341 lines
14 KiB
Factor
341 lines
14 KiB
Factor
USING: assocs debugger hashtables help.markup help.syntax
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quotations sequences math ;
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IN: math.statistics
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HELP: geometric-mean
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{ $values { "seq" sequence } { "x" "a non-negative real number"} }
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{ $description "Computes the geometric mean of all elements in " { $snippet "seq" } ". The geometric mean measures the central tendency of a data set and minimizes the effects of extreme values." }
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{ $examples { $example "USING: math.statistics prettyprint ;" "{ 1 2 3 } geometric-mean ." "1.81712059283214" } }
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{ $errors "Throws a " { $link signal-error. } " (square-root of 0) if the sequence is empty." } ;
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HELP: harmonic-mean
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{ $values { "seq" sequence } { "x" "a non-negative real number"} }
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{ $description "Computes the harmonic mean of the elements in " { $snippet "seq" } ". The harmonic mean is appropriate when the average of rates is desired." }
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{ $notes "Positive reals only." }
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{ $examples { $example "USING: math.statistics prettyprint ;" "{ 1 2 3 } harmonic-mean ." "6/11" } }
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{ $errors "Throws a " { $link signal-error. } " (divide by zero) if the sequence is empty." } ;
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HELP: mean
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{ $values { "seq" sequence } { "x" "a non-negative real number"} }
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{ $description "Computes the arithmetic mean of the elements in " { $snippet "seq" } "." }
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{ $examples { $example "USING: math.statistics prettyprint ;" "{ 1 2 3 } mean ." "2" } }
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{ $errors "Throws a " { $link signal-error. } " (divide by zero) if the sequence is empty." } ;
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HELP: median
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{ $values { "seq" sequence } { "x" "a non-negative real number"} }
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{ $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." }
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{ $examples
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{ $example "USING: math.statistics prettyprint ;" "{ 1 2 3 } median ." "2" }
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{ $example "USING: math.statistics prettyprint ;" "{ 1 2 3 4 } median ." "2+1/2" } }
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{ $errors "Throws a " { $link signal-error. } " (divide by zero) if the sequence is empty." } ;
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HELP: range
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{ $values { "seq" sequence } { "x" "a non-negative real number"} }
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{ $description "Computes the difference of the maximum and minimum values in " { $snippet "seq" } "." }
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{ $examples
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{ $example "USING: math.statistics prettyprint ;" "{ 1 2 3 } range ." "2" }
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{ $example "USING: math.statistics prettyprint ;" "{ 1 2 3 4 } range ." "3" } } ;
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HELP: minmax
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{ $values { "seq" sequence } { "min" real } { "max" real } }
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{ $description "Finds the minimum and maximum elements of " { $snippet "seq" } " in one pass. Throws an error on an empty sequence." }
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{ $examples
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{ $example "USING: arrays math.statistics prettyprint ;"
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"{ 1 2 3 } minmax 2array ."
