diff --git a/collects/math/private/distributions/discrete-dist.rkt b/collects/math/private/distributions/discrete-dist.rkt
index cc5a7a5cc7..4b3f6d0c2c 100644
--- a/collects/math/private/distributions/discrete-dist.rkt
+++ b/collects/math/private/distributions/discrete-dist.rkt
@@ -14,8 +14,8 @@
          discrete-dist-probs)
 
 (begin-encourage-inline
-  (struct: (In Out) discrete-dist-struct dist ([values : (Listof Out)]
-                                               [probs : (Listof Positive-Flonum)])
+  (struct: (In Out) discrete-dist-struct distribution ([values : (Listof Out)]
+                                                       [probs : (Listof Positive-Flonum)])
     #:property prop:custom-print-quotable 'never
     #:property prop:custom-write
     (λ (v port mode)
diff --git a/collects/math/private/distributions/dist-struct.rkt b/collects/math/private/distributions/dist-struct.rkt
index b2262ef39a..b268534388 100644
--- a/collects/math/private/distributions/dist-struct.rkt
+++ b/collects/math/private/distributions/dist-struct.rkt
@@ -1,166 +1,143 @@
-#lang racket/base
+#lang typed/racket/base
+
+(require racket/performance-hint
+         racket/promise
+         "../../flonum.rkt")
 
 (provide
- (all-from-out (submod "." typed-defs))
- ;; Rename transformers
- dist-cdf
- dist-inv-cdf
- dist-min
- dist-max)
+ PDF Sample CDF Inverse-CDF
+ (struct-out distribution)
+ (struct-out ordered-dist)
+ Real-Dist
+ pdf sample cdf inv-cdf real-dist-prob)
 
-(module typed-defs typed/racket/base
-  (require racket/performance-hint
-           racket/promise
-           "../../flonum.rkt")
+(define-type (PDF In)
+  (case-> (In -> Flonum)
+          (In Any -> Flonum)))
+
+(define-type (Sample Out)
+  (case-> (-> Out)
+          (Integer -> (Listof Out))))
+
+(define-type (CDF In)
+  (case-> (In -> Flonum)
+          (In Any -> Flonum)
+          (In Any Any -> Flonum)))
+
+(define-type (Inverse-CDF Out)
+  (case-> (Real -> Out)
+          (Real Any -> Out)
+          (Real Any Any -> Out))) 
+
+(struct: (In Out) distribution ([pdf : (PDF In)]
+                                [sample : (Sample Out)])
+  #:transparent)
+
+(struct: (In Out) ordered-dist distribution
+  ([cdf : (CDF In)]
+   [inv-cdf : (Inverse-CDF Out)]
+   [min : Out]
+   [max : Out]
+   [median : (Promise Out)])
+  #:transparent)
+
+(define-type Real-Dist (ordered-dist Real Flonum))
+
+;; =================================================================================================
+
+(begin-encourage-inline
   
-  (provide
-   PDF Sample CDF Inverse-CDF
-   (struct-out dist)
-   (struct-out ordered-dist)
-   Real-Dist
-   dist-median
-   pdf sample cdf inv-cdf real-dist-prob)
+  (: pdf (All (In Out) (case-> ((distribution In Out) In -> Flonum)
+                               ((distribution In Out) In Any -> Flonum))))
+  (define (pdf d v [log? #f])
+    ((distribution-pdf d) v log?))
   
-  (define-type (PDF In)
-    (case-> (In -> Flonum)
-            (In Any -> Flonum)))
+  (: sample (All (In Out) (case-> ((distribution In Out) -> Out)
+                                  ((distribution In Out) Integer -> (Listof Out)))))
+  (define sample
+    (case-lambda
+      [(d)  ((distribution-sample d))]
+      [(d n)  ((distribution-sample d) n)]))
   
-  (define-type (Sample Out)
-    (case-> (-> Out)
-            (Integer -> (Listof Out))))
+  (: cdf (All (In Out) (case-> ((ordered-dist In Out) In -> Flonum)
+                               ((ordered-dist In Out) In Any -> Flonum)
+                               ((ordered-dist In Out) In Any Any -> Flonum))))
+  (define (cdf d v [log? #f] [1-p? #f])
+    ((ordered-dist-cdf d) v log? 1-p?))
   
