209 lines
9.9 KiB
Factor
209 lines
9.9 KiB
Factor
USING: assocs debugger hashtables help.markup help.syntax
|
|
quotations sequences math ;
|
|
IN: math.statistics
|
|
|
|
HELP: geometric-mean
|
|
{ $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 and 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" 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" sequence } { "x" "a non-negative real number"} }
|
|
{ $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" sequence } { "x" "a non-negative real number"} }
|
|
{ $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" sequence } { "x" "a non-negative real number"} }
|
|
{ $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. Throws an error on an empty sequence." }
|
|
{ $examples
|
|
{ $example "USING: arrays math.statistics prettyprint ;"
|
|
"{ 1 2 3 } minmax 2array ."
|
|
"{ 1 3 }"
|
|
}
|
|
} ;
|
|
|
|
HELP: std
|
|
{ $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 ;" "{ 4 6 8 10 12 14 16 } std ." "4.0" } } ;
|
|
|
|
HELP: ste
|
|
{ $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 ;" "{ 4 6 6 8 10 12 14 14 16 } ste ." "1.333333333333333" }
|
|
} ;
|
|
|
|
HELP: var
|
|
{ $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
|
|
{ $example "USING: math.statistics prettyprint ;" "{ 1 } var ." "0" }
|
|
{ $example "USING: math.statistics prettyprint ;" "{ 1 2 3 } var ." "2/3" }
|
|
{ $example "USING: math.statistics prettyprint ;" "{ 1 2 3 4 5 } var ." "2" } } ;
|
|
|
|
HELP: cov
|
|
{ $values { "{x}" sequence } { "{y}" sequence } { "cov" "a real number" } }
|
|
{ $description "Computes the covariance of two sequences, " { $snippet "{x}" } " and " { $snippet "{y}" } "." } ;
|
|
|
|
HELP: corr
|
|
{ $values { "{x}" sequence } { "{y}" sequence } { "corr" "a real number" } }
|
|
{ $description "Computes the correlation of two sequences, " { $snippet "{x}" } " and " { $snippet "{y}" } "." } ;
|
|
|
|
HELP: histogram
|
|
{ $values
|
|
{ "seq" sequence }
|
|
{ "hashtable" hashtable }
|
|
}
|
|
{ $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." }
|
|
{ $examples
|
|
{ $example "! Count the number of times an element appears in a sequence."
|
|
"USING: prettyprint math.statistics ;"
|
|
"\"aaabc\" histogram ."
|
|
"H{ { 97 3 } { 98 1 } { 99 1 } }"
|
|
}
|
|
} ;
|
|
|
|
|
|
HELP: histogram-by
|
|
{ $values
|
|
{ "seq" sequence }
|
|
{ "quot" { $quotation "( x -- bin )" } }
|
|
{ "hashtable" hashtable }
|
|
}
|
|
{ $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." }
|
|
{ $examples
|
|
{ $unchecked-example "! Count the number of times letters and non-letters appear in a sequence."
|
|
"USING: prettyprint math.statistics unicode.categories ;"
|
|
"\"aaa123bc\" [ letter? ] histogram-by ."
|
|
"H{ { t 5 } { f 3 } }"
|
|
}
|
|
} ;
|
|
|
|
HELP: histogram!
|
|
{ $values
|
|
{ "hashtable" hashtable } { "seq" sequence }
|
|
}
|
|
{ $description "Takes an existing hashtable and uses " { $link histogram } " to continue counting the number of occurrences of each element." }
|
|
{ $examples
|
|
{ $example "! Count the number of times the elements of two sequences appear."
|
|
"USING: prettyprint math.statistics ;"
|
|
"\"aaabc\" histogram \"aaaaaabc\" histogram! ."
