled_inv_chi_square_ccdf_log(vector, real[], row_vector)
-real scaled_inv_chi_square_ccdf_log(vector, real[], real[])
-real scaled_inv_chi_square_ccdf_log(row_vector, real, real)
-real scaled_inv_chi_square_ccdf_log(row_vector, real, vector)
-real scaled_inv_chi_square_ccdf_log(row_vector, real, row_vector)
-real scaled_inv_chi_square_ccdf_log(row_vector, real, real[])
-real scaled_inv_chi_square_ccdf_log(row_vector, vector, real)
-real scaled_inv_chi_square_ccdf_log(row_vector, vector, vector)
-real scaled_inv_chi_square_ccdf_log(row_vector, vector, row_vector)
-real scaled_inv_chi_square_ccdf_log(row_vector, vector, real[])
-real scaled_inv_chi_square_ccdf_log(row_vector, row_vector, real)
-real scaled_inv_chi_square_ccdf_log(row_vector, row_vector, vector)
-real scaled_inv_chi_square_ccdf_log(row_vector, row_vector, row_vector)
-real scaled_inv_chi_square_ccdf_log(row_vector, row_vector, real[])
-real scaled_inv_chi_square_ccdf_log(row_vector, real[], real)
-real scaled_inv_chi_square_ccdf_log(row_vector, real[], vector)
-real scaled_inv_chi_square_ccdf_log(row_vector, real[], row_vector)
-real scaled_inv_chi_square_ccdf_log(row_vector, real[], real[])
-real scaled_inv_chi_square_ccdf_log(real[], real, vector)
-real scaled_inv_chi_square_ccdf_log(real[], real, row_vector)
-real scaled_inv_chi_square_ccdf_log(real[], vector, real)
-real scaled_inv_chi_square_ccdf_log(real[], vector, vector)
-real scaled_inv_chi_square_ccdf_log(real[], vector, row_vector)
-real scaled_inv_chi_square_ccdf_log(real[], vector, real[])
-real scaled_inv_chi_square_ccdf_log(real[], row_vector, real)
-real scaled_inv_chi_square_ccdf_log(real[], row_vector, vector)
-real scaled_inv_chi_square_ccdf_log(real[], row_vector, row_vector)
-real scaled_inv_chi_square_ccdf_log(real[], row_vector, real[])
-real scaled_inv_chi_square_ccdf_log(real[], real[], vector)
-real scaled_inv_chi_square_ccdf_log(real[], real[], row_vector)
-real scaled_inv_chi_square_cdf(real, real, vector)
-real scaled_inv_chi_square_cdf(real, real, row_vector)
-real scaled_inv_chi_square_cdf(real, vector, real)
-real scaled_inv_chi_square_cdf(real, vector, vector)
-real scaled_inv_chi_square_cdf(real, vector, row_vector)
-real scaled_inv_chi_square_cdf(real, vector, real[])
-real scaled_inv_chi_square_cdf(real, row_vector, real)
-real scaled_inv_chi_square_cdf(real, row_vector, vector)
-real scaled_inv_chi_square_cdf(real, row_vector, row_vector)
-real scaled_inv_chi_square_cdf(real, row_vector, real[])
-real scaled_inv_chi_square_cdf(real, real[], vector)
-real scaled_inv_chi_square_cdf(real, real[], row_vector)
-real scaled_inv_chi_square_cdf(vector, real, real)
-real scaled_inv_chi_square_cdf(vector, real, vector)
-real scaled_inv_chi_square_cdf(vector, real, row_vector)
-real scaled_inv_chi_square_cdf(vector, real, real[])
-real scaled_inv_chi_square_cdf(vector, vector, real)
-real scaled_inv_chi_square_cdf(vector, vector, vector)
-real scaled_inv_chi_square_cdf(vector, vector, row_vector)
-real scaled_inv_chi_square_cdf(vector, vector, real[])
-real scaled_inv_chi_square_cdf(vector, row_vector, real)
-real scaled_inv_chi_square_cdf(vector, row_vector, vector)
-real scaled_inv_chi_square_cdf(vector, row_vector, row_vector)
-real scaled_inv_chi_square_cdf(vector, row_vector, real[])