-  (define-type (CDF In)
-    (case-> (In -> Flonum)
-            (In Any -> Flonum)
-            (In Any Any -> Flonum)))
-  
-  (define-type (Inverse-CDF Out)
-    (case-> (Real -> Out)
-            (Real Any -> Out)
-            (Real Any Any -> Out))) 
-  
-  (struct: (In Out) dist ([pdf : (PDF In)]
-                          [sample : (Sample Out)])
-    #:transparent)
-  
-  (struct: (In Out) ordered-dist dist
-    ([cdf : (CDF In)]
-     [inv-cdf : (Inverse-CDF Out)]
-     [min : Out]
-     [max : Out]
-     [median : (Promise Out)])
-    #:transparent)
-  
-  (define-type Real-Dist (ordered-dist Real Flonum))
-  
-  ;; =================================================================================================
-  
-  (begin-encourage-inline
-    
-    (: dist-median (All (In Out) ((ordered-dist In Out) -> Out)))
-    (define (dist-median d) (force (ordered-dist-median d)))
-    
-    (: pdf (All (In Out) (case-> ((dist In Out) In -> Flonum)
-                                 ((dist In Out) In Any -> Flonum))))
-    (define (pdf d v [log? #f])
-      ((dist-pdf d) v log?))
-    
-    (: sample (All (In Out) (case-> ((dist In Out) -> Out)
-                                    ((dist In Out) Integer -> (Listof Out)))))
-    (define sample
-      (case-lambda
-        [(d)  ((dist-sample d))]
-        [(d n)  ((dist-sample d) n)]))
-    
-    (: cdf (All (In Out) (case-> ((ordered-dist In Out) In -> Flonum)
-                                 ((ordered-dist In Out) In Any -> Flonum)
-                                 ((ordered-dist In Out) In Any Any -> Flonum))))
-    (define (cdf d v [log? #f] [1-p? #f])
-      ((ordered-dist-cdf d) v log? 1-p?))
-    
-    (: inv-cdf (All (In Out) (case-> ((ordered-dist In Out) Real -> Out)
-                                     ((ordered-dist In Out) Real Any -> Out)
-                                     ((ordered-dist In Out) Real Any Any -> Out))))
-    (define (inv-cdf d p [log? #f] [1-p? #f])
-      ((ordered-dist-inv-cdf d) p log? 1-p?))
-    
-    )
-  
-  (: real-dist-prob* (Real-Dist Flonum Flonum Any -> Flonum))
-  ;; Assumes a <= b
-  (define (real-dist-prob* d a b 1-p?)
-    (define c (dist-median d))
-    (define cdf (ordered-dist-cdf d))
-    (define p
-      (cond [(a . fl= . b)  (if 1-p? 1.0 0.0)]
-            [1-p?  (fl+ (cdf a #f #f) (cdf b #f #t))]
-            [(b . fl<= . c)
-             ;; Both less than the median; use lower tail only
-             (fl- (cdf b #f #f) (cdf a #f #f))]
-            [(a . fl>= . c)
-             ;; Both greater than the median; use upper tail only
-             (fl- (cdf a #f #t) (cdf b #f #t))]
-            [else
-             ;; Median between a and b; use lower for (a,c] and upper for (c,b]
-             (define P_x<=a (cdf a #f #f))
-             (define P_x>b (cdf b #f #t))
-             (fl+ (fl- 0.5 P_x<=a) (fl- 0.5 P_x>b))]))
-    (max 0.0 (min 1.0 p)))
-  
-  (: real-dist-log-prob* (Real-Dist Flonum Flonum Any -> Flonum))
-  ;; Assumes a <= b
-  (define (real-dist-log-prob* d a b 1-p?)
-    (define c (dist-median d))
-    (define cdf (ordered-dist-cdf d))
-    (define log-p
-      (cond [(a . fl= . b)  (if 1-p? 0.0 -inf.0)]
-            [1-p?  (lg+ (cdf a #t #f) (cdf b #t #t))]
-            [(b . fl<= . c)
-             ;; Both less than the median; use lower tail only
-             (define log-P_x<=a (cdf a #t #f))
-             (define log-P_x<=b (cdf b #t #f))
-             (cond [(log-P_x<=b . fl< . log-P_x<=a)  -inf.0]
-                   [else  (lg- log-P_x<=b log-P_x<=a)])]
-            [(a . fl>= . c)
-             ;; Both greater than the median; use upper tail only
-             (define log-P_x>a (cdf a #t #t))
-             (define log-P_x>b (cdf b #t #t))
-             (cond [(log-P_x>a . fl< . log-P_x>b)  -inf.0]
-                   [else  (lg- log-P_x>a log-P_x>b)])]
-            [else
-             ;; Median between a and b; try 1-upper first
-             (define log-P_x<=a (cdf a #t #f))
-             (define log-P_x>b (cdf b #t #t))
-             (define log-p (lg1- (lg+ log-P_x<=a log-P_x>b)))
-             (cond [(log-p . fl> . (log 0.1))  log-p]
-                   [else
-                    ;; Subtracting from 1.0 (in log space) lost bits; split and add instead
-                    (define log-P_a<x<=c
-                      (cond [((fllog 0.5) . fl< . log-P_x<=a)  -inf.0]
-                            [else  (lg- (fllog 0.5) log-P_x<=a)]))
-                    (define log-P_c<x<=b
-                      (cond [((fllog 0.5) . fl< . log-P_x>b)  -inf.0]
-                            [else  (lg- (fllog 0.5) log-P_x>b)]))
-                    (lg+ log-P_a<x<=c log-P_c<x<=b)])]))
-    (min 0.0 log-p))
-  
-  (: real-dist-prob (case-> (Real-Dist Real Real -> Flonum)
-                            (Real-Dist Real Real Any -> Flonum)
-                            (Real-Dist Real Real Any Any -> Flonum)))
-  (define (real-dist-prob d a b [log? #f] [1-p? #f])
-    (let ([a  (fl a)] [b  (fl b)])
-      (let ([a  (flmin a b)] [b  (flmax a b)])
-        (cond [log?  (define p (real-dist-prob* d a b 1-p?))
-                     (cond [(and (p . fl> . +max-subnormal.0) (p . fl< . 0.9))  (fllog p)]
-                           [else  (real-dist-log-prob* d a b 1-p?)])]
-              [else  (real-dist-prob* d a b 1-p?)]))))
+  (: inv-cdf (All (In Out) (case-> ((ordered-dist In Out) Real -> Out)
+                                   ((ordered-dist In Out) Real Any -> Out)
+                                   ((ordered-dist In Out) Real Any Any -> Out))))
+  (define (inv-cdf d p [log? #f] [1-p? #f])
+    ((ordered-dist-inv-cdf d) p log? 1-p?))
   
   )
 
-(require (submod "." typed-defs)
-         (for-syntax racket/base))
+(: real-dist-prob* (Real-Dist Flonum Flonum Any -> Flonum))
+;; Assumes a <= b
+(define (real-dist-prob* d a b 1-p?)
+  (define c (force (ordered-dist-median d)))
+  (define cdf (ordered-dist-cdf d))
+  (define p
+    (cond [(a . fl= . b)  (if 1-p? 1.0 0.0)]
+          [1-p?  (fl+ (cdf a #f #f) (cdf b #f #t))]
+          [(b . fl<= . c)
+           ;; Both less than the median; use lower tail only
+           (fl- (cdf b #f #f) (cdf a #f #f))]
+          [(a . fl>= . c)
+           ;; Both greater than the median; use upper tail only
+           (fl- (cdf a #f #t) (cdf b #f #t))]
+          [else
+           ;; Median between a and b; use lower for (a,c] and upper for (c,b]
+           (define P_x<=a (cdf a #f #f))
+           (define P_x>b (cdf b #f #t))
+           (fl+ (fl- 0.5 P_x<=a) (fl- 0.5 P_x>b))]))
+  (max 0.0 (min 1.0 p)))
 