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"{ 1 3 }"
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}
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} ;
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HELP: sample-std
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{ $values { "seq" sequence } { "x" "a non-negative real number"} }
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{ $description "Computes the sample standard deviation of " { $snippet "seq" } ", which is the square root of the sample variance. It measures how widely spread the values in a sequence are about the mean for a random subset of a dataset." }
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{ $examples
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{ $example "USING: math.statistics prettyprint ;" "{ 7 8 9 } sample-std ." "1.0" } } ;
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HELP: sample-ste
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{ $values { "seq" sequence } { "x" "a non-negative real number"} }
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{ $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." }
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{ $examples
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{ $example "USING: math.statistics prettyprint ;" "{ -2 2 } sample-ste ." "2.0" }
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} ;
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HELP: sample-var
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{ $values { "seq" sequence } { "x" "a non-negative real number"} }
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{ $description "Computes the variance of " { $snippet "seq" } ". It's a measurement of the spread of values in a sequence." }
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{ $notes "If the number of elements in " { $snippet "seq" } " is 1 or less, it outputs 0." }
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{ $examples
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{ $example "USING: math.statistics prettyprint ;" "{ 1 } sample-var ." "0" }
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{ $example "USING: math.statistics prettyprint ;" "{ 1 2 3 } sample-var ." "1" }
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{ $example "USING: math.statistics prettyprint ;" "{ 1 2 3 4 } sample-var ." "1+2/3" } } ;
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HELP: population-cov
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{ $values { "{x}" sequence } { "{y}" sequence } { "cov" "a real number" } }
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{ $description "Computes the covariance of two sequences, " { $snippet "{x}" } " and " { $snippet "{y}" } "." } ;
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HELP: population-corr
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{ $values { "{x}" sequence } { "{y}" sequence } { "corr" "a real number" } }
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{ $description "Computes the correlation of two sequences, " { $snippet "{x}" } " and " { $snippet "{y}" } "." } ;
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HELP: histogram
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{ $values
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{ "seq" sequence }
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{ "hashtable" hashtable }
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}
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{ $description "Returns a hashtable where the keys are the elements of the sequence and the values are the number of times they appeared in that sequence." }
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{ $examples
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{ $example "! Count the number of times an element appears in a sequence."
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"USING: prettyprint math.statistics ;"
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"\"aaabc\" histogram ."
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"H{ { 97 3 } { 98 1 } { 99 1 } }"
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}
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} ;
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HELP: histogram-by
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{ $values
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{ "seq" sequence }
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{ "quot" { $quotation "( x -- bin )" } }
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{ "hashtable" hashtable }
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}
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{ $description "Returns a hashtable where the keys are the elements of the sequence binned by being passed through " { $snippet "quot" } ", and the values are the number of times members of each bin appeared in that sequence." }
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{ $examples
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{ $unchecked-example "! Count the number of times letters and non-letters appear in a sequence."
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"USING: prettyprint math.statistics unicode.categories ;"
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"\"aaa123bc\" [ letter? ] histogram-by ."
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"H{ { t 5 } { f 3 } }"
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}
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} ;
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HELP: histogram!
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{ $values
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{ "hashtable" hashtable } { "seq" sequence }
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}
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{ $description "Takes an existing hashtable and uses " { $link histogram } " to continue counting the number of occurrences of each element." }
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{ $examples
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{ $example "! Count the number of times the elements of two sequences appear."
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"USING: prettyprint math.statistics ;"
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"\"aaabc\" histogram \"aaaaaabc\" histogram! ."
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"H{ { 97 9 } { 98 2 } { 99 2 } }"
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}
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} ;
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HELP: sorted-histogram
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{ $values
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{ "seq" sequence }
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{ "alist" "an array of key/value pairs" }
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}
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{ $description "Outputs a " { $link histogram } " of a sequence sorted by number of occurrences from lowest to highest." }
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{ $examples
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{ $example "USING: prettyprint math.statistics ;"
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""""abababbbbbbc" sorted-histogram ."""
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"{ { 99 1 } { 97 3 } { 98 8 } }"
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}
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} ;
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HELP: sequence>assoc
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{ $values
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{ "seq" sequence } { "map-quot" $quotation } { "insert-quot" quotation } { "exemplar" "an exemplar assoc" }
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{ "assoc" assoc }
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}
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{ $description "Iterates over a sequence, allowing elements of the sequence to be added to a newly created " { $snippet "assoc" } ". The " { $snippet "map-quot" } " gets passed each element from the sequence. Its outputs are passed along with the assoc being constructed to the " { $snippet "insert-quot" } ", which can modify the assoc in response." }
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{ $examples
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{ $example "! Iterate over a sequence and increment the count at each element"
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"! The first quotation has stack effect ( key -- key ), a no-op"
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"USING: assocs prettyprint kernel math.statistics ;"
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"\"aaabc\" [ ] [ inc-at ] H{ } sequence>assoc ."
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"H{ { 97 3 } { 98 1 } { 99 1 } }"
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}
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} ;
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HELP: sequence>assoc!