-real scaled_inv_chi_square_cdf(vector, real[], real)
-real scaled_inv_chi_square_cdf(vector, real[], vector)
-real scaled_inv_chi_square_cdf(vector, real[], row_vector)
-real scaled_inv_chi_square_cdf(vector, real[], real[])
-real scaled_inv_chi_square_cdf(row_vector, real, real)
-real scaled_inv_chi_square_cdf(row_vector, real, vector)
-real scaled_inv_chi_square_cdf(row_vector, real, row_vector)
-real scaled_inv_chi_square_cdf(row_vector, real, real[])
-real scaled_inv_chi_square_cdf(row_vector, vector, real)
-real scaled_inv_chi_square_cdf(row_vector, vector, vector)
-real scaled_inv_chi_square_cdf(row_vector, vector, row_vector)
-real scaled_inv_chi_square_cdf(row_vector, vector, real[])
-real scaled_inv_chi_square_cdf(row_vector, row_vector, real)
-real scaled_inv_chi_square_cdf(row_vector, row_vector, vector)
-real scaled_inv_chi_square_cdf(row_vector, row_vector, row_vector)
-real scaled_inv_chi_square_cdf(row_vector, row_vector, real[])
-real scaled_inv_chi_square_cdf(row_vector, real[], real)
-real scaled_inv_chi_square_cdf(row_vector, real[], vector)
-real scaled_inv_chi_square_cdf(row_vector, real[], row_vector)
-real scaled_inv_chi_square_cdf(row_vector, real[], real[])
-real scaled_inv_chi_square_cdf(real[], real, vector)
-real scaled_inv_chi_square_cdf(real[], real, row_vector)
-real scaled_inv_chi_square_cdf(real[], vector, real)
-real scaled_inv_chi_square_cdf(real[], vector, vector)
-real scaled_inv_chi_square_cdf(real[], vector, row_vector)
-real scaled_inv_chi_square_cdf(real[], vector, real[])
-real scaled_inv_chi_square_cdf(real[], row_vector, real)
-real scaled_inv_chi_square_cdf(real[], row_vector, vector)
-real scaled_inv_chi_square_cdf(real[], row_vector, row_vector)
-real scaled_inv_chi_square_cdf(real[], row_vector, real[])
-real scaled_inv_chi_square_cdf(real[], real[], vector)
-real scaled_inv_chi_square_cdf(real[], real[], row_vector)
-real scaled_inv_chi_square_cdf_log(real, real, vector)
-real scaled_inv_chi_square_cdf_log(real, real, row_vector)
-real scaled_inv_chi_square_cdf_log(real, vector, real)
-real scaled_inv_chi_square_cdf_log(real, vector, vector)
-real scaled_inv_chi_square_cdf_log(real, vector, row_vector)
-real scaled_inv_chi_square_cdf_log(real, vector, real[])
-real scaled_inv_chi_square_cdf_log(real, row_vector, real)
-real scaled_inv_chi_square_cdf_log(real, row_vector, vector)
-real scaled_inv_chi_square_cdf_log(real, row_vector, row_vector)
-real scaled_inv_chi_square_cdf_log(real, row_vector, real[])
-real scaled_inv_chi_square_cdf_log(real, real[], vector)
-real scaled_inv_chi_square_cdf_log(real, real[], row_vector)
-real scaled_inv_chi_square_cdf_log(vector, real, real)
-real scaled_inv_chi_square_cdf_log(vector, real, vector)
-real scaled_inv_chi_square_cdf_log(vector, real, row_vector)
-real scaled_inv_chi_square_cdf_log(vector, real, real[])
-real scaled_inv_chi_square_cdf_log(vector, vector, real)
-real scaled_inv_chi_square_cdf_log(vector, vector, vector)
-real scaled_inv_chi_square_cdf_log(vector, vector, row_vector)
-real scaled_inv_chi_square_cdf_log(vector, vector, real[])
-real scaled_inv_chi_square_cdf_log(vector, row_vector, real)
-real scaled_inv_chi_square_cdf_log(vector, row_vector, vector)
-real scaled_inv_chi_square_cdf_log(vector, row_vector, row_vector)