-(define-syntax dist-cdf (make-rename-transformer #'ordered-dist-cdf))
-(define-syntax dist-inv-cdf (make-rename-transformer #'ordered-dist-inv-cdf))
-(define-syntax dist-min (make-rename-transformer #'ordered-dist-min))
-(define-syntax dist-max (make-rename-transformer #'ordered-dist-max))
+(: real-dist-log-prob* (Real-Dist Flonum Flonum Any -> Flonum))
+;; Assumes a <= b
+(define (real-dist-log-prob* d a b 1-p?)
+  (define c (force (ordered-dist-median d)))
+  (define cdf (ordered-dist-cdf d))
+  (define log-p
+    (cond [(a . fl= . b)  (if 1-p? 0.0 -inf.0)]
+          [1-p?  (lg+ (cdf a #t #f) (cdf b #t #t))]
+          [(b . fl<= . c)
+           ;; Both less than the median; use lower tail only
+           (define log-P_x<=a (cdf a #t #f))
+           (define log-P_x<=b (cdf b #t #f))
+           (cond [(log-P_x<=b . fl< . log-P_x<=a)  -inf.0]
+                 [else  (lg- log-P_x<=b log-P_x<=a)])]
+          [(a . fl>= . c)
+           ;; Both greater than the median; use upper tail only
+           (define log-P_x>a (cdf a #t #t))
+           (define log-P_x>b (cdf b #t #t))
+           (cond [(log-P_x>a . fl< . log-P_x>b)  -inf.0]
+                 [else  (lg- log-P_x>a log-P_x>b)])]
+          [else
+           ;; Median between a and b; try 1-upper first
+           (define log-P_x<=a (cdf a #t #f))
+           (define log-P_x>b (cdf b #t #t))
+           (define log-p (lg1- (lg+ log-P_x<=a log-P_x>b)))
+           (cond [(log-p . fl> . (log 0.1))  log-p]
+                 [else
+                  ;; Subtracting from 1.0 (in log space) lost bits; split and add instead
+                  (define log-P_a<x<=c
+                    (cond [((fllog 0.5) . fl< . log-P_x<=a)  -inf.0]
+                          [else  (lg- (fllog 0.5) log-P_x<=a)]))
+                  (define log-P_c<x<=b
+                    (cond [((fllog 0.5) . fl< . log-P_x>b)  -inf.0]
+                          [else  (lg- (fllog 0.5) log-P_x>b)]))
+                  (lg+ log-P_a<x<=c log-P_c<x<=b)])]))
+  (min 0.0 log-p))
+
+(: real-dist-prob (case-> (Real-Dist Real Real -> Flonum)
+                          (Real-Dist Real Real Any -> Flonum)
+                          (Real-Dist Real Real Any Any -> Flonum)))
+(define (real-dist-prob d a b [log? #f] [1-p? #f])
+  (let ([a  (fl a)] [b  (fl b)])
+    (let ([a  (flmin a b)] [b  (flmax a b)])
+      (cond [log?  (define p (real-dist-prob* d a b 1-p?))
+                   (cond [(and (p . fl> . +max-subnormal.0) (p . fl< . 0.9))  (fllog p)]
+                         [else  (real-dist-log-prob* d a b 1-p?)])]
+            [else  (real-dist-prob* d a b 1-p?)]))))
diff --git a/collects/math/private/distributions/truncated-dist.rkt b/collects/math/private/distributions/truncated-dist.rkt
index 52fdfa9a13..e7d4ad5d2d 100644
--- a/collects/math/private/distributions/truncated-dist.rkt
+++ b/collects/math/private/distributions/truncated-dist.rkt
@@ -24,16 +24,16 @@
     [(d a)  (truncated-dist d -inf.0 a)]
     [(d a b)
      (let*-values ([(a b)  (values (fl a) (fl b))]
-                   [(a b)  (values (max (dist-min d) (min a b))
-                                   (min (dist-max d) (max a b)))])
+                   [(a b)  (values (max (ordered-dist-min d) (min a b))
+                                   (min (ordered-dist-max d) (max a b)))])
        (unsafe-truncated-dist d a b))]))
 
 (: unsafe-truncated-dist (Real-Dist Float Float -> Truncated-Dist))
 (define (unsafe-truncated-dist d a b)
-  (define orig-pdf (dist-pdf d))
-  (define orig-cdf (dist-cdf d))
-  (define orig-inv-cdf (dist-inv-cdf d))
-  (define orig-sample (dist-sample d))
+  (define orig-pdf (distribution-pdf d))
+  (define orig-cdf (ordered-dist-cdf d))
+  (define orig-inv-cdf (ordered-dist-inv-cdf d))
+  (define orig-sample (distribution-sample d))
   (define log-P_a<x<=b (real-dist-prob d a b #t #f))
   (define log-P_x<=a (delay (orig-cdf a #t #f)))
   (define log-P_x>b (delay (orig-cdf b #t #t)))
diff --git a/collects/math/private/distributions/utils.rkt b/collects/math/private/distributions/utils.rkt
index c9a3b26a0e..247e7ea428 100644
--- a/collects/math/private/distributions/utils.rkt
+++ b/collects/math/private/distributions/utils.rkt
@@ -53,45 +53,6 @@
              (: proc-names (type-name -> arg-types)) ...
              (define (proc-names v) (struct-proc-names v)) ...))))]))
 