|
|
"H{ { 97 9 } { 98 2 } { 99 2 } }"
|
|
}
|
|
} ;
|
|
|
|
HELP: sorted-histogram
|
|
{ $values
|
|
{ "seq" sequence }
|
|
{ "alist" "an array of key/value pairs" }
|
|
}
|
|
{ $description "Outputs a " { $link histogram } " of a sequence sorted by number of occurrences from lowest to highest." }
|
|
{ $examples
|
|
{ $example "USING: prettyprint math.statistics ;"
|
|
""""abababbbbbbc" sorted-histogram ."""
|
|
"{ { 99 1 } { 97 3 } { 98 8 } }"
|
|
}
|
|
} ;
|
|
|
|
HELP: sequence>assoc
|
|
{ $values
|
|
{ "seq" sequence } { "map-quot" { $quotation "( x -- ..y )" } } { "insert-quot" { $quotation "( ..y assoc -- )" } } { "exemplar" "an exemplar assoc" }
|
|
{ "assoc" assoc }
|
|
}
|
|
{ $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." }
|
|
{ $examples
|
|
{ $example "! Iterate over a sequence and increment the count at each element"
|
|
"! The first quotation has stack effect ( key -- key ), a no-op"
|
|
"USING: assocs prettyprint math.statistics ;"
|
|
"\"aaabc\" [ ] [ inc-at ] H{ } sequence>assoc ."
|
|
"H{ { 97 3 } { 98 1 } { 99 1 } }"
|
|
}
|
|
} ;
|
|
|
|
HELP: sequence>assoc!
|
|
{ $values
|
|
{ "assoc" assoc } { "seq" sequence } { "map-quot" { $quotation "( x -- ..y )" } } { "insert-quot" { $quotation "( ..y assoc -- )" } }
|
|
}
|
|
{ $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." }
|
|
{ $examples
|
|
{ $example "! Iterate over a sequence and add the counts to an existing assoc"
|
|
"USING: assocs prettyprint math.statistics kernel ;"
|
|
"H{ { 97 2 } { 98 1 } } clone \"aaabc\" [ ] [ inc-at ] sequence>assoc! ."
|
|
"H{ { 97 5 } { 98 2 } { 99 1 } }"
|
|
}
|
|
} ;
|
|
|
|
HELP: sequence>hashtable
|
|
{ $values
|
|
{ "seq" sequence } { "map-quot" { $quotation "( x -- ..y )" } } { "insert-quot" { $quotation "( ..y assoc -- )" } }
|
|
{ "hashtable" hashtable }
|
|
}
|
|
{ $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." }
|
|
{ $examples
|
|
{ $example "! Count the number of times an element occurs in a sequence"
|
|
"USING: assocs prettyprint math.statistics ;"
|
|
"\"aaabc\" [ ] [ inc-at ] sequence>hashtable ."
|
|
"H{ { 97 3 } { 98 1 } { 99 1 } }"
|
|
}
|
|
} ;
|
|
|
|
ARTICLE: "histogram" "Computing histograms"
|
|
"Counting elements in a sequence:"
|
|
{ $subsections
|
|
histogram
|
|
histogram-by
|
|
histogram!
|
|
sorted-histogram
|
|
}
|
|
"Combinators for implementing histogram:"
|
|
{ $subsections
|
|
sequence>assoc
|
|
sequence>assoc!
|
|
sequence>hashtable
|
|
} ;
|
|
|
|
ARTICLE: "math.statistics" "Statistics"
|
|
"Computing the mean:"
|
|
{ $subsections mean geometric-mean harmonic-mean }
|
|
"Computing the median:"
|
|
{ $subsections median lower-median upper-median medians }
|
|
"Computing the mode:"
|
|
{ $subsections mode }
|
|
"Computing the standard deviation, standard error, and variance:"
|
|
{ $subsections std ste var }
|
|
"Computing the range and minimum and maximum elements:"
|
|
{ $subsections range minmax }
|
|
"Computing the kth smallest element:"
|
|
{ $subsections kth-smallest }
|
|
"Counting the frequency of occurrence of elements:"
|
|
{ $subsection "histogram" } ;
|
|
|
|
ABOUT: "math.statistics"
|