-real scaled_inv_chi_square_cdf_log(vector, row_vector, real[])
-real scaled_inv_chi_square_cdf_log(vector, real[], real)
-real scaled_inv_chi_square_cdf_log(vector, real[], vector)
-real scaled_inv_chi_square_cdf_log(vector, real[], row_vector)
-real scaled_inv_chi_square_cdf_log(vector, real[], real[])
-real scaled_inv_chi_square_cdf_log(row_vector, real, real)
-real scaled_inv_chi_square_cdf_log(row_vector, real, vector)
-real scaled_inv_chi_square_cdf_log(row_vector, real, row_vector)
-real scaled_inv_chi_square_cdf_log(row_vector, real, real[])
-real scaled_inv_chi_square_cdf_log(row_vector, vector, real)
-real scaled_inv_chi_square_cdf_log(row_vector, vector, vector)
-real scaled_inv_chi_square_cdf_log(row_vector, vector, row_vector)
-real scaled_inv_chi_square_cdf_log(row_vector, vector, real[])
-real scaled_inv_chi_square_cdf_log(row_vector, row_vector, real)
-real scaled_inv_chi_square_cdf_log(row_vector, row_vector, vector)
-real scaled_inv_chi_square_cdf_log(row_vector, row_vector, row_vector)
-real scaled_inv_chi_square_cdf_log(row_vector, row_vector, real[])
-real scaled_inv_chi_square_cdf_log(row_vector, real[], real)
-real scaled_inv_chi_square_cdf_log(row_vector, real[], vector)
-real scaled_inv_chi_square_cdf_log(row_vector, real[], row_vector)
-real scaled_inv_chi_square_cdf_log(row_vector, real[], real[])
-real scaled_inv_chi_square_cdf_log(real[], real, vector)
-real scaled_inv_chi_square_cdf_log(real[], real, row_vector)
-real scaled_inv_chi_square_cdf_log(real[], vector, real)
-real scaled_inv_chi_square_cdf_log(real[], vector, vector)
-real scaled_inv_chi_square_cdf_log(real[], vector, row_vector)
-real scaled_inv_chi_square_cdf_log(real[], vector, real[])
-real scaled_inv_chi_square_cdf_log(real[], row_vector, real)
-real scaled_inv_chi_square_cdf_log(real[], row_vector, vector)
-real scaled_inv_chi_square_cdf_log(real[], row_vector, row_vector)
-real scaled_inv_chi_square_cdf_log(real[], row_vector, real[])
-real scaled_inv_chi_square_cdf_log(real[], real[], vector)
-real scaled_inv_chi_square_cdf_log(real[], real[], row_vector)
-real scaled_inv_chi_square_lccdf(real, real, vector)
-real scaled_inv_chi_square_lccdf(real, real, row_vector)
-real scaled_inv_chi_square_lccdf(real, vector, real)
-real scaled_inv_chi_square_lccdf(real, vector, vector)
-real scaled_inv_chi_square_lccdf(real, vector, row_vector)
-real scaled_inv_chi_square_lccdf(real, vector, real[])
-real scaled_inv_chi_square_lccdf(real, row_vector, real)
-real scaled_inv_chi_square_lccdf(real, row_vector, vector)
-real scaled_inv_chi_square_lccdf(real, row_vector, row_vector)
-real scaled_inv_chi_square_lccdf(real, row_vector, real[])
-real scaled_inv_chi_square_lccdf(real, real[], vector)
-real scaled_inv_chi_square_lccdf(real, real[], row_vector)
-real scaled_inv_chi_square_lccdf(vector, real, real)
-real scaled_inv_chi_square_lccdf(vector, real, vector)
-real scaled_inv_chi_square_lccdf(vector, real, row_vector)
-real scaled_inv_chi_square_lccdf(vector, real, real[])
-real scaled_inv_chi_square_lccdf(vector, vector, real)
-real scaled_inv_chi_square_lccdf(vector, vector, vector)
-real scaled_inv_chi_square_lccdf(vector, vector, row_vector)
-real scaled_inv_chi_square_lccdf(vector, vector, real[])
-real scaled_inv_chi_square_lccdf(vector, row_vector, real)