-(define-syntax (define-distribution-type: stx)
-  (syntax-case stx (:)
-    [(_ (type-name T ...) (parent-type-name In Out)
-        (A B) name ([arg-names : arg-type] ...))
-     (let ([arg-name-lst  (syntax->list #'(arg-names ...))])
-       (with-syntax* ([struct-type-name  (format-id #'type-name "~a-struct" #'type-name)]
-                      [(struct-proc-names ...)  (map (λ (arg-name)
-                                                         (format-id #'type-name
-                                                                    "~a-~a"
-                                                                    #'struct-type-name
-                                                                    arg-name))
-                                                       arg-name-lst)]
-                      [struct-pred-name  (format-id #'type-name "~a?" #'struct-type-name)]
-                      [make-name  (format-id #'name "make-~a" #'name)]
-                      [(proc-names ...)  (map (λ (arg-name)
-                                                (format-id #'name "~a-~a" #'name arg-name))
-                                              arg-name-lst)]
-                      [pred-name  (format-id #'name "~a?" #'name)]
-                      [format-str
-                       (string-append "(~a "
-                                      (string-join (build-list (length arg-name-lst) (λ _ "~v")))
-                                      ")")])
-         (syntax/loc stx
-           (begin
-             (struct: (A B) struct-type-name parent-type-name ([arg-names : arg-types] ...)
-               #:property prop:custom-print-quotable 'never
-               #:property prop:custom-write
-               (λ (v port write?)
-                 (fprintf port format-str 'name (proc-names v) ...)))
-             (define-type (type-name T ...) (struct-type-name In Out))
-             (: proc-names ((type-name T ...) -> arg-types)) ...
-             (define (proc-names d) (struct-proc-names d)) ...
-             (define make-name struct-type-name)
-             (define pred-name struct-pred-name)))))]
-    [(_ type-name (parent-type-name In Out) name ([arg-names arg-opts ...] ...))
-     (syntax/loc stx
-       (define-distribution-type: (type-name) (parent-type-name In Out)
-         (A B) name ([arg-names arg-opts ...] ...)))]))
-
 ;; ===================================================================================================
 ;; One-sided scale family distributions (e.g. exponential)
 
diff --git a/collects/math/private/flonum/flonum-more-functions.rkt b/collects/math/private/flonum/flonum-more-functions.rkt
index 1a4e133fda..a8d21903e8 100644
--- a/collects/math/private/flonum/flonum-more-functions.rkt
+++ b/collects/math/private/flonum/flonum-more-functions.rkt
@@ -11,7 +11,7 @@
 (provide flsqrt1pm1
          flsinh flcosh fltanh
          flasinh flacosh flatanh
-         make-flexp/base flexpt+ flexpt1p)
+         make-flexpt flexpt+ flexpt1p)
 
 ;; ---------------------------------------------------------------------------------------------------
 ;; sqrt(1+x)-1
@@ -163,8 +163,8 @@
 
 (begin-encourage-inline
   
-  (: make-flexp/base (Positive-Exact-Rational -> (Flonum -> Flonum)))
-  (define (make-flexp/base b)
+  (: make-flexpt (Positive-Exact-Rational -> (Flonum -> Flonum)))
+  (define (make-flexpt b)
     (define b-hi (fl b))
     (define b-lo (fl (- (/ (inexact->exact b-hi) b) 1)))
     (cond [(fl= b-lo 0.0)  (λ: ([x : Flonum]) (flexpt b-hi x))]
diff --git a/collects/math/private/functions/psi.rkt b/collects/math/private/functions/psi.rkt
index 212052eb74..d57d2c5e81 100644
--- a/collects/math/private/functions/psi.rkt
+++ b/collects/math/private/functions/psi.rkt
@@ -211,7 +211,7 @@
 (define pi.128 267257146016241686964920093290467695825/85070591730234615865843651857942052864)
 
 (: flexppi (Flonum -> Flonum))
-(define flexppi (make-flexp/base pi.128))
+(define flexppi (make-flexpt pi.128))
 
 (: flpsi (Integer Flonum -> Flonum))
 (define (flpsi m x)
diff --git a/collects/math/private/functions/zeta.rkt b/collects/math/private/functions/zeta.rkt
index a4fd030d68..fc91d296bb 100644
--- a/collects/math/private/functions/zeta.rkt
+++ b/collects/math/private/functions/zeta.rkt
@@ -107,7 +107,7 @@ P. Borwein. An Efficient Algorithm for the Riemann Zeta Function.
 (define pi.128 267257146016241686964920093290467695825/85070591730234615865843651857942052864)
 
 (: flexppi (Flonum -> Flonum))
-(define flexppi (make-flexp/base pi.128))
+(define flexppi (make-flexpt pi.128))
 
 (require math/bigfloat)
 (: fleta (Flonum -> Flonum))
@@ -124,7 +124,7 @@ P. Borwein. An Efficient Algorithm for the Riemann Zeta Function.
                       [(fleven? (fltruncate (* 0.5 s)))  +inf.0]
                       [else  -inf.0])]
                [(s . fl< . -171.0)
-                (define f (make-flexp/base (/ (* euler.64 pi.64) (inexact->exact (- s)))))
+                (define f (make-flexpt (/ (* euler.64 pi.64) (inexact->exact (- s)))))
                 (* (/ 4.0 pi)
                    (flexp-stirling (- s))
                    (flsqrt (/ pi (* -0.5 s)))
@@ -160,7 +160,7 @@ P. Borwein. An Efficient Algorithm for the Riemann Zeta Function.
                  [else  (- (flexpm1 (fl* (fl- 1.0 s) (fllog 2.0))))]))
          (fl/ (fleta s) c)]
         [(and (s . fl> . -266.5) (s . fl< . 0.0))  ; s < 0 keeps TR happy
-         (define f (make-flexp/base (/ (* euler.64 pi.64) (inexact->exact (- s)))))
+         (define f (make-flexpt (/ (* euler.64 pi.64) (inexact->exact (- s)))))
          (* (/ 4.0 pi)
             (flexp-stirling (- s))
             (flsqrt (/ pi (* -0.5 s)))
diff --git a/collects/math/scribblings/math-distributions.scrbl b/collects/math/scribblings/math-distributions.scrbl
index 82aa14a8d0..3f62bd1291 100644
--- a/collects/math/scribblings/math-distributions.scrbl
+++ b/collects/math/scribblings/math-distributions.scrbl
@@ -12,7 +12,7 @@
 @(define untyped-eval (make-untyped-math-eval))
 @interaction-eval[#:eval untyped-eval (require racket/list)]
 