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{ $values
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{ "assoc" assoc } { "seq" sequence } { "map-quot" quotation } { "insert-quot" quotation } }
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{ $description "Iterates over a sequence, allowing elements of the sequence to be added to an existing " { $snippet "assoc" } ". The " { $snippet "map-quot" } " gets passed each element from the sequence. Its outputs are passed along with the assoc being constructed to the " { $snippet "insert-quot" } ", which can modify the assoc in response." }
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{ $examples
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{ $example "! Iterate over a sequence and add the counts to an existing assoc"
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"USING: assocs prettyprint math.statistics kernel ;"
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"H{ { 97 2 } { 98 1 } } clone \"aaabc\" [ ] [ inc-at ] sequence>assoc! ."
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"H{ { 97 5 } { 98 2 } { 99 1 } }"
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}
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} ;
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HELP: sequence>hashtable
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{ $values
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{ "seq" sequence } { "map-quot" quotation } { "insert-quot" quotation }
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{ "hashtable" hashtable }
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}
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{ $description "Iterates over a sequence, allowing elements of the sequence to be added to a newly created hashtable. The " { $snippet "map-quot" } " gets passed each element from the sequence. Its outputs are passed along with the assoc being constructed to the " { $snippet "insert-quot" } ", which can modify the assoc in response." }
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{ $examples
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{ $example "! Count the number of times an element occurs in a sequence"
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"USING: assocs kernel prettyprint math.statistics ;"
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"\"aaabc\" [ ] [ inc-at ] sequence>hashtable ."
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"H{ { 97 3 } { 98 1 } { 99 1 } }"
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}
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} ;
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HELP: cum-sum
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{ $values { "seq" sequence } { "seq'" sequence } }
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{ $description "Returns the cumulative sum of " { $snippet "seq" } "." }
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{ $examples
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{ $example "USING: math.statistics prettyprint ;"
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"{ 1 -1 2 -1 4 } cum-sum ."
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"{ 1 0 2 1 5 }"
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}
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} ;
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HELP: cum-count
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{ $values { "seq" sequence } { "quot" quotation } { "seq'" sequence } }
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{ $description "Returns the cumulative count of how many times " { $snippet "quot" } " returns true." }
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{ $examples
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{ $example "USING: math math.statistics prettyprint ;"
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"{ 1 -1 2 -1 4 } [ 0 < ] cum-count ."
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"{ 0 1 1 2 2 }"
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}
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} ;
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HELP: cum-product
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{ $values { "seq" sequence } { "seq'" sequence } }
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{ $description "Returns the cumulative product of " { $snippet "seq" } "." }
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{ $examples
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{ $example "USING: math.statistics prettyprint ;"
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"{ 1 2 3 4 } cum-product ."
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"{ 1 2 6 24 }"
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}
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} ;
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HELP: cum-min
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{ $values { "seq" sequence } { "seq'" sequence } }
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{ $description "Returns the cumulative min of " { $snippet "seq" } "." }
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{ $examples
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{ $example "USING: math.statistics prettyprint ;"
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"{ 5 3 4 1 } cum-min ."
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"{ 5 3 3 1 }"
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}
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} ;
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HELP: cum-max
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{ $values { "seq" sequence } { "seq'" sequence } }
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{ $description "Returns the cumulative max of " { $snippet "seq" } "." }
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{ $examples
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{ $example "USING: math.statistics prettyprint ;"
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"{ 1 -1 3 5 } cum-max ."
