slightly better math.statistics docs

basis/math/statistics/statistics-docs.factor

@@ -1,57 +1,71 @@
 USING: assocs debugger hashtables help.markup help.syntax
-quotations sequences ;
+quotations sequences math ;
 IN: math.statistics
 
 HELP: geometric-mean
-{ $values { "seq" "a sequence of numbers" } { "x" "a non-negative real number"} }
+{ $values { "seq" sequence } { "x" "a non-negative real number"} }
 { $description "Computes the geometric mean of all elements in " { $snippet "seq" } ". The geometric mean measures the central tendency of a data set that minimizes the effects of extreme values." }
 { $examples { $example "USING: math.statistics prettyprint ;" "{ 1 2 3 } geometric-mean ." "1.81712059283214" } }
 { $errors "Throws a " { $link signal-error. } " (square-root of 0) if the sequence is empty." } ;
 
 HELP: harmonic-mean
-{ $values { "seq" "a sequence of numbers" } { "x" "a non-negative real number"} }
+{ $values { "seq" sequence } { "x" "a non-negative real number"} }
 { $description "Computes the harmonic mean of the elements in " { $snippet "seq" } ". The harmonic mean is appropriate when the average of rates is desired." }
 { $notes "Positive reals only." }
 { $examples { $example "USING: math.statistics prettyprint ;" "{ 1 2 3 } harmonic-mean ." "6/11" } }
 { $errors "Throws a " { $link signal-error. } " (divide by zero) if the sequence is empty." } ;
 
 HELP: mean
-{ $values { "seq" "a sequence of numbers" } { "x" "a non-negative real number"} }
+{ $values { "seq" sequence } { "x" "a non-negative real number"} }
-{ $description "Computes the arithmetic mean of all elements in " { $snippet "seq" } "." }
+{ $description "Computes the arithmetic mean of the elements in " { $snippet "seq" } "." }
 { $examples { $example "USING: math.statistics prettyprint ;" "{ 1 2 3 } mean ." "2" } }
 { $errors "Throws a " { $link signal-error. } " (divide by zero) if the sequence is empty." } ;
 
 HELP: median
-{ $values { "seq" "a sequence of numbers" } { "x" "a non-negative real number"} }
+{ $values { "seq" sequence } { "x" "a non-negative real number"} }
-{ $description "Computes the median of " { $snippet "seq" } " by sorting the sequence from lowest value to highest and outputting the middle one. If there is an even number of elements in the sequence, the median is not unique, so the mean of the two middle values is outputted." }
+{ $description "Computes the median of " { $snippet "seq" } " by finding the middle element of the sequence using " { $link kth-smallest } ". If there is an even number of elements in the sequence, the median is not unique, so the mean of the two middle values is output." }
 { $examples
   { $example "USING: math.statistics prettyprint ;" "{ 1 2 3 } median ." "2" }
   { $example "USING: math.statistics prettyprint ;" "{ 1 2 3 4 } median ." "2+1/2" } }
 { $errors "Throws a " { $link signal-error. } " (divide by zero) if the sequence is empty." } ;
 
 HELP: range
-{ $values { "seq" "a sequence of numbers" } { "x" "a non-negative real number"} }
+{ $values { "seq" sequence } { "x" "a non-negative real number"} }
-{ $description "Computes the distance of the maximum and minimum values in " { $snippet "seq" } "." }
+{ $description "Computes the difference of the maximum and minimum values in " { $snippet "seq" } "." }
 { $examples
   { $example "USING: math.statistics prettyprint ;" "{ 1 2 3 } range ." "2" }
   { $example "USING: math.statistics prettyprint ;" "{ 1 2 3 4 } range ." "3" } }  ;
 
+HELP: minmax
+{ $values { "seq" sequence } { "min" real } { "max" real } }
+{ $description "Finds the minimum and maximum elements of " { $snippet "seq" } " in one pass." }
+{ $examples
+    { $example "USING: arrays math.statistics prettyprint ;"
+        "{ 1 2 3 } minmax 2array ."
+        "{ 1 3 }"
+    }
+    { $example "USING: arrays math.statistics prettyprint ;"
+        "{ 1 2 3 4 } minmax 2array ."
+        "{ 1 4 }"
+    }
+} ;
+
 HELP: std
-{ $values { "seq" "a sequence of numbers" } { "x" "a non-negative real number"} }
+{ $values { "seq" sequence } { "x" "a non-negative real number"} }
 { $description "Computes the standard deviation of " { $snippet "seq" } ", which is the square root of the variance. It measures how widely spread the values in a sequence are about the mean." }
 { $examples
   { $example "USING: math.statistics prettyprint ;" "{ 1 2 3 } std ." "1.0" }
   { $example "USING: math.statistics prettyprint ;" "{ 1 2 3 4 } std ." "1.290994448735806" } } ;
 
 HELP: ste
-  { $values { "seq" "a sequence of numbers" } { "x" "a non-negative real number"} }
+  { $values { "seq" sequence } { "x" "a non-negative real number"} }
   { $description "Computes the standard error of the mean for " { $snippet "seq" } ". It's defined as the standard deviation divided by the square root of the length of the sequence, and measures uncertainty associated with the estimate of the mean." }
   { $examples
     { $example "USING: math.statistics prettyprint ;" "{ -2 2 } ste ." "2.0" }
     { $example "USING: math.statistics prettyprint ;" "{ -2 2 2 } ste ." "1.333333333333333" } } ;
 
 HELP: var
-{ $values { "seq" "a sequence of numbers" } { "x" "a non-negative real number"} }
+{ $values { "seq" sequence } { "x" "a non-negative real number"} }
 { $description "Computes the variance of " { $snippet "seq" } ". It's a measurement of the spread of values in a sequence. The larger the variance, the larger the distance of values from the mean." }
 { $notes "If the number of elements in " { $snippet "seq" } " is 1 or less, it outputs 0." }
 { $examples
@@ -150,8 +164,8 @@ ARTICLE: "math.statistics" "Statistics"
 { $subsections median lower-median upper-median medians }
 "Computing the mode:"
 { $subsections mode }
-"Computing the standard deviation and variance:"
+"Computing the standard deviation, standard error, and variance:"
-{ $subsections std var }
+{ $subsections std ste var }
 "Computing the range and minimum and maximum elements:"
 { $subsections range minmax }
 "Computing the kth smallest element:"