-@title[#:tag "dist"]{Probability Distributions}
+@title[#:tag "dist" #:style 'toc]{Probability Distributions}
 @(author-neil)
 
 @defmodule[math/distributions]
@@ -57,7 +57,7 @@ half-open interval (1/2,1], and computes another approximation from random sampl
 
 This plots the pdf and a kernel density estimate of the pdf from random samples:
 @interaction[#:eval untyped-eval
-                    (plot (list (function (dist-pdf d) #:color 0 #:style 'dot)
+                    (plot (list (function (distribution-pdf d) #:color 0 #:style 'dot)
                                 (density xs))
                           #:x-label "x" #:y-label "density of N(2,5)")]
 
@@ -69,7 +69,7 @@ the probabilities within the interval:
                     (define d-trunc (truncated-dist d -inf.0 5))
                     (real-dist-prob d-trunc 5 6)
                     (real-dist-prob d-trunc 0.5 1.0)
-                    (plot (list (function (dist-pdf d-trunc) #:color 0 #:style 'dot)
+                    (plot (list (function (distribution-pdf d-trunc) #:color 0 #:style 'dot)
                                 (density (sample d-trunc 1000)))
                           #:x-label "x" #:y-label "density of T(N(2,5),-∞,5)")]
 
@@ -132,7 +132,7 @@ When distribution object constructors receive parameters outside their domains,
                     (cdf (beta-dist 0 0) 1/2)
                     (inv-cdf (geometric-dist 1.1) 0.2)]
 
-@section{Basic Distribution Types and Operations}
+@section{Distribution Types and Operations}
 
 @defform[(PDF In)]{
 The type of probability density functions, or @tech{pdfs}, defined as
@@ -150,38 +150,6 @@ When given a nonnegative integer @racket[n] as an argument, a sampling procedure
 a length-@racket[n] list of independent, random samples.
 }
 
-@defstruct*[dist ([pdf (PDF In)] [sample (Sample Out)])]{
-The parent type of @tech{distribution objects}. The @racket[In] type parameter is the data type a
-distribution accepts as arguments to its @tech{pdf}. The @racket[Out] type parameter is the data
-type a distribution returns as random samples.
-
-@examples[#:eval untyped-eval
-                 (dist? (discrete-dist '(a b c)))
-                 (dist? (normal-dist))
-                 ((dist-pdf (normal-dist)) 0)
-                 ((dist-sample (normal-dist)))]
-See @racket[pdf] and @racket[sample] for uncurried forms of @racket[dist-pdf] and
-@racket[dist-sample].
-}
-
-@defproc[(pdf [d (dist In Out)] [v In] [log? Any #f]) Flonum]{
-An uncurried form of @racket[dist-pdf]. When @racket[log?] is not @racket[#f], returns a
-log density.
-@examples[#:eval untyped-eval
-                 (pdf (discrete-dist '(a b c) '(1 2 3)) 'a)
-                 (pdf (discrete-dist '(a b c) '(1 2 3)) 'a #t)]
-}
-
-@defproc*[([(sample [d (dist In Out)]) Out]
-           [(sample [d (dist In Out)] [n Integer]) (Listof Out)])]{
-An uncurried form of @racket[dist-sample].
-@examples[#:eval untyped-eval
-                 (sample (exponential-dist))
-                 (sample (exponential-dist) 3)]
-}
-
-@section{Ordered Distribution Types and Operations}
-
 @defform[(CDF In)]{
 The type of cumulative distribution functions, or @tech{cdfs}, defined as
 @racketblock[(case-> (In -> Flonum)
@@ -200,17 +168,32 @@ For any function of this type, both optional arguments should default to @racket
 interpreted as specified in the description of @racket[inv-cdf].
 }
 
-@defstruct*[(ordered-dist dist) ([cdf (CDF In)]
-                                 [inv-cdf (Inverse-CDF Out)]
-                                 [min Out]
-                                 [max Out]
-                                 [median (Promise Out)])]{
+@defstruct*[distribution ([pdf (PDF In)] [sample (Sample Out)])]{
+The parent type of @tech{distribution objects}. The @racket[In] type parameter is the data type a
+distribution accepts as arguments to its @tech{pdf}. The @racket[Out] type parameter is the data
+type a distribution returns as random samples.
+
+@examples[#:eval untyped-eval
+                 (distribution? (discrete-dist '(a b c)))
+                 (distribution? (normal-dist))
+                 ((distribution-pdf (normal-dist)) 0)
+                 ((distribution-sample (normal-dist)))]
+See @racket[pdf] and @racket[sample] for uncurried forms of @racket[distribution-pdf] and
+@racket[distribution-sample].
+}
+
+@defstruct*[(ordered-dist distribution) ([cdf (CDF In)]
+                                         [inv-cdf (Inverse-CDF Out)]
+                                         [min Out]
+                                         [max Out]
+                                         [median (Promise Out)])]{
 The parent type of @italic{ordered} @tech{distribution objects}.
 
-Similarly to @racket[dist], the @racket[In] type parameter is the data type an ordered distribution
-accepts as arguments to its @tech{pdf}, and the @racket[Out] type parameter is the data type an
-ordered distribution returns as random samples. Additionally, its @tech{cdf} accepts values of type
-@racket[In], and its @tech{inverse cdf} returns values of type @racket[Out].
+Similarly to @racket[distribution], the @racket[In] type parameter is the data type an ordered
+distribution accepts as arguments to its @tech{pdf}, and the @racket[Out] type parameter is the
+data type an ordered distribution returns as random samples. Additionally, its @tech{cdf}
+accepts values of type @racket[In], and its @tech{inverse cdf} returns values of type
+@racket[Out].
 