-real scaled_inv_chi_square_lccdf(vector, row_vector, vector)
-real scaled_inv_chi_square_lccdf(vector, row_vector, row_vector)
-real scaled_inv_chi_square_lccdf(vector, row_vector, real[])
-real scaled_inv_chi_square_lccdf(vector, real[], real)
-real scaled_inv_chi_square_lccdf(vector, real[], vector)
-real scaled_inv_chi_square_lccdf(vector, real[], row_vector)
-real scaled_inv_chi_square_lccdf(vector, real[], real[])
-real scaled_inv_chi_square_lccdf(row_vector, real, real)
-real scaled_inv_chi_square_lccdf(row_vector, real, vector)
-real scaled_inv_chi_square_lccdf(row_vector, real, row_vector)
-real scaled_inv_chi_square_lccdf(row_vector, real, real[])
-real scaled_inv_chi_square_lccdf(row_vector, vector, real)
-real scaled_inv_chi_square_lccdf(row_vector, vector, vector)
-real scaled_inv_chi_square_lccdf(row_vector, vector, row_vector)
-real scaled_inv_chi_square_lccdf(row_vector, vector, real[])
-real scaled_inv_chi_square_lccdf(row_vector, row_vector, real)
-real scaled_inv_chi_square_lccdf(row_vector, row_vector, vector)
-real scaled_inv_chi_square_lccdf(row_vector, row_vector, row_vector)
-real scaled_inv_chi_square_lccdf(row_vector, row_vector, real[])
-real scaled_inv_chi_square_lccdf(row_vector, real[], real)
-real scaled_inv_chi_square_lccdf(row_vector, real[], vector)
-real scaled_inv_chi_square_lccdf(row_vector, real[], row_vector)
-real scaled_inv_chi_square_lccdf(row_vector, real[], real[])
-real scaled_inv_chi_square_lccdf(real[], real, vector)
-real scaled_inv_chi_square_lccdf(real[], real, row_vector)
-real scaled_inv_chi_square_lccdf(real[], vector, real)
-real scaled_inv_chi_square_lccdf(real[], vector, vector)
-real scaled_inv_chi_square_lccdf(real[], vector, row_vector)
-real scaled_inv_chi_square_lccdf(real[], vector, real[])
-real scaled_inv_chi_square_lccdf(real[], row_vector, real)
-real scaled_inv_chi_square_lccdf(real[], row_vector, vector)
-real scaled_inv_chi_square_lccdf(real[], row_vector, row_vector)
-real scaled_inv_chi_square_lccdf(real[], row_vector, real[])
-real scaled_inv_chi_square_lccdf(real[], real[], vector)
-real scaled_inv_chi_square_lccdf(real[], real[], row_vector)
-real scaled_inv_chi_square_lcdf(real, real, vector)
-real scaled_inv_chi_square_lcdf(real, real, row_vector)
-real scaled_inv_chi_square_lcdf(real, vector, real)
-real scaled_inv_chi_square_lcdf(real, vector, vector)
-real scaled_inv_chi_square_lcdf(real, vector, row_vector)
-real scaled_inv_chi_square_lcdf(real, vector, real[])
-real scaled_inv_chi_square_lcdf(real, row_vector, real)
-real scaled_inv_chi_square_lcdf(real, row_vector, vector)
-real scaled_inv_chi_square_lcdf(real, row_vector, row_vector)
-real scaled_inv_chi_square_lcdf(real, row_vector, real[])
-real scaled_inv_chi_square_lcdf(real, real[], vector)
-real scaled_inv_chi_square_lcdf(real, real[], row_vector)
-real scaled_inv_chi_square_lcdf(vector, real, real)
-real scaled_inv_chi_square_lcdf(vector, real, vector)
-real scaled_inv_chi_square_lcdf(vector, real, row_vector)
-real scaled_inv_chi_square_lcdf(vector, real, real[])
-real scaled_inv_chi_square_lcdf(vector, vector, real)
-real scaled_inv_chi_square_lcdf(vector, vector, vector)
-real scaled_inv_chi_square_lcdf(vector, vector, row_vector)