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"{ 1 1 3 5 }"
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}
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} ;
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HELP: standardize
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{ $values { "u" sequence } { "v" sequence } }
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{ $description "Shifts and rescales the elements of " { $snippet "u" } " to have zero mean and unit sample variance." } ;
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HELP: differences
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{ $values { "u" sequence } { "v" sequence } }
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{ $description "Returns the successive differences of elements in " { $snippet "u" } "." } ;
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HELP: rescale
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{ $values { "u" sequence } { "v" sequence } }
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{ $description "Returns " { $snippet "u" } " rescaled to run from 0 to 1 over the range min to max." } ;
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HELP: collect-by
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{ $values
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{ "seq" sequence } { "quot" { $quotation "( obj -- ? )" } }
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{ "hashtable" hashtable }
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}
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{ $description "Applies a quotation to each element in the input sequence and returns a " { $snippet "hashtable" } " of like elements. The keys of this " { $snippet "hashtable" } " are the output of " { $snippet "quot" } " and the values at each key are the elements that transformed to that key." }
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{ $examples
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"Collect even and odd elements:"
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{ $example
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"USING: math math.statistics prettyprint ;"
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"{ 11 12 13 14 14 13 12 11 } [ odd? ] collect-by ."
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"H{ { f V{ 12 14 14 12 } } { t V{ 11 13 13 11 } } }"
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}
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}
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{ $notes "May be named " { $snippet "group-by" } " in other languages." } ;
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HELP: collect-index-by
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{ $values
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{ "seq" sequence } { "quot" { $quotation "( obj -- ? )" } }
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{ "hashtable" hashtable }
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}
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{ $description "Applies a quotation to each element in the input sequence and returns a " { $snippet "hashtable" } " of like elements. The keys of this " { $snippet "hashtable" } " are the output of " { $snippet "quot" } " and the values at each key are the indices for the elements that transformed to that key." }
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{ $examples
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"Collect even and odd elements:"
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{ $example
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"USING: math math.statistics prettyprint ;"
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"{ 11 12 13 14 14 13 12 11 } [ odd? ] collect-index-by ."
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"H{ { f V{ 1 3 4 6 } } { t V{ 0 2 5 7 } } }"
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}
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} ;
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HELP: z-score
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{ $values { "seq" sequence } { "n" number } }
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{ $description "Calculates the Z-Score for " { $snippet "seq" } "." } ;
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ARTICLE: "histogram" "Computing histograms"
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"Counting elements in a sequence:"
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{ $subsections
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histogram
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histogram-by
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histogram!
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sorted-histogram
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}
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"Combinators for implementing histogram:"
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{ $subsections
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sequence>assoc
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sequence>assoc!
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sequence>hashtable
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} ;
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ARTICLE: "cumulative" "Computing cumulative sequences"
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"Cumulative mapping combinators:"
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{ $subsections
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cum-map
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}
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"Cumulative math:"
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{ $subsections
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cum-sum
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cum-sum0
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cum-product
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}
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"Cumulative comparisons:"
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{ $subsections
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cum-min
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cum-max
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}
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"Cumulative counting:"
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{ $subsections
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cum-count
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} ;
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ARTICLE: "math.statistics" "Statistics"
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"Computing the mean:"
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{ $subsections mean geometric-mean harmonic-mean }
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"Computing the median:"
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{ $subsections median lower-median upper-median medians }
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"Computing the mode:"
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{ $subsections mode }
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"Computing the population standard deviation, standard error, and variance:"
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{ $subsections population-std population-ste population-var }
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"Computing the sample standard deviation, standard error, and variance:"
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{ $subsections sample-std sample-ste sample-var }
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"Computing the nth delta-degrees-of-freedom statistics:"
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{ $subsections std-ddof ste-ddof var-ddof }
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"Computing the range and minimum and maximum elements:"
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{ $subsections range minmax }
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"Computing the kth smallest element:"
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{ $subsections kth-smallest }
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"Counting the frequency of occurrence of elements:"
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{ $subsections "histogram" }
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"Collecting related items:"
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{ $subsections collect-by collect-index-by }
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"Computing cumulative sequences:"
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{ $subsections "cumulative" } ;
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ABOUT: "math.statistics"
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{ var-ddof population-var sample-var } related-words
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{ std-ddof population-std sample-std } related-words
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{ ste-ddof population-ste sample-ste } related-words
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{ corr-ddof population-corr sample-corr } related-words
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{ cov-ddof population-cov sample-cov } related-words
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