 @examples[#:eval untyped-eval
                  (ordered-dist? (discrete-dist '(a b c)))
@@ -227,8 +210,24 @@ The parent type of real-valued distributions, such as any distribution returned
 @racket[normal-dist]. Equivalent to the type @racket[(ordered-dist Real Flonum)].
 }
 
+@defproc[(pdf [d (dist In Out)] [v In] [log? Any #f]) Flonum]{
+An uncurried form of @racket[distribution-pdf]. When @racket[log?] is not @racket[#f], returns a
+log density.
+@examples[#:eval untyped-eval
+                 (pdf (discrete-dist '(a b c) '(1 2 3)) 'a)
+                 (pdf (discrete-dist '(a b c) '(1 2 3)) 'a #t)]
+}
+
+@defproc*[([(sample [d (dist In Out)]) Out]
+           [(sample [d (dist In Out)] [n Integer]) (Listof Out)])]{
+An uncurried form of @racket[distribution-sample].
+@examples[#:eval untyped-eval
+                 (sample (exponential-dist))
+                 (sample (exponential-dist) 3)]
+}
+
 @defproc[(cdf [d (ordered-dist In Out)] [v In] [log? Any #f] [1-p? Any #f]) Flonum]{
-An uncurried form of @racket[dist-cdf].
+An uncurried form of @racket[ordered-dist-cdf].
 
 When @racket[log?] is @racket[#f], @racket[cdf] returns a probability; otherwise, it returns a log
 probability.
@@ -238,7 +237,7 @@ When @racket[1-p?] is @racket[#f], @racket[cdf] returns a lower-tail probability
 }
 
 @defproc[(inv-cdf [d (ordered-dist In Out)] [p Real] [log? Any #f] [1-p? Any #f]) Out]{
-An uncurried form of @racket[dist-inv-cdf].
+An uncurried form of @racket[ordered-dist-inv-cdf].
 
 When @racket[log?] is @racket[#f], @racket[inv-cdf] interprets @racket[p] as a probability; otherwise,
 it interprets @racket[p] as a log probability.
@@ -254,22 +253,6 @@ the two endpoints are swapped first.) The @racket[log?] and @racket[1-p?] argume
 meaning of the return value in the same way as the corresponding arguments to @racket[cdf].
 }
 
-@deftogether[(@defproc[(dist-cdf [d (ordered-dist In Out)]) (CDF In)]
-              @defproc[(dist-inv-cdf [d (ordered-dist In Out)]) (Inverse-CDF Out)]
-              @defproc[(dist-min [d (ordered-dist In Out)]) Out]
-              @defproc[(dist-max [d (ordered-dist In Out)]) Out]
-              @defproc[(dist-median [d (ordered-dist In Out)]) Out])]{
-The first four are synonyms for @racket[ordered-dist-cdf], @racket[ordered-dist-inv-cdf],
-@racket[ordered-dist-min] and @racket[ordered-dist-max]. The last is equivalent to
-@racket[(force (ordered-dist-median d))].
-
-@examples[#:eval untyped-eval
-                 (dist-min (normal-dist))
-                 (dist-min (geometric-dist 1/3))
-                 (dist-max (uniform-dist 1 2))
-                 (dist-median (gamma-dist 4 2))]
-}
-
 @section{Finite Distribution Families}
 
 @subsection{Unordered Discrete Distributions}
@@ -299,7 +282,7 @@ random samples.
                  (define n 500)
                  (define h (samples->hash (sample d n)))
                  (plot (list (discrete-histogram
-                              (map vector xs (map (dist-pdf d) xs))
+                              (map vector xs (map (distribution-pdf d) xs))
                               #:x-min 0 #:skip 2 #:label "P[x]")
                              (discrete-histogram
                               (map vector xs (map (λ (x) (/ (hash-ref h x) n)) xs))
@@ -354,11 +337,11 @@ on it are faster.
 
 @examples[#:eval untyped-eval
                  (define d (bernoulli-dist 0.75))
-                 (map (dist-pdf d) '(0 1))
-                 (map (dist-cdf d) '(0 1))
+                 (map (distribution-pdf d) '(0 1))
+                 (map (ordered-dist-cdf d) '(0 1))
                  (define d (binomial-dist 1 0.75))
-                 (map (dist-pdf d) '(0 1))
-                 (map (dist-cdf d) '(0 1))]
+                 (map (distribution-pdf d) '(0 1))
+                 (map (ordered-dist-cdf d) '(0 1))]
 }
 
 @subsection{Binomial Distributions}
@@ -375,9 +358,9 @@ probability of success.
 @examples[#:eval untyped-eval
                  (define d (binomial-dist 15 0.6))
                  (plot (discrete-histogram
-                        (map vector (build-list 16 values) (build-list 16 (dist-pdf d))))
+                        (map vector (build-list 16 values) (build-list 16 (distribution-pdf d))))
                        #:x-label "number of successes" #:y-label "probability")
-                 (plot (function-interval (λ (x) 0) (dist-cdf d) -0.5 15.5)
+                 (plot (function-interval (λ (x) 0) (ordered-dist-cdf d) -0.5 15.5)
                        #:x-label "at-most number of successes" #:y-label "probability")]
 }
 
@@ -395,9 +378,9 @@ first success starting from zero.
 @examples[#:eval untyped-eval
                  (define d (geometric-dist 0.25))
                  (plot (discrete-histogram
-                        (map vector (build-list 16 values) (build-list 16 (dist-pdf d))))
+                        (map vector (build-list 16 values) (build-list 16 (distribution-pdf d))))
                        #:x-label "first success index" #:y-label "probability")
-                 (plot (function-interval (λ (x) 0) (dist-cdf d) -0.5 15.5)
+                 (plot (function-interval (λ (x) 0) (ordered-dist-cdf d) -0.5 15.5)
                        #:x-label "at-most first success index" #:y-label "probability"
                        #:y-max 1)]
 }
@@ -415,9 +398,9 @@ independent events.
 @examples[#:eval untyped-eval
                  (define d (poisson-dist 6.2))
                  (plot (discrete-histogram
-                        (map vector (build-list 16 values) (build-list 16 (dist-pdf d))))
+                        (map vector (build-list 16 values) (build-list 16 (distribution-pdf d))))
                        #:x-label "number of events" #:y-label "probability")
-                 (plot (function-interval (λ (x) 0) (dist-cdf d) -0.5 15.5)
+                 (plot (function-interval (λ (x) 0) (ordered-dist-cdf d) -0.5 15.5)
                        #:x-label "at-most number of events" #:y-label "probability"
                        #:y-max 1)]
 }
@@ -468,14 +451,14 @@ which must both be nonnegative.
                  (plot (for/list ([α  (in-list '(1 2 3 1/2))]
                                   [β  (in-list '(1 3 1 1/2))]
                                   [i  (in-naturals)])
-                         (function (dist-pdf (beta-dist α β))
+                         (function (distribution-pdf (beta-dist α β))
                                    #:color i #:label (format "Beta(~a,~a)" α β)))
                        #:x-min 0 #:x-max 1 #:y-max 4 #:y-label "density")
                  