-real scaled_inv_chi_square_lcdf(vector, vector, real[])
-real scaled_inv_chi_square_lcdf(vector, row_vector, real)
-real scaled_inv_chi_square_lcdf(vector, row_vector, vector)
-real scaled_inv_chi_square_lcdf(vector, row_vector, row_vector)
-real scaled_inv_chi_square_lcdf(vector, row_vector, real[])
-real scaled_inv_chi_square_lcdf(vector, real[], real)
-real scaled_inv_chi_square_lcdf(vector, real[], vector)
-real scaled_inv_chi_square_lcdf(vector, real[], row_vector)
-real scaled_inv_chi_square_lcdf(vector, real[], real[])
-real scaled_inv_chi_square_lcdf(row_vector, real, real)
-real scaled_inv_chi_square_lcdf(row_vector, real, vector)
-real scaled_inv_chi_square_lcdf(row_vector, real, row_vector)
-real scaled_inv_chi_square_lcdf(row_vector, real, real[])
-real scaled_inv_chi_square_lcdf(row_vector, vector, real)
-real scaled_inv_chi_square_lcdf(row_vector, vector, vector)
-real scaled_inv_chi_square_lcdf(row_vector, vector, row_vector)
-real scaled_inv_chi_square_lcdf(row_vector, vector, real[])
-real scaled_inv_chi_square_lcdf(row_vector, row_vector, real)
-real scaled_inv_chi_square_lcdf(row_vector, row_vector, vector)
-real scaled_inv_chi_square_lcdf(row_vector, row_vector, row_vector)
-real scaled_inv_chi_square_lcdf(row_vector, row_vector, real[])
-real scaled_inv_chi_square_lcdf(row_vector, real[], real)
-real scaled_inv_chi_square_lcdf(row_vector, real[], vector)
-real scaled_inv_chi_square_lcdf(row_vector, real[], row_vector)
-real scaled_inv_chi_square_lcdf(row_vector, real[], real[])
-real scaled_inv_chi_square_lcdf(real[], real, vector)
-real scaled_inv_chi_square_lcdf(real[], real, row_vector)
-real scaled_inv_chi_square_lcdf(real[], vector, real)
-real scaled_inv_chi_square_lcdf(real[], vector, vector)
-real scaled_inv_chi_square_lcdf(real[], vector, row_vector)
-real scaled_inv_chi_square_lcdf(real[], vector, real[])
-real scaled_inv_chi_square_lcdf(real[], row_vector, real)
-real scaled_inv_chi_square_lcdf(real[], row_vector, vector)
-real scaled_inv_chi_square_lcdf(real[], row_vector, row_vector)
-real scaled_inv_chi_square_lcdf(real[], row_vector, real[])
-real scaled_inv_chi_square_lcdf(real[], real[], vector)
-real scaled_inv_chi_square_lcdf(real[], real[], row_vector)
-real scaled_inv_chi_square_log(real, real, vector)
-real scaled_inv_chi_square_log(real, real, row_vector)
-real scaled_inv_chi_square_log(real, vector, real)
-real scaled_inv_chi_square_log(real, vector, vector)
-real scaled_inv_chi_square_log(real, vector, row_vector)
-real scaled_inv_chi_square_log(real, vector, real[])
-real scaled_inv_chi_square_log(real, row_vector, real)
-real scaled_inv_chi_square_log(real, row_vector, vector)
-real scaled_inv_chi_square_log(real, row_vector, row_vector)
-real scaled_inv_chi_square_log(real, row_vector, real[])
-real scaled_inv_chi_square_log(real, real[], vector)
-real scaled_inv_chi_square_log(real, real[], row_vector)
-real scaled_inv_chi_square_log(vector, real, real)
-real scaled_inv_chi_square_log(vector, real, vector)
-real scaled_inv_chi_square_log(vector, real, row_vector)
-real scaled_inv_chi_square_log(vector, real, real[])
-real scaled_inv_chi_square_log(vector, vector, real)
-real scaled_inv_chi_square_log(vector, vector, vector)
-real scaled_inv_chi_square_log(vector, vector, row_vector)
-real scaled_inv_chi_square_log(vector, vector, real[])
-real scaled_inv_chi_square_log(vector, row_vector, real)
-real scaled_inv_chi_square_log(vector, row_vector, vector)
-real scaled_inv_chi_square_log(vector, row_vector, row_vector)
-real scaled_inv_chi_square_log(vector, row_vector, real[])
-real scaled_inv_chi_square_log(vector, real[], real)
-real scaled_inv_chi_square_log(vector, real[], vector)
-real scaled_inv_chi_square_log(vector, real[], row_vector)
-real scaled_inv_chi_square_log(vector, real[], real[])
-real scaled_inv_chi_square_log(row_vector, real, real)
-real scaled_inv_chi_square_log(row_vector, real, vector)
-real scaled_inv_chi_square_log(row_vector, real, row_vector)
-real scaled_inv_chi_square_log(row_vector, real, real[])
-real scaled_inv_chi_square_log(row_vector, vector, real)
-real scaled_inv_chi_square_log(row_vector, vector, vector)
-real scaled_inv_chi_square_log(row_vector, vector, row_vector)
-real scaled_inv_chi_square_log(row_vector, vector, real[])
-real scaled_inv_chi_square_log(row_vector, row_vector, real)
-real scaled_inv_chi_square_log(row_vector, row_vector, vector)
-real scaled_inv_chi_square_log(row_vector, row_vector, row_vector)
-real scaled_inv_chi_square_log(row_vector, row_vector, real[])
-real scaled_inv_chi_square_log(row_vector, real[], real)
-real scaled_inv_chi_square_log(row_vector, real[], vector)
-real scaled_inv_chi_square_log(row_vector, real[], row_vector)
-real scaled_inv_chi_square_log(row_vector, real[], real[])
-real scaled_inv_chi_square_log(real[], real, vector)
-real scaled_inv_chi_square_log(real[], real, row_vector)
-real scaled_inv_chi_square_log(real[], vector, real)
-real scaled_inv_chi_square_log(real[], vector, vector)
-real scaled_inv_chi_square_log(real[], vector, row_vector)
-real scaled_inv_chi_square_log(real[], vector, real[])
-real scaled_inv_chi_square_log(real[], row_vector, real)
-real scaled_inv_chi_square_log(real[], row_vector, vector)
-real scaled_inv_chi_square_log(real[], row_vector, row_vector)
-real scaled_inv_chi_square_log(real[], row_vector, real[])
-real scaled_inv_chi_square_log(real[], real[], vector)
-real scaled_inv_chi_square_log(real[], real[], row_vector)
-real scaled_inv_chi_square_lpdf(real, real, vector)
-real scaled_inv_chi_square_lpdf(real, real, row_vector)
-real scaled_inv_chi_square_lpdf(real, vector, real)
-real scaled_inv_chi_square_lpdf(real, vector, vector)
-real scaled_inv_chi_square_lpdf(real, vector, row_vector)
-real scaled_inv_chi_square_lpdf(real, vector, real[])
-real scaled_inv_chi_square_lpdf(real, row_vector, real)
-real scaled_inv_chi_square_lpdf(real, row_vector, vector)
-real scaled_inv_chi_square_lpdf(real, row_vector, row_vector)
-real scaled_inv_chi_square_lpdf(real, row_vector, real[])
-real scaled_inv_chi_square_lpdf(real, real[], vector)
-real scaled_inv_chi_square_lpdf(real, real[], row_vector)
-real scaled_inv_chi_square_lpdf(vector, real, real)
-real scaled_inv_chi_square_lpdf(vector, real, vector)
-real scaled_inv_chi_square_lpdf(vector, real, row_vector)
-real scaled_inv_chi_square_lpdf(vector, real, real[])
-real scaled_inv_chi_square_lpdf(vector, vector, real)
-real scaled_inv_chi_square_lpdf(vector, vector, vector)
-real scaled_inv_chi_square_lpdf(vector, vector, row_vector)