                  (plot (for/list ([α  (in-list '(1 2 3 1/2))]
                                   [β  (in-list '(1 3 1 1/2))]
                                   [i  (in-naturals)])
-                         (function (dist-cdf (beta-dist α β))
+                         (function (ordered-dist-cdf (beta-dist α β))
                                    #:color i #:label (format "Beta(~a,~a)" α β)))
                        #:x-min 0 #:x-max 1 #:y-label "probability")]
 
@@ -502,7 +485,7 @@ Represents the Cauchy distribution family parameterized by mode and scale.
                  (plot (for/list ([m  (in-list '(0 -1 0 2))]
                                   [s  (in-list '(1 1/2 2.25 0.7))]
                                   [i  (in-naturals)])
-                         (function (dist-pdf (cauchy-dist m s))
+                         (function (distribution-pdf (cauchy-dist m s))
                                    #:color i #:label (format "Cauchy(~a,~a)" m s)))
                        #:x-min -8 #:x-max 8 #:y-label "density"
                        #:legend-anchor 'top-right)
@@ -510,7 +493,7 @@ Represents the Cauchy distribution family parameterized by mode and scale.
                  (plot (for/list ([m  (in-list '(0 -1 0 2))]
                                   [s  (in-list '(1 1/2 2.25 0.7))]
                                   [i  (in-naturals)])
-                         (function (dist-cdf (cauchy-dist m s))
+                         (function (ordered-dist-cdf (cauchy-dist m s))
                                    #:color i #:label (format "Cauchy(~a,~a)" m s)))
                        #:x-min -8 #:x-max 8 #:y-label "probability")]
 }
@@ -529,7 +512,7 @@ Represents the family of distributions whose densities are Dirac delta functions
                  (pdf (delta-dist) 1)
                  (plot (for/list ([μ  (in-list '(-1 0 1))]
                                   [i  (in-naturals)])
-                         (function (dist-cdf (delta-dist μ))
+                         (function (ordered-dist-cdf (delta-dist μ))
                                    #:color i #:style i #:label (format "δ(~a)" μ)))
                        #:x-min -2 #:x-max 2 #:y-label "probability")]
 }
@@ -551,14 +534,14 @@ is the reciprocal of mean or scale. Construct exponential distributions from rat
 @examples[#:eval untyped-eval
                  (plot (for/list ([μ  (in-list '(2/3 1 2))]
                                   [i  (in-naturals)])
-                         (function (dist-pdf (exponential-dist μ))
+                         (function (distribution-pdf (exponential-dist μ))
                                    #:color i #:label (format "Exponential(~a)" μ)))
                        #:x-min 0 #:x-max 5 #:y-label "density"
                        #:legend-anchor 'top-right)
                  
                  (plot (for/list ([μ  (in-list '(2/3 1 2))]
                                   [i  (in-naturals)])
-                         (function (dist-cdf (exponential-dist μ))
+                         (function (ordered-dist-cdf (exponential-dist μ))
                                    #:color i #:label (format "Exponential(~a)" μ)))
                        #:x-min 0 #:x-max 5 #:y-label "probability"
                        #:legend-anchor 'bottom-right)]
@@ -583,7 +566,7 @@ which is the reciprocal of scale. Construct gamma distributions from rates using
                  (plot (for/list ([k  (in-list '(1 2 3 9))]
                                   [s  (in-list '(2 2 3 1/2))]
                                   [i  (in-naturals)])
-                         (function (dist-pdf (gamma-dist k s))
+                         (function (distribution-pdf (gamma-dist k s))
                                    #:color i #:label (format "Gamma(~a,~a)" k s)))
                        #:x-min 0 #:x-max 15 #:y-label "density"
                        #:legend-anchor 'top-right)
@@ -591,7 +574,7 @@ which is the reciprocal of scale. Construct gamma distributions from rates using
                  (plot (for/list ([k  (in-list '(1 2 3 9))]
                                   [s  (in-list '(2 2 3 1/2))]
                                   [i  (in-naturals)])
-                         (function (dist-cdf (gamma-dist k s))
+                         (function (ordered-dist-cdf (gamma-dist k s))
                                    #:color i #:label (format "Gamma(~a,~a)" k s)))
                        #:x-min 0 #:x-max 15 #:y-label "probability"
                        #:legend-anchor 'bottom-right)]
@@ -621,7 +604,7 @@ and scale. In this parameterization, the variance is @racket[(* 1/3 (sqr (* pi s
                  (plot (for/list ([μ  (in-list '(0 -1 0 2))]
                                   [s  (in-list '(1 1/2 2.25 0.7))]
                                   [i  (in-naturals)])
-                         (function (dist-pdf (logistic-dist μ s))
+                         (function (distribution-pdf (logistic-dist μ s))
                                    #:color i #:label (format "Logistic(~a,~a)" μ s)))
                        #:x-min -8 #:x-max 8 #:y-label "density"
                        #:legend-anchor 'top-right)
@@ -629,7 +612,7 @@ and scale. In this parameterization, the variance is @racket[(* 1/3 (sqr (* pi s
                  (plot (for/list ([μ  (in-list '(0 -1 0 2))]
                                   [s  (in-list '(1 1/2 2.25 0.7))]
                                   [i  (in-naturals)])
-                         (function (dist-cdf (logistic-dist μ s))
+                         (function (ordered-dist-cdf (logistic-dist μ s))
                                    #:color i #:label (format "Logistic(~a,~a)" μ s)))
                        #:x-min -8 #:x-max 8 #:y-label "probability")]
 }
@@ -652,14 +635,14 @@ which is the square of standard deviation. Construct normal distributions from v
                  (plot (for/list ([μ  (in-list '(0 -1 0 2))]
                                   [σ  (in-list '(1 1/2 2.25 0.7))]
                                   [i  (in-naturals)])
-                         (function (dist-pdf (normal-dist μ σ))
+                         (function (distribution-pdf (normal-dist μ σ))
                                    #:color i #:label (format "N(~a,~a)" μ σ)))
                        #:x-min -5 #:x-max 5 #:y-label "density")
                  