-real scaled_inv_chi_square_lpdf(vector, vector, real[])
-real scaled_inv_chi_square_lpdf(vector, row_vector, real)
-real scaled_inv_chi_square_lpdf(vector, row_vector, vector)
-real scaled_inv_chi_square_lpdf(vector, row_vector, row_vector)
-real scaled_inv_chi_square_lpdf(vector, row_vector, real[])
-real scaled_inv_chi_square_lpdf(vector, real[], real)
-real scaled_inv_chi_square_lpdf(vector, real[], vector)
-real scaled_inv_chi_square_lpdf(vector, real[], row_vector)
-real scaled_inv_chi_square_lpdf(vector, real[], real[])
-real scaled_inv_chi_square_lpdf(row_vector, real, real)
-real scaled_inv_chi_square_lpdf(row_vector, real, vector)
-real scaled_inv_chi_square_lpdf(row_vector, real, row_vector)
-real scaled_inv_chi_square_lpdf(row_vector, real, real[])
-real scaled_inv_chi_square_lpdf(row_vector, vector, real)
-real scaled_inv_chi_square_lpdf(row_vector, vector, vector)
-real scaled_inv_chi_square_lpdf(row_vector, vector, row_vector)
-real scaled_inv_chi_square_lpdf(row_vector, vector, real[])
-real scaled_inv_chi_square_lpdf(row_vector, row_vector, real)
-real scaled_inv_chi_square_lpdf(row_vector, row_vector, vector)
-real scaled_inv_chi_square_lpdf(row_vector, row_vector, row_vector)
-real scaled_inv_chi_square_lpdf(row_vector, row_vector, real[])
-real scaled_inv_chi_square_lpdf(row_vector, real[], real)
-real scaled_inv_chi_square_lpdf(row_vector, real[], vector)
-real scaled_inv_chi_square_lpdf(row_vector, real[], row_vector)
-real scaled_inv_chi_square_lpdf(row_vector, real[], real[])
-real scaled_inv_chi_square_lpdf(real[], real, vector)
-real scaled_inv_chi_square_lpdf(real[], real, row_vector)
-real scaled_inv_chi_square_lpdf(real[], vector, real)
-real scaled_inv_chi_square_lpdf(real[], vector, vector)
-real scaled_inv_chi_square_lpdf(real[], vector, row_vector)
-real scaled_inv_chi_square_lpdf(real[], vector, real[])
-real scaled_inv_chi_square_lpdf(real[], row_vector, real)
-real scaled_inv_chi_square_lpdf(real[], row_vector, vector)
-real scaled_inv_chi_square_lpdf(real[], row_vector, row_vector)
-real scaled_inv_chi_square_lpdf(real[], row_vector, real[])
-real scaled_inv_chi_square_lpdf(real[], real[], vector)
-real scaled_inv_chi_square_lpdf(real[], real[], row_vector)
-real[] scaled_inv_chi_square_rng(int, vector)
-real[] scaled_inv_chi_square_rng(int, row_vector)
-real[] scaled_inv_chi_square_rng(real, vector)
-real[] scaled_inv_chi_square_rng(real, row_vector)
-real[] scaled_inv_chi_square_rng(vector, int)
-real[] scaled_inv_chi_square_rng(vector, real)
-real[] scaled_inv_chi_square_rng(vector, vector)
-real[] scaled_inv_chi_square_rng(vector, row_vector)
-real[] scaled_inv_chi_square_rng(vector, int[])
-real[] scaled_inv_chi_square_rng(vector, real[])
-real[] scaled_inv_chi_square_rng(row_vector, int)
-real[] scaled_inv_chi_square_rng(row_vector, real)
-real[] scaled_inv_chi_square_rng(row_vector, vector)
-real[] scaled_inv_chi_square_rng(row_vector, row_vector)
-real[] scaled_inv_chi_square_rng(row_vector, int[])
-real[] scaled_inv_chi_square_rng(row_vector, real[])
-real[] scaled_inv_chi_square_rng(int[], vector)
-real[] scaled_inv_chi_square_rng(int[], row_vector)
-real[] scaled_inv_chi_square_rng(real[], vector)
-real[] scaled_inv_chi_square_rng(real[], row_vector)
 real sd(vector)
 real sd(row_vector)
 real sd(matrix)