                  (plot (for/list ([μ  (in-list '(0 -1 0 2))]
                                   [σ  (in-list '(1 1/2 2.25 0.7))]
                                   [i  (in-naturals)])
-                         (function (dist-cdf (normal-dist μ σ))
+                         (function (ordered-dist-cdf (normal-dist μ σ))
                                    #:color i #:label (format "N(~a,~a)" μ σ)))
                        #:x-min -5 #:x-max 5 #:y-label "probability")]
 }
@@ -685,7 +668,7 @@ before constructing the distribution object.
                                   [b  (in-list '(0 1 3))]
                                   [m  (in-list '(-2 0 2))]
                                   [i  (in-naturals)])
-                         (function (dist-pdf (triangle-dist a b m)) #:color i
+                         (function (distribution-pdf (triangle-dist a b m)) #:color i
                                    #:label (format "Triangle(~a,~a,~a)" a b m)))
                        #:x-min -3.5 #:x-max 3.5 #:y-label "density")
                  
@@ -693,7 +676,7 @@ before constructing the distribution object.
                                   [b  (in-list '(0 1 3))]
                                   [m  (in-list '(-2 0 2))]
                                   [i  (in-naturals)])
-                         (function (dist-cdf (triangle-dist a b m)) #:color i
+                         (function (ordered-dist-cdf (triangle-dist a b m)) #:color i
                                    #:label (format "Triangle(~a,~a,~a)" a b m)))
                        #:x-min -3.5 #:x-max 3.5 #:y-label "probability")]
 
@@ -724,11 +707,11 @@ Samples are taken by applying the truncated distribution's @tech{inverse cdf} to
                  (define d (normal-dist))
                  (define t (truncated-dist d -2 1))
                  t
-                 (plot (list (function (dist-pdf d) #:label "N(0,1)" #:color 0)
-                             (function (dist-pdf t) #:label "T(N(0,1),-2,1)"))
+                 (plot (list (function (distribution-pdf d) #:label "N(0,1)" #:color 0)
+                             (function (distribution-pdf t) #:label "T(N(0,1),-2,1)"))
                        #:x-min -3.5 #:x-max 3.5 #:y-label "density")
-                 (plot (list (function (dist-cdf d) #:label "N(0,1)" #:color 0)
-                             (function (dist-cdf t) #:label "T(N(0,1),-2,1)"))
+                 (plot (list (function (ordered-dist-cdf d) #:label "N(0,1)" #:color 0)
+                             (function (ordered-dist-cdf t) #:label "T(N(0,1),-2,1)"))
                        #:x-min -3.5 #:x-max 3.5 #:y-label "probability")]
 }
 
@@ -754,14 +737,14 @@ they are swapped before constructing the distribution object.
                  (plot (for/list ([a  (in-list '(-3 -1 -2))]
                                   [b  (in-list '(0 1 3))]
                                   [i  (in-naturals)])
-                         (function (dist-pdf (uniform-dist a b)) #:color i
+                         (function (distribution-pdf (uniform-dist a b)) #:color i
                                    #:label (format "Uniform(~a,~a)" a b)))
                        #:x-min -3.5 #:x-max 3.5 #:y-label "density")
                  
                  (plot (for/list ([a  (in-list '(-3 -1 -2))]
                                   [b  (in-list '(0 1 3))]
                                   [i  (in-naturals)])
-                         (function (dist-cdf (uniform-dist a b)) #:color i
+                         (function (ordered-dist-cdf (uniform-dist a b)) #:color i
                                    #:label (format "Uniform(~a,~a)" a b)))
                        #:x-min -3.5 #:x-max 3.5 #:y-label "probability")]
 
diff --git a/collects/math/scribblings/math-flonum.scrbl b/collects/math/scribblings/math-flonum.scrbl
index b3c89d3cbf..dac1a53154 100644
--- a/collects/math/scribblings/math-flonum.scrbl
+++ b/collects/math/scribblings/math-flonum.scrbl
@@ -164,7 +164,7 @@ But see @racket[flexpt1p], which is more accurate still.
 Like @racket[(flexpt (+ 1.0 x) y)], but accurate for any @racket[x] and @racket[y].
 }
 
-@defproc[(make-flexp/base [x Real]) (Flonum -> Flonum)]{
+@defproc[(make-flexpt [x Real]) (Flonum -> Flonum)]{
 Equivalent to @racket[(λ (y) (flexpt x y))] when @racket[x] is a flonum, but much more
 accurate for large @racket[y] when @racket[x] cannot be exactly represented
 by a flonum.
@@ -181,9 +181,9 @@ the error is low near zero, but grows with distance from the origin:
                                (eval:result ""))
                     (eval:alts (flulp-error (flexpt pi y) pi^y)
                                (eval:result @racketresultfont{43.12619934359266}))]
-Using @racket[make-flexp/base], the error is near rounding error everywhere:
+Using @racket[make-flexpt], the error is near rounding error everywhere:
 @interaction[#:eval untyped-eval
-                    (eval:alts (define flexppi (make-flexp/base (bigfloat->rational pi.bf)))
+                    (eval:alts (define flexppi (make-flexpt (bigfloat->rational pi.bf)))
                                (eval:result ""))
                     (eval:alts (flulp-error (flexppi y) pi^y)
                                (eval:result @racketresultfont{0.8738006564073412}))]